The ICC maintains and publishes a list of batting, bowling and all-rounder rankings for each format on their Rankings Website. Players are assigned ratings on a scale of 0 to 1000 based on their recent performances, and then ranked in decreasing order of rating.

These ratings (and therefore rankings) are updated regularly: usually at least once a week per format when international cricket is played in that format. At any given time, the top 100 ranked batsmen, bowlers and all-rounders and their ratings in each format can be viewed on the rankings website.

As an official list published by ICC, the player rankings are often referenced by professionals and journalists covering cricket. They may even affect players’ impression on selectors and other leaders in their clubs, leagues and associations. Rankings can, therefore, impact players' chances of selection on teams, the longevity of their careers, status and/or compensation.

We believe that a ranking system that can have real-world consequences on players’ careers must hold up to scrutiny by independent, third-party analysis.

In this document we are going to do a deep-dive into what player ratings look like, how they are distributed, and how they change over time. In this process, we will identify some quirks about the rating system that can impact players’ rankings in unexpected ways. Finally, we are going to recommend some changes to the rating system that can address these concerns.

The ICC does not disclose the algorithms used for calculating players’ ratings. We can only gather the following information from the “About Rankings” and “Player Rankings FAQs” pages on their website:

• After each match, each player involved in the match is assigned two scores between 0 and 1000, one each for their batting and bowling performances in that match.
  • Let’s call these scores the player’s batting and bowling R-scores for that match.

• The r-scores assigned for each inning can depend on several factors such as strength of opposition and playing conditions. All of these are “pre-programmed” mathematical calculations and no subjective assessment is made in assigning these r-scores. There is a different set of calculations for Tests, ODI and T20Is.
• A player’s overall batting and bowling ratings at any time in each format is a “sophisticated moving average” of their respective batting and bowling r-scores in each match that they have played in that format. Recent performances contribute more to a the overall rating. As a moving average of r-scores in individual matches, the overall rating also falls on a scale of 0 to 1000.
• All-rounder ratings for each player are calculated by combining their batting and bowling ratings.
• Players lose rating points for each match they miss for their national team, and are removed from rankings if they haven’t played any matches for their team for about a year, or if they announce retirement. Similarly, new players don’t appear on the rankings list until they have played enough matches to have a high enough rating.
• A rating of 500 or more is considered a “good, solid rating”, 750 or more usually means “world top 10”, and 900 or more is a “supreme achievement”.

  These aren’t our opinions. We are summarising and quoting from what’s written on the official website.

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We do not have any details about the rating algorithm, so we cannot rebuild current or historical ratings data ourselves.

Let’s assume that there is a complex set of calculations involved that are backed by strong statistical methods, and that the ratings are calculated and published accurately and in good faith.

We can, however, do the next best thing.

These ratings have been calculated back in time all the way to the first international matches in each format. The ICC makes all-time best ratings, as well as date-specific top 100 ratings, for both batting and bowling and for each format available publicly.

With some computer internet magic, we were able to obtain a full history of ratings for every day going back to the year 1901.

Our dataset contains ratings for each format on every day in the following time periods:

Format	Start Date	End Date
Test Cricket	1901-01-01	2024-07-01
ODIs	1975-01-01	2024-07-01
T20Is	2007-01-01	2024-07-01

We would like to point out the following limitations of our dataset:

• We don’t have data for inning-by-inning r-scores for players, but only for the ratings as they appear in the charts after the “sophisticated moving average” of r-scores has been calculated.

  This means that we cannot do any analysis on the distribution of r-scores assigned to individual innings.

• We only have ratings for the top 100 batsmen and bowlers on any given date. If there were more than 100 players playing in a format on any date, we are missing data at the lower end of the rating scale.

  For ODIs and T20Is, this means that most of our analyses will be restricted to players with ratings higher than 500. For Test cricket, it depends on the decade. More on this later.

• Since we only have daily ratings data, we may not have data on match-by-match changes during periods when a lot of cricket was played, for example during a World Cup or when more than one concurrent international series were going on.

  This is not an issue for us since we will be doing aggregate analysis on long time periods (one year or longer).

We have a large dataset spanning 124 years. Let us trim it down to only the useful bits first.

First, we remove those dates when there was no change in ratings per format, that is, no international matches were played in that format or the ratings weren’t updated on those days for other reasons. Table 0.1 below shows the total number of days remaining per decade in each format.

View Table 0.1

Decade	Test Cricket	ODIs	T20Is
1900s	42
1910s	29
1920s	50
1930s	85
1940s	44
1950s	164
1960s	175
1970s	188	48
1980s	254	459
1990s	314	817
2000s	419	1191	77
2010s	386	948	583
2020s	143	400	537
TOTAL	2293	3863	1197

Table 0.1: No. of days of rating changes by decade for each format.

Next, we remove all players that have a rating of zero from each day’s ratings. Table 0.2 below contains a summary of how many total data points we are left with in our dataset for each format and type.

View Table 0.2

Format	Type	Total Data Points
Test	Batting	221 022
Test	Bowling	193 897
ODI	Batting	386 166
ODI	Bowling	383 345
T20I	Batting	119 700
T20I	Bowling	114 351

Table 0.2: Total data points by Format (Test, ODI, T20I) and Type (Batting, Bowling).

In total we have more than 1.4 million data points to analyse.

To make sense of it all, we will be using a lot of graphs to visualise our dataset. Many of these graphs will come in 6 variations: One each for pairs of the 3 formats and 2 types, similar to table 0.2 above.

Graphs that only cover past time periods will only come in those formats that were played at that time. For example, graphs from the 1990s may only be for Tests, ODIs or both. Similarly, those from the 1960s may only come in 2 variations (Batting and Bowling for Test Cricket only).

The data from Table 0.1 is shown in Figure 0.1 below, but instead of total days for each decade, we have plotted the total days for every year on a bar chart. This graph comes in 3 variations: one each for Test cricket, ODIs and T20Is.

About this Figure

• On the horizontal axis (bottom scale) is time. There is one green bar for every year.
• On the vertical axis (left scale) is the number of days when there was a change in ratings.

  The taller a bar, the more days in that year had a change in ratings.

  The height of bars should be approximately equal to the total number of matches played in each year, assuming that:

  • No two matches concluded on the same day,
  • At least one player involved in a match had a top 100 rank before or after the match, and
  • No player retirements were reflected in ratings outside of days with concluded matches.

View Figure 0.1

• Test Cricket

  
  
• ODIs

  
  
• T20Is

  
  

Figure 0.1: Data points in each year by format

• Note the empty years between 1915-1920 and 1940-1945 for Test cricket. Those are the two World Wars. No international cricket was played during those years.

  We will skip these years in our analysis.

• Note how little Test cricket was played in the years before 1950, and how much of it was played after 1990. The increase after 1990 can be seen for ODIs as well.

  This can be explained by more teams gaining full member status over the years and more frequent international tours since the advent of air travel.

• Test cricket peaked in 2002, and ODIs in 2023.
• 1970 and 2020 were the worst years for Test cricket, and 2018 and 2020 were the worst for ODIs.

  We will skip the year 2020 in most of our longer-period analyses.

In each section and subsection below, you will see graphs and their accompanying explanations similar to figure 0.1 above. This will be followed by observations that we made from the graph, and any conclusions depending on what we were looking for in the graph.

In addition to graphs, we will use some basic terms from the field of statistics to talk about the data, for example: averages, medians, percentiles, quartiles, distributions, etc.

With all this understood, let’s dive right in. This is going to be a long read, so sit back and relax with a cup of tea 🍵.

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Let’s warm-up with some simple graphs over time about the players at the top. The ICC has made claims about the meaning of 500+, 750+ and 900+ ratings, so let’s look into them.

How many players have had a 500+ rating throughout history? Take a look at Figure 1.1 below.

About this Figure

• On the horizontal axis (bottom scale) is time: starting in 1901 for Test cricket, in 1975 for ODIs and in 2007 for T20Is. Each scale ends on 2024-07-01. Data for every date in these time periods is plotted.
• On the vertical axis (left scale) is the number of players that have a rating above a threshold on each date.
  • The blue line at the top is the number of players with a rating above 0 on each date, or in other words, the total number of players we have non-zero ratings for.
  • The red line at the bottom is the number of players with a rating of at least 500 on each date, or what the ICC describes as a “good, solid rating”. Solid red bars show the average number of players per decade for Test cricket and per 5 years for ODIs and T20Is.

View Figure 1.1

• Test Batsmen

  
  
• Test Bowlers

  
  
• ODI Batsmen

  
  
• ODI Bowlers

  
  
• T20I Batsmen

  
  
• T20I Bowlers

  
  

Figure 1.1: No. of players with ratings above 0 (blue) and 500 (red). Average no. of players above 500 are shown as solid red bars.

• Not surprisingly, the total number of players caps at 100 for each format and type except for test batsmen before 1950 and test bowlers before 1990.

  This is because, as mentioned above under Data Limitations, we only have access to the top 100 players in each format and type on any given date.

• Test cricket

  • There were about ~60% as many bowlers as there were batsmen in Test cricket between 1901 and 1950 (see blue line on top). Similarly, we see about ~60% as many bowlers with ratings above 500 compared to batsmen, a trend that continues beyond 1950 to present day.

    Time span	Batsmen over 500	Bowlers over 500
    1900s - 1940s	10 ~ 15	~ 5
    1950s - 1990s	25 ~ 35	15 ~ 20
    2000s - 2010s	45 ~ 50	25 ~ 30
    2020s (ongoing)	~ 55	~ 35

• ODIs

  • The number of players with ratings above 500 is small to start with but stabilises after 1985. After that, it seems to grow gradually as more teams start playing ODI cricket, but only for batsmen.
    • The number of batsmen with ratings above 500 has grown gradually from ~40 in the 1980s to ~65 since 2015.
    • The number of bowlers with ratings above 500, on the other hand, has stayed consistent at around 40 ~ 45 since 1995.
  • Unlike Test cricket, we don’t see a 60% ratio between the number of batsmen and bowlers with ratings above 500.

• T20Is

  • Player counts above a rating of 500 stabilised around 2010-2012.
  • Both batsmen and bowlers have similar player counts above a rating of 500: about 25 ~ 30 up to 2015 and 35 ~ 40 after 2015.

    These numbers haven’t changed much in recent years even though about 70+ teams have been playing enough T20 internationals since 2019 to feature in ICC’s official team rankings.

In summary, the number of players with a “good, solid rating” of 500 is not consistent across formats. It has grown over time as expected, but even in recent years we see a wide range between batting and bowling and across formats. Here is a summary for recent years:

Format	Batsmen over 500	Bowlers over 500
Test cricket	45 ~ 55	25 ~ 35
ODIs	60 ~ 65	40 ~ 45
T20Is	35 ~ 40	35 ~ 40

How many players have had a rating above 750 throughout history? And how many above 900? Take a look at figure 1.2 below.

About this Figure

These graphs are similar to those in figure 1.1, except for the rating thresholds of the lines.

• The blue line at the top is the number of players with a rating of at least 750, or what ICC describes as “usually in the top 10”. Solid blue bars show the average number of players per decade for Test cricket and per 5 years for ODIs and T20Is.
• The red line at the bottom is the number of players with a rating of at least 900, or what the ICC describes as a “supreme achievement”.

View Figure 1.2

• Test Batsmen

  
  
• Test Bowlers

  
  
• ODI Batsmen

  
  
• ODI Bowlers

  
  
• T20I Batsmen

  
  
• T20I Bowlers

  
  

Figure 1.2: No. of players with ratings above 750 (blue) and 900 (red). Average no. of players above 750 are shown as solid blue bars.

• Test cricket
  • There have been about 10 test batsmen above a rating of 750 on most days since the 2000s, but there were only 3-5 on average for the majority of years during 1950-2000.
  • About 10 test bowlers have had a rating above 750 on most days since 2015, but only about 5 on average did for most of the years during 1950-2015.
  • Between 1-3 test batsmen frequently breach the 900 mark. 1-2 test bowlers have breached the 900 mark on several occasions, and more of them seem to be doing it in recent years.
• ODIs
  • There were 10 or more ODI batsmen above a rating of 750 during 2017-2021, but on most other days throughout history only 4-8 ODI batsmen on average had a rating above 750.
  • Only 3-5 ODI bowlers have a rating above 750 on most days up to 2008. Since 2008, it has been so rare that a rating of 750 by itself can be considered a “supreme achievement”.
  • Between 1-3 ODI batsmen and 1-2 ODI bowlers frequently had a rating above 900 during the 1980s in spite of fewer teams playing ODIs at that time. It has been very rare since then and non-existent for ODI bowlers since 2009.
• T20Is
  • Only 4 T20I batsmen on average have a rating above 750. T20I batsmen have breached the 900 mark on only 3 occasions.
  • Only 1-2 T20I bowlers on average have a rating above 750. No T20I bowler has had a rating above 750 since mid-2022. No T20I bowler has ever had a rating above 900.

In summary, we find the ICC’s claim that a 750+ rating is “usually world top 10” to be incorrect for most years that cricket has been played. It certainly holds true for test cricket in recent years, but in all other formats today and in all formats throughout history there have been far fewer players with ratings above 750. Limited-overs bowlers in particular hardly ever have a 750+ rating. The “supreme achievement” of a 900+ rating is only supreme in Test cricket and for limited-overs batsmen. For everyone else, it is more of an “impossible achievement”.

Here is a summary for recent years:

Format	Batsmen over 750	Bowlers over 750
Test cricket	9 ~ 11	8 ~ 11
ODIs	3 ~ 12	1 ~ 2
T20Is	3 ~ 5	1 ~ 2

So what rating threshold actually makes a top 10 player? Or top 5? Or the top player? Take a look at figure 1.3 below.

About this Figure

• Similar to figures 1.1 and 1.2, the horizontal axis (bottom scale) represents time.
• The vertical axis (left scale) represents the player rating for whoever has the 1st, 5th and 10th ranks on each date.

  Note that this scale starts at 500 because we are only looking at the ratings of highly ranked players.

  • The top line in blue is the rating of the top-ranked player, or the player with the highest rating on each day.
  • The pink-red line in the middle is the rating of the player ranked 5th on each day.
  • The orange-yellowish line at the bottom is the rating of the player ranked 10th on each day.
• Average values are shown as bars for each line, per decade for Test cricket and per 5 years for ODIs and T20Is.

View Figure 1.3

• Test Batsmen

  
  
• Test Bowlers

  
  
• ODI Batsmen

  
  
• ODI Bowlers

  
  
• T20I Batsmen

  
  
• T20I Bowlers

  
  

Figure 1.3: Ratings for players with ranks 1 (blue), 5 (pink-red) and 10 (orange-yellow). Average ratings at each rank are shown as solid bars.

• Here is a summary of the actual rating thresholds above which players have usually qualified as Top 10 and Top 5 for each type and format in recent years (since around 2010) as per the graphs.

  Format	Type	Top 10 Rating Threshold	Top 5 Rating Threshold
  Test	Batting	750	825
  Test	Bowling	725	800
  ODI	Batting	725	775
  ODI	Bowling	650	675
  T20I	Batting	650	725
  T20I	Bowling	650	675

• We see a drop in ratings for all three ranks of ODI bowlers around 2008, similar to that in figure 1.2. The top rating dropped from 850+ to ~750, along with corresponding drops in Ranks 5 and 10, and these ratings have stayed there since then.

  Turns out this was due to the retirement of Shaun Pollock on 2008-02-04, who finished his ODI career at 894 points. The next best, Shane Bond, took over the top-ranked spot the next day with only 754 points. Similarly, all other ranks moved up by one. This is why the drop is so large at Rank 1 but barely noticeable for Rank 10.

  However, this does not explain why no other ODI bowler has been able to get ratings that high since then.

• Similarly, we see an increase in Test batting ratings during 1994-2008, and a temporary drop in top ODI batting ratings during 2002-2010. However, these are more gradual changes.

  These might be explained away by the changing balance between bat and bowl in international cricket.

In summary:

• T20I rating thresholds at both ranks are lower than those for Test cricket and ODIs.
• Bowling ratings thresholds are lower than batting ratings across formats. They have been especially low for T20I and ODI bowlers since 2008-09.

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With that warm-up round out of the way, let’s dive into our full dataset and see what the entire range of ratings looks like.

When we started this study we went in with the assumption that the ratings would be more or less normally distributed (more players in the middle with mean at 500 and less on both sides around it), especially because the ICC had given interpretations of ratings above 500, 750 and 900 which we thought were based on standard deviations above the mean. This assumption was (very) incorrect.

To study the full range of ratings, we are looking for periods of time with the following properties:

• It was long enough (at least one decade),
• Enough cricket was played (at least ~10 matches per year) during the period,
• Enough players were playing international cricket (50+ batsmen and 30+ bowlers) during the period, and
• Not more than 100 players with non-zero ratings were playing each day during the period.

  We cannot build a full distribution without players ranked lower than 100.

Take a look at figure 1.1 again. Only the blue line at the top this time.

View Figure 1.1

• Test Batsmen

  
  
• Test Bowlers

  
  
• ODI Batsmen

  
  
• ODI Bowlers

  
  
• T20I Batsmen

  
  
• T20I Bowlers

  
  

Figure 1.1: No. of players with ratings above 0 (blue) and 500 (red). Average no. of players above 500 are shown as solid red bars.

No time period fits all our criteria for both ODI and T20I formats. There are always 100 or more players in these formats except during short periods at the very beginning of each format, which are all much shorter than a decade. We therefore cannot use ODI and T20I ratings for analysing the full distribution of ratings.

For Test cricket, we make the following observations:

• Not enough cricket was played in the 1900s, 1910s, 1920s and 1940s (see figure 0.1). There were also less than 50 batsmen and 30 bowlers active in international cricket in those decades (see figure 1.1).
• The 1930s fits all our criteria for both batsmen and bowlers. There are about 60-95 batsmen and 45-60 bowlers active on all days during this period, and we have 85 total days of rating changes to aggregate over.
• There were more than 100 test batsmen but less than 100 bowlers during 1950-1990, so those four decades fit our criteria for bowlers only.
• There were more than 100 test batsmen and bowlers each after 1992, so those years don’t fit our criteria.

We have therefore identified the following decades to do our analysis:

• The 1930s for test batsmen
• The 1930s, 50s, 60s, 70s and 80s for test bowlers

  We will also be looking at the entire period of 1952-1992 for Test bowlers in some sectons.

Let’s continue.

Let’s go back in time to Test cricket in the 1930s.

As mentioned above (and shown in figure 1.1), this is a great time period to look at the full range of ratings for both batting and bowling.

Figure 2.1 shows rating distributions of all 80 batsmen and 44 bowlers in test cricket on the first day of the decade (on 1930-01-01).

About this Figure

This is a histogram.

• On the horizontal axis (bottom scale) are ratings, grouped into intervals of 100 each from left to right.

  The first interval contains all players with ratings 1-100, the second 101-200, and so on until the last one on the right would contain the absolute best players with ratings 901-1000 (if there were any).

• On the vertical axis (left scale) is the number of players in each interval.

  The taller the bar for an interval, the more players have ratings in that interval.

• The three dotted lines represent percentiles in the data:
  • p50 is the 50th percentile, or median.

    This is the middle value in the ratings. In other words, half of all players have a lesser rating than p50 and the other half have a higher rating than p50.

  • p75 is the 75th percentile, or the upper quartile.

    3 out of 4 players have a rating below p75 and the other 1 out of 4 (the top 25%) have a rating above p75.

  • p90 is the 90th percentile, or the top decile.

    9 out of 10 players have a rating below p90 and the other 1 out of 10 (the top 10%) have a rating above p90.

• The total number of players is in the upper right corner.

We’ll be seeing a lot more histograms so make yourself familiar with it.

View Figure 2.1

• Test Batsmen: 1930-01-01

  
  
• Test Bowlers: 1930-01-01

  
  

Figure 2.1: Distribution of Test cricket ratings on 1930-01-01.

We can now see that the ratings look nothing like a normal distribution. In fact, they follow a mostly decreasing trend. More than half the players have a rating below 195 and 140 for batting and bowling respectively (see p50), and only about 10% of players have ratings above 500 (see p90).

However, these are just ratings for one day. Let us now aggregate these ratings over the entire decade (the 1930s).

We now take player counts in each rating interval on every date in the 1930s and plot the average histogram for the entire decade. We will normalise the total number of players to 100 for each of these dates, so that the average histogram has equal weight from each of these dates.

Take a look at figure 2.2 below.

About this Figure

This is the same histogram as figure 2.1, with the following changes:

• Percentiles are now plotted at increments of 10.

  This is averaged interval data, so we can’t make more precise estimates about where those percentiles lie.

• The total number of players on each date has been normalised to 100 before averaging the counts for each interval over those dates.

  Normalisation is just a fancy way of saying that if there were, say, 50 total players on a date, we counted each player twice on that date so that the graph thinks that there were a total of 100 players instead. If there were 40 players on another date, we counted each player 2.5 times on that date to make the total 100. If there were 30 players, each player 3.33 times. If there were 60 players, each player 1.67 times. And similarly for every date.

  The final averaged histogram, then, has equal contribution from each date and it also shows interval counts assuming a total of 100 players.

• Skewness and Excess Kurtosis for the distribution are also shown in the upper right corner.

  Skewness is a measure of symmetry. Perfectly symmetrical distributions have skewness 0.

  In our ratings data: the higher the skewness, the more the players are concentrated on the left side of the distribution (at lower ratings).

  Excess Kurtosis is a measure of outliers. We have plotted it here for informational purposes only and won't be discussing it until chapter 6.

View Figure 2.2

• Test Batsmen: 1930s

  
  
• Test Bowlers: 1930s

  
  

Figure 2.2: Distribution of average Test cricket ratings in the 1930s (years 1930 to 1939).

• We can now see that the decreasing trend in the previous graph was not an anomaly for that date. There really are a lot more players at low ratings than at high ratings.

  On first glance, the averaged counts for ratings seem to be following a half-normal distribution (with skewness close to 1). More on this later.

• The distribution is flatter for batsmen than for bowlers, that is, more bowlers have lower ratings and fewer bowlers have higher ratings compared to batsmen.
  • The median rating (p50) is about ~200.

    In other words, half of all players on average had a rating above this value in the 1930s.

  • The upper quartile (p75) is ~370.

    Only one out of four players on average had a rating above this value in the 1930s.

  • p90 diverges between batsmen and bowlers due to a flatter distribution for batsmen.

In case you are wondering, yes that fraction of one guy above 900 on the batting distribution is Don Bradman. In 1931, he reached a maximum rating of 960: the highest ever rating, batting or bowling, in any format.

In summary, the distribution follows a decreasing trend. It is flatter for batsmen than for bowlers. The median and upper quartile appear at ratings of about ~200 and ~370 respectively.

Let us now see if the same distribution appears for test bowlers in later decades (for decades when we have the full range of ratings).

Figure 2.3 below shows the distribution for bowlers during the four decades between 1950 and 1990. The 1930s are also shown for comparison.

We skip the 1940s due to World War 2.

About this Figure

• These graphs are similar to figure 2.2 but for bowlers only.
• The aggregated periods are the 1930s, 1950s, 1960s, 1970s and 1980s.

Note that even though the actual total number of bowlers went up during these decades as more countries started playing test cricket, each of our graphs is still normalised to 100 players similar to figure 2.2, so they can be compared to each other without making adjustments for total player count.

View Figure 2.3

• Test Bowlers: 1930s

  
  
• Test Bowlers: 1950s

  
  
• Test Bowlers: 1960s

  
  
• Test Bowlers: 1970s

  
  
• Test Bowlers: 1980s

  
  

Figure 2.3: Distribution of average Test bowling ratings in the 1930s, 50s, 60s, 70s and 80s (average ratings by decade).

We see that the graphs for each decade look very similar

• The rating distribution follows a decreasing trend in every decade.
  • The median (p50) is at an average rating of ~220 with range 190 ~ 260 during these decades.
  • The upper quartile (p75) is at an average rating of ~430 with range 370 ~ 500.
  • The top decile (p90) is at an average rating of ~650 with range 550 ~ 720.
  • The skewness changes by quite a lot between decades. It is as low as 0.52 in the 1970s.
• There is an odd bump in interval counts at around a rating of 300, that we also saw in the batting graph for the 1930s.

  We don’t know what causes this bump, but its presence in almost every graph is interesting. It might be due to an underlying quirk in the rating algorithm.

In summary, we find that the averaged distribution of ratings looks similar in every decade and follows a similar decreasing trend. The percentiles appear in the same vicinity in each decade but have a wide range across decades.

We saw in figure 2.3 above that the percentiles appear in similar spots in each decade. Let us now get a more accurate value for each percentile. Since more Test cricket was played after 1950 compared to the 1930s (see figure 0.1), we can look at yearly averages instead of decadal.

Figure 2.4 below shows the distribution of various percentiles on yearly averaged data for 40 years from 1952 to 1992.

Note that we are still only looking at test bowlers.

About this Figure

This is a new kind of histogram.

• There are 3 histograms in this chart: One each for 50th, 75th and 90th percentiles in blue, red and yellow colours respectively.
• On the horizontal axis (bottom scale) we still have ratings, but this time the intervals are smaller (size 50 each).

  The intervals are 1-50, 51-100, 101-150 and so on up to 951-1000.

• On the vertical axis (left scale) is the number of years out of 40 total years when the p50 rating was in the rating range of each interval.
• For each percentile, the average rating out of 40 years is shown above in text, along with a confidence interval.

  The confidence interval is one standard deviation around the average, written as “average +/- std”).

• There is a small overlap between histograms. Both p75 and p90 values were in the 550-600 rating interval, for 4 and 1 year(s) out of 40 respectively.

  Note though that they didn’t appear in this interval in the same year. These 5 occurences were each in some distinct year during the 40 year period.

View Figure 2.4

• Test Bowlers: 1952-1992

  
  

Figure 2.4: Distribution of average yearly ratings at 50th, 75th and 90th percentiles for Test Bowlers during 1952-1992. Overall average rating and one standard deviation interval for each percentile are also shown.

• In 20 out of 40 years (half of all years), the median rating (p50) falls in the interval 200-250. The top end of the confidence interval (229 + 37) is at about ~265.

  We therefore have an indication that a test bowler with a ~260+ rating in the years 1952-1992 was likely in the top 50% of bowlers.

• The upper quartile (p75) is at 460 +/- 60. The top decile (p90) is similarly at 672 +/- 52.
• We find that at higher percentiles the histograms become flatter and the confidence intervals wider.

  We will therefore not identify one rating as an indication that players could be in the top 25% or 10% like we did with p50 above.

In summary, a rating above ~260 during 1952-1992 likely put a player in the top 50% of test bowlers.

Let’s now ask the opposite question: At what percentile do ratings 100, 250 and 500 usually appear in the same 40 years for test bowlers?

Take a look at figure 2.5 below. It aggregates the averages from all years into intervals, one each for various rating thresholds. Each interval shows how the average percentage of players that have a rating above the corresponding rating threshold varies by year.

Note that the percentage of players above a rating threshold shown here is the opposite of the percentile at that rating: $PercentAboveRating = 100 - PercentileAtRating$.

About this Figure

This is an interval graph, sometimes also called a boxplot.

• The rating intervals from the horizontal axis (bottom scale) in previous graphs have now moved to the vertical axis (left scale). Ratings thresholds between 0 and 1000 are shown in steps of 50.

  The top end of the scale is trimmed if no players have ever had a rating that high. For example, 1000 doesn’t appear on the scale in any of the graphs.

• On the horizontal axis (bottom scale) is the yearly average of the percentage of players that have a rating higher than the rating threshold on the left.

  In other words: Of all the active players in a year, what percentage on average had a rating above the rating threshold on the left?

  Alternatively: For each year, take the sum of all bin heights between the rating threshold and 1000 from the average rating distribution graph for that year.

• For each rating threshold on the left scale, the intervals in the graph represent the following:

  • The blue cross is the average across all years of yearly average percentage of players above rating threshold.
  • The green interval covers the middle 50% (p25 to p75) range of yearly averages.

    In other words: The yearly average percentage of players above this rating threshold was between the numbers on the bottom scale covered by the green bar for half of all years.

  • Similarly, the grey interval covers the middle 80% (p10 to p90) range of yearly averages.

    In other words: The yearly average percentage of players above this rating threshold was between the numbers on the bottom scale covered by the grey bar for 4 out of 5 years.

  • Finally, the black line with red dots covers the full range of yearly averages.

    In other words: The yearly average percentage of players above this rating threshold was between the numbers on the bottom scale covered by the black line for every year. The red dots are the minimum and maximum yearly average percentages among the 40 years covered.

• Visualisation quirks

  • If one or both ends of the grey scale do not appear it means that it is the same value as the corresponding green bar.

    That is, the respective lower or upper bound for 80% of years is the same as that for 50% of years.

  • If a green or grey interval does not appear at all it means that the percentages were the same for 50% or 80% of years respectively.
  • Similarly, if the black line also does not appear it means that the percentages were the same as the average percentage (blue cross) for all years.

    This can be seen at rating threshold 0 in the lower right corner, as the percentage of players above rating threshold 0 is always 100% (by definition) in every year.

View Figure 2.5

• Test Bowlers: 1952-1992

  
  

Figure 2.5: Average yearly no. of players above rating thresholds for Test Bowlers between 1952 and 1992.

The following statistics on yearly average percentages are shown: Average of yearly averages (blue cross), 50% and 80% middle intervals of sorted yearly averages (green and grey bars respectively) and full range of yearly averages (black lines with red dots).

There is a lot of information on this graph. For example, at Rating threshold 100 we can see the following:

• On average, 69% of all players in each year have a rating above 100.
• In half of all years, between 66% and 73% of players have a rating above 100.
• In 4 out of 5 years, 63% - 74%, and across all years, 61% - 78%.

We make the following observations:

• Only 79% of players on average have a rating above 50, and the other 21% below 50. The black line ends at 87%, so at least 13% (or 1 out of 8) of all ODI bowlers have a rating below 50 in every year.

  A reminder that we are excluding players with zero ratings, so these are players with ratings between 1 and 50.

• We noted in figure 2.4 above that a rating of ~260+ might be in the top 50% of players. We can now make more accurate statements about the top 50% of players:
  • A rating of 300 is guaranteed to be in the top 52% of that year’s average ratings.

    The black line at threshold 300 is completely to the left of 52%.

  • A rating of 250 is in the top 50% in 3 out of 4 years.

    The green interval at threshold 250 ends at 50%.

  • A rating of 200 is in the top 49% in only 1 out of 10 years, and in the top 51% in 1 out of 4 years.

    The starts of the gray and green intervals at threshold 200 are at 49% and 51% respectively.

  • We also note that a rating of 250 is in the top 48% on average across all years.
• On average, a rating of 500 has 23% of players above it, and more than 28% in 4 out of 5 years.

  This is important for us because all analysis in Chapter 3 will only be on the top half of the rating range (500 - 1000) and it is good to know that we will likely be looking at roughly the top one-fourth of players.

• The intervals become tighter as we move to higher rating thresholds. At 750, for example, the average percentage of players is 6 with 80% interval of 3-10.

  We can therefore say with reasonable confidence that a player with rating 750 is likely to be at least in the top 10% of all players. Also, since the black line does not start at zero, there is at least one player above rating 750 in all 40 years. This is not true for any higher rating thresholds.

We wish that we had data on the full range of ratings from 0 to 1000 for more decades and in more formats to do a more comprehensive analysis of its distribution, especially for more recent years and also for ODIs and T20Is. Unfortunately, that would have to wait until the ICC makes more ratings data publicly available, if ever. For now, let’s move on to the next section.

---

We will now look at ratings distributions for all formats, but limited to ratings between 500 and 1000, or the upper half of the range of ratings. This will let us compare distributions across formats for both batsmen and bowlers and for all years.

As we saw above, this likely means that we are only looking at about one-fourth of active players at any time.

Let’s dive deeper into what the ratings for this creamy layer of players looks like.

Figure 3.1 below shows animated graphs of the distribution of yearly averaged ratings for all formats during the following years:

Format	Start Year	End Year
Test Cricket	1952	2023
ODIs	1983	2023
T20Is	2011	2024

We start at these years because not enough matches were played before these respective start years in each format (see figure 0.1), and the number of players with ratings above 500 had not stabilised (see figure 1.1).

We end in 2023 for Tests and ODIs because there haven’t been enough matches in 2024 in those formats as of this writing.

About this Figure

This is the same histogram that we saw in figures 2.2 and 2.3, with the following differences:

• Each animated graph shows the average distribution of ratings by year, instead of by decade.

• The horizontal axis (bottom scale) now starts at 500 instead of 0. The interval sizes are now 50 each.

  The intervals are 501-550, 551-600, and so on up to 951-1000.

• Instead of plotting the ratings at 50th, 75th and 90th percentiles, we now plot the fraction of rating on the scale of 500-1000 at each percentile. Let’s call these “percentile fractions”, and label the median, upper quartile and top decile values as pf50, pf75 and pf90 respectively.

  We name them "percentile fractions" because these aren’t true percentiles on the full range of 0-1000 ratings, but on a reduced range of 500-1000 ratings that we are looking at.

  We plot these only so that we can visually compare the distributions between years on the animated graph. The ratings at specific percentile fractions don't give us any statistical insights.

  Some examples of percentile fractions:

  • Example 1: If the middle value is at a rating of 600, pf50 is $\frac{600-500}{1000-500} = 0.2$.
  • Example 2: If the upper quartile is at a rating of 720, pf75 is $\frac{720-500}{1000-500} = 0.44$.

  Similarly, the skew and kurtosis are also shown for informational purposes only. They do not give us any statistical insights into the data.

Note that we are still looking at averages over all days of a year in each graph, and the player counts are normalised to 100 as usual.

Show Figure 3.1

• Test Batsmen: 1952-2023

  
  
• Test Bowlers: 1952-2023

  
  
• ODI Batsmen: 1983-2023

  
  
• ODI Bowlers: 1983-2023

  
  
• T20I Batsmen: 2011-2024

  
  
• T20I Bowlers: 2011-2024

  
  

Figure 3.1: Animated distributions of yearly average rating distributions for batting and bowling in each format during specified time periods. Only players with ratings above 500 are included.

• The distribution of ratings is wildly inconsistent across years, for both batting and bowling and across all three formats.
• There is a general decreasing trend in the 500-1000 ratings range, but it is less prominent than the one we saw on the full range of ratings in figures 2.2 and 2.3.

  In some years, the distributions are almost flat.

• The percentile fractions also move all over the ratings scale.

  When we look at the graph of distribution of percentile fractions across years similar to figure 2.4 above (we don’t show it here), we notice that there is a huge overlap between pf50, pf75 and pf90 values.

• Once again, we notice the abrupt shift to the left (towards lower ratings) for ODI bowlers during around 2008.

  Before 2008, pf90 was 0.45 ~ 0.50. Since 2008, pf90 has been only 0.30 ~ 0.40.

• The distribution for T20I bowlers is almost fully concentrated in the left for every year.

  This again reinforces our earlier observation that limited-overs bowlers since 2008 are rated unfairly and never have a chance of matching the ratings of the best batsmen.

In summary, we did not find any consistent pattern in the distribution of ratings in the 500-1000 range, except that they generally follow a decreasing trend. We noticed once again that limited-overs bowlers since 2008 do not achieve high ratings like batsmen do.

Figure 3.2 below shows the same data as figure 3.1 above but aggregates the averages from all years into intervals on a single graph, similar to figure 2.5.

About this Figure

This is the same type of interval graph as figure 2.5, with the following differences:

• The vertical axis (left scale) now has Rating thresholds between 500 and 1000 in increments of 20.

  The top end of the scale is trimmed if no players have ever had a rating that high. For example, 980 never appears on the scale in any graph.

• On the horizontal axis (bottom scale) is now the yearly average of the percentage of 500+ players that have a rating higher than the rating theshold on the left.

  “500+ players” here means players with a rating above 500.

  In other words, of all the players that have a rating above 500 in each year, what percentage on average in each year have a rating above the rating threshold on the left?

• For each rating threshold on the left, the intervals in the graph represent the same statistics as in figure 2.5 (also shown in the upper right as legend).

Note: Data from the year 2020 has been excluded from this graph.

Show Figure 3.2

• Test Batsmen: 1952-2023

  
  
• Test Bowling: 1952-2023

  
  
• ODI Batsmen: 1983-2023

  
  
• ODI Bowling: 1983-2023

  
  
• T20I Batsmen: 2011-2024

  
  
• T20I Bowling: 2011-2024

  
  

Figure 3.2: Interval graph of yearly average ratings for batting and bowling in each format during specified time periods. Only players with ratings above 500 are included.

The following statistics on yearly average percentages are shown: Average of yearly averages (blue cross), 50% and 80% middle intervals of sorted yearly averages (green and grey bars respectively) and full range of yearly averages (black lines with red dots).

• Test Cricket

  • In Tests, the intervals for batsmen are much narrower than those for bowlers.

    This means that the yearly average rating distributions are more consistent for batsmen than for bowlers. For example, we see the following intervals for Test cricket at Rating threshold 700:

    Stat	Batting Interval	Bowling Interval
    Average	28	40
    Middle 50%	22 - 33 (width: 11)	33 - 47 (width: 14)
    Middle 80%	18 - 38 (width: 20)	24 - 53 (width: 29)
    Full Range	14 - 43 (width: 29)	17 - 60 (width: 43)

  • On the other hand, the averages for Test bowlers almost follow a straight line.

    This means that even though there is a large year-by-year variance in the average number of players above each rating threshold, Test bowlers’ ratings are more fairly distributed over the entire range of years (1952-2023).

    In other words, the ratings distribution is overall flat in the 500-1000 range.

  • Test batsmen’s averages follow a curve.

    This indicates that there are more players at lower ratings than at higher ratings on average.

  • In at least 90% of years, the highest rating for Test bowlers was more than 860.

    The left edge of the grey interval is greater than 0.

    This is the highest rating threshold for a non-zero start of the 80% interval among all six graphs.

  • In at least 75% of years, the highest rating for both Test batsmen and bowlers is more than 880.

    The left edge of the green interval is greater than 0.

    This is at a higher threshold than for both limited over formats.

• ODIs
  • The averages for ODI bowlers follows a steeper curve than for ODI batsmen.

    This confirms again that ODI bowlers have lower ratings on average than ODI batsmen.

  • ODI batsmen and bowlers have similar widths for 50% and 80% intervals. However, the full range of average yearly ratings (black lines outside grey intervals) is much wider for ODI bowlers than for batsmen.

    This may partly be due to the drop in ODI bowlers’ ratings in 2008 that we noticed earlier, and partly due to a large number of ODI bowlers with high ratings in the early years of ODIs (see years 1983-87 in figure 1.3).

  • The average for ODI bowlers lies outside the middle 50% interval for rating thresholds 800-900, and almost on the right edge of the middle 50% interval for 740-800.

    This is likely another consequence of the ratings drop since 2008.

• T20Is
  • All intervals are wider for batsmen and narrower for bowlers in T20Is. In fact, T20I bowlers seem to have the narrowest middle 50% and 80% intervals among all six graphs.

    This means that the average yearly distribution for T20I bowlers is the most consistent, though a short span of only 14 years might explain away the consistency.

  • T20I bowlers have the steepest curve of all six graphs. The average at rating threshold 700, for example, is only 8. Even the right edge of the 80% interval at 660 is only 20.

    At the same time, no T20I bowler has ever had a rating above 860, also the lowest among all six graphs.

  • T20I batsmen have wide 80% intervals, as well as averages outside the 50% interval for rating thresholds 680-720.

    This indicates a short period of higher yearly average ratings than usual, likely during 2022-24. However, we consider this an artefact due to the short 14-year span of T20I ratings.

  • Both T20I graphs also show a point of inflection (the curve of averages is convex on one side and concave on the other around rating threshold 600 ~ 620).

    We attribute this anomaly to the short span of T20Is as well.

In summary, all six graphs follow different trends.

• Test batsmen and bowlers both have more players on average at very high (800+) ratings.
• Test bowlers have had the most fair distribution of ratings across years (straight line of averages), but with the least consistency between years (wide intervals).
• T20I bowlers have had the most consistency between years (narrow intervals), but the least fair distribution (steepest curve) overall.
• Both Test and ODI batsmen have the most balanced rating distributions, with a slight decreasing trend (gentle curve of averages) and generally decent consistency (neither narrow nor wide intervals).

  ODI batsmen’s intervals are slightly narrower but Test batsmen’s span 30 more years, so we think that they are equally balanced overall.

• ODI bowlers and T20I batsmen both seem to suffer from outliers caused by shifts in rating distributions.

  The outliers are more significant and consequential for ODI bowlers due to their longer span (40 years vs only 14 for T20Is).

---

Let us wrap up our discussion on distributions now and move on to more locally isolated changes and quirks of the rating algorithm. In this section, we will look at single-day changes in ratings and their patterns.

We have noticed that players' ratings are penalised during the first few years of their careers. This can be seen very prominently when we plot players’ ratings in the first few years of their careers.

Figure 4.1 shows ratings over the first 3 years of some famous players’ careers along with ratings for some established players at the time.

Players Shown

Format & Type	3-Year Period	New Player(s)	Established Top Player(s)
Test Batting	1929 - 1932	Don Bradman (AUS)	Herbert Sutcliffe (ENG) Jack Hobbs (ENG)
Test Bowling	1992 - 1995	Shane Warne (AUS)	Curtly Ambrose (WI) Waqar Younis (PAK)
ODI Batting	2005 - 2008	MS Dhoni (IND) Kevin Pietersen (ENG)	Ricky Ponting (AUS)
ODI Bowling	1996 - 1999	Shaun Pollock (SA)	Wasim Akram (PAK) Chaminda Vaas (SL)
T20I Batting	2021 - 2024	Suryakumar Yadav (IND) Aiden Markram (SA)	Babar Azam (PAK)
T20I Bowling	2016 - 2019	Rashid Khan (AFG) Jasprit Bumrah (IND)	Imran Tahir (SA)

About this Figure

This is a line chart that shows day-by-day ratings over time, similar to the figures from Chapter 1, with the following changes:

• The time span is limited to the first three calendar years after the debut of new player(s).
• Players are colour-coded by country.

Show Figure 4.1

• Test Batsmen: 1929-1932

  
  
• Test Bowlers: 1992-1995

  
  
• ODI Batsmen: 2005-2008

  
  
• ODI Bowlers: 1996-1999

  
  
• T20I Batsmen: 2021-2024

  
  
• T20I Bowlers: 2016-2019

  
  

Figure 4.1: Ratings of selected player(s) during the first 3 years of their careers compared to ratings of top player(s) at the time.

Example: Don Bradman’s rating during 1929-1932:

• Bradman's rating went up to 603 in the four matches he played during 1928-29.

  Bradman scored two hundreds in those four matches.

• It then went up only 157 points from 603 to 760 during Australia’s tour of England in the summer of 1930.

  Bradman scored a hundred, two double hundreds and a triple hundred in seven innings.

  His rating stayed lower than the established English batsman Herbert Sutcliffe, who maintained an 800+ rating during the same series in spite of not matching Bradman’s performance.

• It took Bradman more than four years (1928-12-04 to 1933-02-27) to get to a 900+ rating.

  He had scored 3091 runs in 37 innings at an average of 99.71 from 23 matches by then.

  It is clear to us that there was some kind of early-career penalty applied to Bradman's ratings in the first 3-4 years of his career.

We identify the following patterns about early career ratings:

• Both Bradman and Warne took 2-3 years to get to the top in Test cricket.
• MS Dhoni, Kevin Pietersen and Shaun Pollock all took 1-2 years to get to the top in ODIs.
• Rashid Khan and Jasprit Bumrah both reached top rankings in only 6 months in T20Is, but Aiden Markram and Suryakumar Yadav took 1-1.5 years to get there.

  Very early days for limited-overs players are not shown because the players' ratings were too low to be included in the top 100 ranks.

We notice that all players, batsmen and bowlers, across all three formats and throughout history start their career with a low rating and slowly build up towards a stable rating. This happens regardless of a player’s actual performances during their first few matches.

We also notice that the time it takes to lose this early-career penalty seems to depend not on calendar time, but on the number of matches played. In Test cricket, it takes more than a year to play enough matches to get to the top. In limited-overs matches, it can be done in less than a year.

In the case of T20I bowlers in figure 4.1 above, the 2016 T20 World Cup significantly accelerated the process.

Our best guess about why we see these patterns:

• As per the ICC, a player’s rating is a "sophisticated moving average" of r-scores in each of their innings.
• We think that this average might be calculated on at least a minimum number of innings, with recent innings likely weighed higher. If less than the minimum number of innings have been played, the moving average assumes zero ratings for the remaining innings.
• The moving average therefore stays low until enough innings have been played to match the minimum number of innings.

This is just a guess though. It is equally likely that players' ratings are intentionally reduced at the beginning of their careers and allowed to gradually recover as they play more games.

It is said that player ratings measure a player’s current and recent form. Part of it is due to the changing moving average as a player puts in good or bad performances, but an equally important part is selection on the national team.

If a player misses matches for their national team, they start to slowly lose rating points.

Let us now look at some examples of these rating drops. Figure 4.2 shows ratings for some notable players during periods of absence from international cricket.

Players Shown

Format + Type	Period	Players	Event
Test Batting	Mar 2018 - Mar 2019	Steven Smith (AUS) David Warner (AUS)	Both players were suspended for one year
ODI Batting	Jan 2005 - Jan 2008	Sachin Tendulkar (IND) Rahul Dravid (IND) Sourav Ganguly (IND)	Ganguly was dropped between Mar 2005 - Jan 2007
T20I Batting	Jul 2021 - Jul 2024	Virat Kohli (IND) Rohit Sharma (IND) Rishabh Pant (IND)	Pant was injured Jan 2023 - Jun 2024, Kohli and Sharma were rested for all of 2023

About this Figure

This graph shows player ratings over time similar to figure 4.1, but players are not colour-coded by country.

Show Figure 4.2

• Test Batsmen: 2018-2019

  
  
• ODI Batsmen: 2005-2008

  
  
• T20I Batsmen: 2021-2024

  
  

Figure 4.2: Ratings of selected player(s) during periods of inactivity with optional comparisons to ratings of some other players at the time.

The absolute rating drops on each day are also shown on the first graph for Test Batsmen.

As expected, players’ ratings decrease after each match that they missed for their national team. We see the following patterns:

• For Warner and Smith, we have plotted the drop in ratings for each player after every missed match. Starting 2018-04-01, we notice that the ratings drop by almost the same amounts after each match for either player.

  Smith’s ratings drop by 9 for most matches but also by 8 and 10 once each. Warner’s ratings drop by 8 for most matches but also by 7 and 9 once each.

  The +/- 1 range of values for each player are likely because the ratings are getting rounded to the nearest integer after each match.

  • Smith’s rating drops may be larger because his rating is higher. It is possible that both players are losing the same percentage of their ratings after each match.

    This percentage seems to be 1% per match, but we can’t say this conclusively right now.

• The graph with Tendulkar, Dravid and Ganguly shows how a player loses rating points over longer periods, and only when their team plays a match.

  Ganguly loses rating points only when Tendulkar and Dravid’s rating also show a change.

  • Ganguly’s rating went from 576 in Oct 2005 to 469 in Dec 2026, dropping by 2-3 after every missed match. During this time, India played 41 ODIs without him.

    Starting at 576, if we decrement 0.5% of the rating at the time of each match for 41 matches, we get exactly 469:

    $576*(0.995^{41})=469$.

• The graph with Kohli, Sharma and Pant shows Pant losing rating points during his absence due to injury, but also Kohli and Sharma losing rating points during their long rest period for the entirety of 2023.

  • Kohli's rating dropped from 650 to 516 and Sharma's dropped from 579 to 460, while India played 23 T20Is without them in 2023.

  The drops are exactly 1% per match:

  • $650*(0.99^{23})=516$
  • $579*(0.99^{23})=460$

  We note that Kohli and Sharma lost rating points not because they were injured or out-of-form, but merely because they were rested.

  • Pant’s rating dropped from 406 in Dec 2022 to 371 in Aug 2023, by 3-4 in each match, after which he dropped below Rank 100. India played 9 matches during this period.

    Once again, the drop is exactly 1% per match: $406*(0.99^9)=371$.

In summary, players lose rating points in a format when they miss a match for their national team in that format. They lose ratings not just due to injury or because they are dropped or banned, but also when they are rested. We have evidence that players’ ratings drop by 1% per missed match in some situations and by 0.5% in others.

Let us now see how all single-day changes in ratings are distributed. Take a look at figure 4.3.

About this Figure

This is a histogram, similar to the ones we saw in sections 2 and 3.

• On the horizontal axis (bottom scale) is the single-day change in ratings: Gains are positive and drops are negative. The scale starts at -100 and goes up to 100, with intervals of size 5 each.

  The intervals are -2 to +2 in the middle, then -7 to -3 and +3 to +7 on either side, then -12 to -8 and +8 to +12, and so on up to -100 and +100 respectively on each side.

  • 100+ single-day gains and drops are not shown on the graph but their total counts are mentioned in the upper right corner, along with those for 50+ single-day gains and drops for comparison.
• On the vertical axis (left scale) is the total number of changes in each interval for all players on every date in history.

  A reminder that only changes where the rating was at least 500 on the previous day are included to keep the data consistent between years and formats.

Note that if ratings do not change for a player on a day (zero gain or drop), we do not include it here.

Show Figure 4.3

• Test Batsmen

  
  
• Test Bowlers

  
  
• ODI Batsmen

  
  
• ODI Bowlers

  
  
• T20I Batsmen

  
  
• T20I Bowlers

  
  

Figure 4.3: Distribution of single-day changes in Ratings by format.

Only changes where the previous day's rating was at least 500 are included.

• Drops are much more common than gains.

  This might be because a lot more rating points are lost due to missed matches as we saw above, compared to gains which only occur after matches played and only if the player’s performance was good enough to result in a gain.

• Test cricket has a much wider range of single-day gains and drops compared to limited-over formats.
• Very few single-day drops are 50+, and almost none are 100+ across formats. On the other hand, quite a few gains are 50+, and a small number are 100+ gains across formats as well.

  The large gains might be due to big jumps in rating points after each match early in players' careers like we saw in figure 4.1. However, we are only looking at single-day changes where the rating on the previous day was at least 500, so those large gains should have minimal effect.

• The interval(s) with the most changes are -3 to -7 for Tests and ODIs and -3 to -12 for T20Is.

  This might be due to the 0.5% and 1% respective drops per match we noticed above in figure 4.2.

In summary, there are a lot more drops in ratings than there are gains, possibly due to many players losing rating points while out-of-form, injured or rested. Single-day gains tend to be higher than single-day drops in general. Gains and drops are more spread out for Test cricket vs limited-over formats.

Let us now look at single-day rating changes again, but this time as a percentage gain or drop vs the rating on the previous day. Take a look at figure 4.4.

About this Figure

This is a similar histogram as above, with the following changes:

• The horizontal axis (bottom scale) now shows intervals of single-day percent changes in rating instead of absolute changes.
  • The intervals are now much narrower, only 0.2% wide each.

    The middle interval is -0.1% to +0.1%, the adjacent intervals are -0.3% to -0.1% and +0.1% to +0.3% on either side, and so on up to -10% and +10% respectively on each side.

  • This time, up to 10% single-day gains and drops are shown on the graph. Total counts of 10%+ single-day gains and drops are mentioned in the upper right corner, along with those for 5%+ single-day gains and drops for comparison.

Show Figure 4.4

• Test Batsmen

  
  
• Test Bowlers

  
  
• ODI Batsmen

  
  
• ODI Bowlers

  
  
• T20I Batsmen

  
  
• T20I Bowlers

  
  

Figure 4.4: Distribution of single-day percent changes in Ratings by format.

Only percentage changes where the previous day's rating was at least 500 are included.

• It is now abundantly clear that drops in ratings for inactive players are 0.5%, 1% and sometimes even 2% per match, as shown by the massive peaks in those intervals.
  • In Test cricket, 1% of rating points are lost per missed match.
  • For ODI bowlers, 0.5% of rating points are lost per missed match but there is some indication of 1% rating points being lost in some cases.
  • For ODI batsmen, the rating points lost can be 0.5% or 1%. There are a large number of drops concentrated in the three intervals between -1.7% and -1.1% as well.
  • In T20Is, 1% or 2% of rating points are lost per missed match, with 2% more common.
• Even with the intervals for these percentage drops ignored on the graphs, we see that:
  • Single-day gains and drops in Test cricket as much more spread out than those in limited-over formats.
  • Drops in general are smaller than gains across formats. It is not uncommon for players’ ratings to jump 5% or more in a single day, but drops larger than 5% are relatively rare.

    A reminder that only days with ratings changes when the previous rating was 500+ are included here.

In summary, we have clear evidence that rating drops due to missed matches are 0.5%, 1.0% or 2.0%, with no clear indication of why there are different values for drops between (and even within) formats. We’re more certain now that gains in general are larger than drops, even if the intervals for drops due to missed matches are ignored.

To fully unravel the mystery of rating point gains and drops, we will now plot the same distribution, but with changes grouped by year in a heatmap. Take a look at figure 4.5 below.

About this Figure

This is a heatmap. It shows the same data as figure 4.4, but split into years.

• The horizontal axis (bottom scale) shows years.
• The vertical axis (left scale) now shows the same intervals for percentage gains and drops that we saw on the horizontal axis (bottom scale) in figure 4.4.

  Bigger daily percentage gains are higher up on the scale and bigger daily percentage drops are lower down, with zero in the middle.

• Counts in each interval from figure 4.4 are normalised by year. We refer to the yearly normalised counts as the "Interval Frequencies" for that year.
• The colour of the box for each interval in each year now represents the interval frequency for that interval in that year.

  A darker colour means that less change percentages were in that interval in that year, while a lighter colour means that more change percentages were in that interval in that year.

  • The colours are shown on a logarithmic scale on the right along with the interval frequencies they represent.

    A logarithmic scale helps identify variations at lower interval frequencies.

Show Figure 4.5

• Test Batsmen

  
  
• Test Bowlers

  
  
• ODI Batsmen

  
  
• ODI Bowlers

  
  
• T20I Batsmen

  
  
• T20I Bowlers

  
  

Figure 4.5: Heatmap of single-day percent changes in ratings per year by format. Interval frequencies of percent changes in ratings are visualised as colours on a log scale, as shown in the colour bar on the right.

Only percentage changes where the previous day's rating was at least 500 are included.

We now see why we were seeing different values of percentage drops in figures 4.2 - 4.4.

The bright horizontal lines in figure 4.5 just below zero show these drops.

• It is clear that in 2021-22, the ICC changed the percentage drop value due to missed matches in limited-overs formats.
  • For Test cricket, the percentage drop has always been 1%.
  • For ODIs, the percentage drop used to be 0.5% until 2021. It was changed to 1% starting in 2022.

    This is why we saw two different peaks for ODI batsmen and bowlers in figure 4.3.

  • Similarly for T20Is, the percentage drop used to be 2% until 2021. It was changed to 1% starting in 2022.

We also get a more clear picture of the differences between single-day percentage gains and drops.

• We see once again that gains, in general, are larger than drops.

  Gains (changes in the top half of the heatmaps) are more spread out than drops (changes in the bottom half).

• In Test cricket, gains and drops in ratings are both spread out over the -6% to +10% range.

  We do not see any bright spots except the expected one at 1%.

• In limited overs cricket, both gains and drops are more concentrated at lower percentages compared to Test cricket.
  • In ODIs, most gains are below +5%, and most drops are above -3%. The drops in particular are even more densely packed for ODI batsmen, where we see few below -2% and hardly any below -2.5%.

    This is likely why we saw so many changes between -1.7% and -1.1% for ODI batsmen in figure 4.4.

  • In T20Is, we see a range similar to that for ODI bowlers.

In summary, we found that the percentage rating drop for missed matches has always been 1% for Test cricket, but was changed in 2022 when it increased from 0.5% to 1% for ODIs and decreased from 2% to 1% for T20Is. It is now 1% in every format.

We note that these changes have not been retroactively applied to past ratings.

We also noted that limited-overs gains and drops are highly concentrated at lower percentages, with ODI batsmen seeing particularly small single-day drops as a percentage of rating.

We have noticed more than once in this chapter that single-day gains are larger than drops. Let us now take a closer look at this difference.

Table 4.1 below shows a summary of all single-day gains and drops in all formats.

Show Table 4.1

Format	Type	Change	No. of Changes	Average Change	Median Change	Total Change
Test	Batting	Gain	8 080	+27.23	+20	+219 978
Test	Batting	Drop	14 688	-14.84	-10	-217 919
Test	Bowling	Gain	4 592	+26.65	+19	+122 360
Test	Bowling	Drop	9 082	-11.97	-7	-108 693
ODI	Batting	Gain	13 501	+13.22	+9	+178 458
ODI	Batting	Drop	27 206	-6.15	-5	-167 334
ODI	Bowling	Gain	10 080	+13.70	+11	+138 092
ODI	Bowling	Drop	23 135	-5.51	-3	-127 458
T20I	Batting	Gain	1 898	+21.63	+14	+41 046
T20I	Batting	Drop	4 291	-10.60	-10	-45 496
T20I	Bowling	Gain	2 293	+17.54	+14	+40 210
T20I	Bowling	Drop	4 180	-9.60	-10	-40 131

Table 4.1: Summary of single-day changes in all formats.

Only changes where the previous day's rating was at least 500 are included.

We note the following:

• There are about 1.5x ~ 2.5x as many drops than gains in every format.
• The average gains are 1.5x ~ 2.5x larger than drops in every format.
• The total change for gains and drops are almost equal in some formats (Test Batsmen and T20I Bowlers), and within +/-10% of each other in other formats.

In summary, we find that even though there is an imbalance in the total number of gains and drops and in the rating points gained or lost in each change, the total number of rating points gained and lost over time are mysteriously balanced.

We don't understand what causes this mystery balance, but it alleviates our earlier concerns about the imbalance between gains and drops.

What happens if we now remove the drops due to missed matches? Let's find out.

We don't know exactly which drops are due to missed matches.

For example, a test bowler may lose 1% of rating points because they missed a match, or because their r-score for that match was lower than their existing rating.

We will therefore make a guess. Let's take all drops in the rating interval(s) containing 0.5%, 1% or 2% (depending on format and year) from figure 4.4, then sample them down to the average counts of their adjacent intervals.

We are left with what should be a representative sample of drops from played matches in those intervals.

The results aren't perfect, but they are good enough to make sense of aggregate numbers.

Table 4.2 below shows the same single-day change data as in Table 4.1, but for likely played matches only.

Note that the gains in table 4.2 are the same as in table 4.1. Only values for drops have changed.

Show Table 4.2

Format	Type	Change	No. of Changes	Average Change	Median Change	Total Change
Test	Batting	Gain	8 080	+27.23	+20	+219 978
Test	Batting	Drop	10 096	-18.76	-17	-189 384
Test	Bowling	Gain	4 592	+26.65	+19	+122 360
Test	Bowling	Drop	4 553	-17.50	-15	-79 657
ODI	Batting	Gain	13 501	+13.22	+9	+178 458
ODI	Batting	Drop	18 905	-7.32	-7	-138 389
ODI	Bowling	Gain	10 080	+13.70	+11	+138 092
ODI	Bowling	Drop	13 492	-7.09	-6	-95 615
T20I	Batting	Gain	1 898	+21.63	+14	+41 046
T20I	Batting	Drop	2 287	-11.06	-8	-25 303
T20I	Bowling	Gain	2 293	+17.54	+14	+40 210
T20I	Bowling	Drop	1 803	-9.57	-7	-17 263

Table 4.2: Summary of single-day changes from likely played matches in all formats.

Only changes where the previous day's rating was at least 500 are included.

We note the following:

• The number of changes for gains and drops are roughly balanced now.
• Total changes are no longer balanced, as expected.
• Both average and median values for gains are larger than drops, as we noticed in figures 4.3 - 4.5 above.
  • In Test cricket, the average gains are ~1.5x larger than average drops.
  • In limited-overs formats, the average gains are ~2x larger than average drops.
  • The average gains and drops are almost identical between batting and bowling in Tests and ODIs.

    In T20Is, they are about 20% larger for batting.

• Average gains and drops in Test cricket are about 2x larger than in ODIs.

  This is why we saw that changes were spread out for Test cricket but concentrated around the middle for ODIs in the heatmap in figure 4.5.

• Average gains and drops in T20Is fall in between those for Tests and ODIs.

In summary, we find that single-day changes after played matches for Test players are twice as large as those for ODI players. Average gains after played matches are 1.5x ~ 2x larger than average drops in all formats. All single-day changes within each format are similar between batting and bowling.

With this extensive look at gains and drops done, let's wrap up our discussion of single-day changes.

---

Let us now move on to all-rounders (who we have conveniently ignored so far).

The ICC provides a simple formula for calculating the all-rounder rating for any player as a combination of their individual batting and bowling ratings:

$$AllrounderRating = \frac{BattingRating*BowlingRating}{1000}$$

Test All-rounder ratings from the 1930s are shown in figure 5.1 below.

About this Figure

This is the same graph that we saw in figure 2.2: It shows the average distribution of batting and bowling ratings during the 1930s. We also plot the 50th, 75th and 90th percentiles as usual.

We make the following changes:

• We have added all-rounder ratings using the above formula as the third graph, along with the same percentiles for comparison.
• On the horizontal axis (bottom scale), we have made the intervals smaller. They are now 50 rating points wide each.

  The intervals are 0-50, 51-100, 101-150, … 951-1000.

Show Figure 5.1

• Test Batsmen: 1930s

  
  
• Test Bowlers: 1930s

  
  
• Test All-Rounders: 1930s

  
  

Figure 5.1: Distribution of average Test cricket ratings in the 1930s (years 1930 to 1939) for batsmen, bowlers and all-rounders.

• The rating distribution for all-rounders looks nothing like that for batsmen and bowlers.

  We had earlier identified some common trends for batsmen and bowlers (e.g. the percentiles appear at similar locations and the distribution follows a similar decreasing trend). None of those trends apply to all-rounders.

• We see that all-rounders have very low ratings in general. For example, 82% of all-rounders have a rating below 100.

  It may seem fair at first because very few players are good all-rounders. However, we see that only 27% batsmen and only 31% bowlers have ratings below 100. Even if we assume that all the worst batsmen and all the worst bowlers have no overlap, that’s still only 58% of total players.

  Moreover, 35% batsmen and 43% bowlers each have a rating below 150, or overall 78% assuming no overlap, which is still less than the number of all-rounders below rating 100.

• The skewness for all-rounders is twice as large as the batting and bowling distributions, and much higher than any other distribution we have seen in sections 2 and 3.
• All the percentiles also lie at very low ratings for all-rounders.
  • The median rating (p50) is only 20.

    How can half of all players have an all-rounder rating below 20? The median rating for batsmen and bowlers are 210 and 190 respectively, and this is not even close.

    A reminder that we have removed zero ratings from these graphs. 50% of all-rounder ratings (for players who batted and bowled during the 1930s) really do lie between 1 and 20.

  • 75% of all-rounders have a rating below 70, vs 370 each for batsmen and bowlers
  • 90% of all-rounders have a rating below 160, vs 590 and 550 for batsmen and bowlers respectively.

In summary, we find that all-rounder ratings are extremely low compared to batsmen and bowlers with abnormally high skewness. Half of all all-rounders have ratings below 20.

This makes the 0-1000 scale useless for rating all-rounders.

So why are all-rounder ratings so low? The answer lies in the formula used.

Take the following example: A player has "good, solid ratings" of 500 for both batting and bowling. Without doing the math, what do you think his all-rounder rating should be?

Table 5.1 below shows some combinations of batting and bowling ratings and the resulting all-rounder ratings.

Show Table 5.1

Batting Rating	Bowling Rating	All-Rounder Rating
100	100	10
200	200	40
500	500	250
900	100	90
300	700	210
900	500	450
750	750	563
1000	500	500
Any Rating	0	0

Table 5.1: All-rounder ratings for selected combinations of batting and bowling ratings.

We now see the problem with this formula.

• Ratings of 200 each (approximate median values) for batting and bowling produce an all-rounder rating of only 40.
• Ratings of 500 each result in an all-rounder rating of only 250.

  Does 250 feel like a “good, solid” all-rounder rating out of 1000?

• Ratings of 900 and 500 result in an all-rounder rating of only 450.

  Imagine being one of the best batsmen in the World and a top ~25% bowler as well. Is it fair for this player to have an all-rounder rating of only 450?

• Same player as above but he does not bowl. Ratings 900 and 0. All-rounder rating of zero.

  That’s fair, actually, since a player isn’t an all-rounder if he doesn’t bowl.

Most of these are non-intuitive results, and are likely to be more confusing than helpful. Clearly, this formula can use some change. Let’s see if we can do better.

Let’s take the simplest approach first and define the all-rounder rating as the average of batting and bowling ratings. So, our formula is:

$$AllrounderRating = \frac{BattingRating+BowlingRating}{2}$$

Here is table 5.2 with a few all-rounder ratings according to the original and new formulae:

Show Table 5.2

Batting Rating	Bowling Rating	All-Rounder Rating (classic)	All-Rounder Rating (average)
500	500	250	500
300	300	90	300
300	700	210	500
900	500	450	700
450	450	203	450
900	0	0	450

Table 5.2: All-rounder ratings for selected combinations of batting and bowling ratings, using both classic and average formulae.

The formula looks simple enough, and produces fair results. However, notice the last row where we combine ratings of 900 and 0.

It does not make sense to give a player who does not bowl at all the same all-rounder rating as a decent all-rounder with batting and bowling ratings of 450 each.

This is why it is necessary to multiply the two ratings together, so that one zero value would always result in a zero result.

Here’s a second attempt at a new formula:

$$AllrounderRating = \sqrt{BattingRating*BowlingRating}$$

Here, we take the product of the two ratings as in the original formula, but instead of dividing the result by 1000, we take the square root of the result.

This is known as the Geometric Mean (GM) of two numbers, and is a widely used and commonly known statistic.

This GM formula is also simple enough, just like the classic and average formulae.

Table 5.3 below shows the results of the same combinations of batting and bowling ratings as in table 5.2 above, along with the resulting all-rounder ratings for all three formulae.

Show Table 5.3

Batting Rating	Bowling Rating	All-Rounder Rating (classic)	All-Rounder Rating (average)	All-Rounder Rating (GM)
500	500	250	500	500
300	300	90	300	300
300	700	210	500	458
900	500	450	700	671
450	450	202	450	450
900	0	0	450	0

Table 5.3: All-rounder ratings for selected combinations of batting and bowling ratings, using classic, average and GM formulae.

This formula produces fair results, and also produces zero ratings as expected.

Let us now look at how the original and new formulae compare. Figure 5.2 below shows combinations for all possible batting and bowling ratings between 0 and 1000 and their resulting all-rounder ratings using both the classic formula and our geometric mean (GM) formula.

About this Figure

This is a heatmap, similar to the one we saw in figure 4.4, but a much simpler one.

• On the horizontal axis (bottom scale) are batting ratings from 0 - 1000. There are no intervals or counts, just all possible values for ratings.
• On the vertical axis (left scale) are bowling ratings from 0 - 1000.
• The colour of the graph is the resulting all-rounder ratings, with brighter colours showing higher ratings as shown in the Rating Scale on the right.
• At ratings 100, 200, 300, … , 900 for both batting and bowling we have also shown the value of the all-rounder rating obtained by combining the respective batting and bowling ratings.
• Finally, contour lines in white are drawn along the combinations of batting and bowling ratings that produce all-rounder ratings of 100, 200, 300, … , 900 respectively.

Show Figure 5.2

• All-Rounder Ratings (classic formula)

  
  
• All-Rounder Ratings (GM formula)

  
  

Figure 5.2: Comparison of all-rounder ratings for all combinations of batting and bowling ratings. Results for both classic and GM formulae are shown.

We see now just how unfair the classic formula really is.

• The entire lower-left quarter of the graph is dark, and so are the upper-left and lower-right corners. Only the upper-right quarter is bright.
• Only a small triangular section at the top contains all all-rounder ratings above 500.
• The all-rounder rating is always less than both of the combined ratings.

  The only exception is when one of the ratings is theoretically 1000, in which case the all-rounder rating would be exactly the other rating.

• One low rating completely overwhelms the other.

  For example, if one rating is 100 the all-rounder rating can only be between 0 and 100.

• More than half of the graph area (half of all possible combinations) has a rating below 200. In fact, the median all-rounder rating of all 10,000 possible combinations of batting and bowling ratings is only 186, and 90% of all possible combinations are less than 587.

The geometric mean (GM) formula is much more fair:

• We see just how much brighter most of the graph is in comparison.
• The all-rounder rating is always less than or equal to the larger of the combined ratings, and always greater than or equal to the smaller one.

  In other words, the all-rounder rating is always somewhere between the batting and bowling ratings.

  In fact, it is always closer to the smaller one like it should be for all-rounders.

• Equal batting and bowling ratings produce the same all-rounder rating every time.

  For example, if a player has batting and bowling ratings of 700 each, he will have the exact same all-rounder rating of 700.

• One low rating does not overwhelm the other.

  Even if one rating is only 100, the all-rounder rating can be as high as 316. If one rating is 500, the all-rounder rating can be as high as 707.

• The median all-rounder rating of all possible combinations of batting and bowling ratings is 432, and 90% of all possible combinations are less than 766, both very reasonable ratings.

In summary, the GM formula produces all-rounder ratings that are more spread out over the 0-1000 range, and more representative of a player's individual batting and bowling ratings.

Let us now look at the distributions for test cricket in the 1930s just like in figure 5.1, but also include all-rounders’ ratings with our recommended GM formula. Take a look at figure 5.3 below.

About this Figure

These are the same graphs as in figure 5.1, but with two graphs for all-rounders. The third graph uses the classic formula for all-rounder ratings, and the fourth one uses the GM formula.

Show Figure 5.3

• Test Batsmen: 1930s

  
  
• Test Bowlers: 1930s

  
  
• Test All-Rounders (classic): 1930s

  
  
• Test All-Rounders (GM): 1930s

  
  

Figure 5.3: Distribution of average Test cricket ratings in the 1930s (years 1930 to 1939) for batsmen, bowlers, all-rounders (classic formula) and all-rounders (GM formula).

We see that our new all-rounder distribution looks very similar to batting and bowling distributions.

• There is a smaller number of players in the 1-50 bucket, but otherwise we see the same decreasing trend.
• The highest count in an interval is 18, which is between 15 and 23 (highest counts for batting and bowling intervals respectively).
• The 50th, 75th and 90th percentiles, while lower than those for batting and bowling, are still spaced out somewhat equally and at high enough ratings.
• At 0.89, the skewness is ~10% less than those for batting and bowling, but is still in the usual range that we saw in sections 2 and 3.
• Overall, all-rounder ratings are lower than individual batting and bowling ratings, like they should be, but not so low that 90% players are lumped into ratings below 160 like with the classic formula.

In summary, our recommended GM formula is much more intuitive than the one being used currently. At the same time, it produces a more fair distribution that closely resembles those for batting and bowling while still allowing exceptional all-rounders to shine with higher ratings.

Finally, since we have defined a new rating formula for all-rounders, we list the top 10 best-ever ratings for all-rounders in each format according to our GM formula in tables 5.4 to 5.6 below.

We note that apart from a couple of reorderings at very close ratings, these are the same rankings of best-ever all-rounders in each format as we get with the current formula, but with ratings more representative of each player’s individual batting and bowling ratings at the time.

The Best-Ever Test All-Rounders

Show Table 5.4

Rank	Test Player	Best Rating	Date
1	Garry Sobers (WI)	818	1967-01-04
2	Ian Botham (ENG)	803	1980-02-19
3	Jacques Kallis (SA)	784	2002-12-30
4	Keith Miller (AUS)	756	1952-01-29
5	Richie Benaud (AUS)	729	1959-11-17
6	Imran Khan (PAK)	719	1983-01-18
7	Tony Greig (ENG)	713	1975-03-04
8	Andrew Flintoff (ENG)	708	2005-11-16
9	Aubrey Faulkner (SA)	707	1911-01-11
9	Chris Cairns (NZ)	707	2000-09-23

Table 5.4: The Best-ever Ratings for Test all-rounders according to the GM formula.

The Best-Ever ODI All-Rounders

Show Table 5.5

Rank	Test Player	Best Rating	Date
1	Kapil Dev (IND)	794	1985-03-22
2	Greg Chappell (AUS)	754	1982-01-17
3	Andrew Flintoff (ENG)	737	2004-09-18
4	Viv Richards (WI)	729	1985-04-17
5	Lance Klusener (SA)	722	1999-06-05
6	Chris Gayle (WI)	713	2003-11-30
7	Jacques Kallis (SA)	711	2001-05-09
8	Steve Waugh (AUS)	708	1988-01-19
9	Shaun Pollock (SA)	703	2008-02-03
10	Imran Khan (PAK)	693	1982-06-20

Table 5.5: The Best-ever Ratings for ODI all-rounders according to the GM formula.

The Best-Ever T20I All-Rounders

Show Table 5.6

Rank	Test Player	Best Rating	Date
1	Shane Watson (AUS)	746	2012-09-30
2	Mohammad Hafeez (PAK)	663	2013-12-11
3	Shahid Afridi (PAK)	642	2009-11-13
4	Shakib Al Hasan (BAN)	639	2015-04-24
5	Glenn Maxwell (AUS)	630	2019-10-27
6	Yuvraj Singh (IND)	602	2013-10-10
7	Sanath Jayasuriya (SL)	601	2010-04-30
8	Mohammad Nabi (AFG)	595	2019-09-15
9	David Hussey (AUS)	591	2012-02-03
10	Marlon Samuels (WI)	566	2014-03-03

Table 5.6: The Best-ever Ratings for T20I all-rounders according to the GM formula.

---

At the beginning of Chapter 2, we mentioned that before we started this study we had an assumption that the ratings were normally distributed, which we found was far from accurate. We also mentioned at the end of Chapter 3 that the ratings do not seem to fit any particular distribution.

We now ask the question: What if the ratings really were normally distributed? What would the ratings look like and would it solve some of the shortcomings that we have identified in Chapters 1 - 4?

Let’s take a look.

If we are to rescale the rating distribution to look Normal, we will need the full range of ratings from 0 to 1000. We will therefore look, once again, at Test players in the 1930s, and Test bowlers in the forty year period of 1952-1992.

For these periods, we will apply a Yeo-Johnson (YJ) transformation to the average rating distribution, which rescales the overall distribution to a Standard Normal Distribution (mean 0 and standard deviation 1), while still maintaining its local variances (peaks and troughs in the distribution). We will then scale this standard normal distribution to mean 500 and standard deviation 200, so that it fits a 0 - 1000 scale once again.

Let’s take a look at the results.

Figure 6.1 below shows distributions of batting, bowling and allrounder(GM) ratings that we have seen before in figure 5.3, along with their rescaled (normal distribution) versions.

About this Figure

Each of batting, bowling and allrounder(GM) graphs are accompanied by the result of applying a YJ transformation and scaling the result to mean: 500 and std: 200

Note that the interval size for all graphs is 50, so the intervals are 1-50, 51-100, … , 951-1000.

Show Figure 6.1

• Test Batsmen: 1930s

  
  
• Test Batsmen: 1930s (Rescaled)

  
  
• Test Bowlers: 1930s

  
  
• Test Bowlers: 1930s (Rescaled)

  
  
• Test All-Rounders (GM): 1930s

  
  
• Test All-Rounders (GM): 1930s (Rescaled)

  
  

Figure 6.1: Distribution of regular and rescaled versions of average Test cricket ratings in the 1930s (years 1930 to 1939) for batsmen, bowlers and all-rounders (GM formula).

The rescaled distributions are not perfectly (or even nearly) normal in shape. They maintain their local variances but just look flatter.

• The large concentration of players at lower rankings (0-200) has now been spread out to roughly the 0-500 range. For example, the 1-50 interval for bowlers with height 23 in the original distribution is now spread out between 150 and 300.
• The median is now located right in the middle at ~500.

  In other words, half the players have ratings below 500 and the other half above 500.

  500 is now the rating of the “average, middle-of-the-pack” player, exactly what it intuitively suggests.

• The higher percentiles, too, are at similar ratings in all three graphs: ~650 for p75 and ~780 for p90.
• The skewness has also been reduced to near-zero in all rescaled graph.
• We note that there are hardly any players with ratings below 150 or above 900 in the rescaled batting and bowling graphs.

  This is a property of the normal distribution: Ratings become rarer as we move away from the middle value.

  However, we note that Kurtosis is about -1 in each rescaled graph, indicating that outliers are less frequent than they would be in a normal distribution.

In summary, the rescaled ratings have a flatter distribution with median in the middle at 500. While numerically normally distributed, the distribution retains its local variances with fewer outliers.

Let us take another look at test bowling in the forty year period 1952-1992, but instead of the average distributions by decade we will look at yearly average distributions for each year in the time period, and compare them to their rescaled normal versions.

Take a look at figure 6.2 below.

About this Figure

These animated graphs show yearly average rating distributions for Test bowlers in the time period 1952-1992. Both the original distribution and its rescaled normal version is shown. The rating intervals are 50 wide each.

Show Figure 6.2

• Test Bowlers: 1952-1992

  
  
• Test Bowlers: 1952-1992 (Rescaled)

  
  

Figure 6.2: Animated distribution of regular and rescaled versions of yearly average rating distributions for Test bowling in each format during specified time periods.

We notice the following.

• The yearly average distributions in the graphs change by a lot each year, both in the original and rescaled normal graphs.
  • In the original graph, the players move all over the place, concentrated at lower ratings in some years and spread out across the rating scale in others.
  • However, in the rescaled normal graph they are always centrally located around rating 500 and only the average counts of the intervals changes between years.
• Skewness is anywhere between 0.28 and 1.01 in the original graphs, but is always between 0 and 0.2 in the rescaled graphs.
• The percentiles also move all over the place in the original graph, but are remarkably consistent in the rescaled normal version.

  This makes it possible to say, for example, that a player with rating above 780 is likely to be in the top 10% of players.

• There is an imbalance in outliers between lower and higher ratings in the rescaled graphs, similar to figure 6.1 above.
  • There are hardly any players below a rating of 200 in the rescaled normal graph, and none below 150 at all.

    This is similar to what we saw in figure 6.1 above: A property of the normal distribution but with fewer outliers (negative kurtosis)

  • On the other side of the scale, we see that in the rescaled normal graph some players are always in the 800-900 rating range and sometimes there are players above 900 as well.

    This is because the original distribution was more concentrated at lower ratings and more spread out at higher ratings.

    This works in our favor, because we do want players at high ratings to continue to be spread out beyond 900+ so that we can identify and rank the best players.

Overall, we find that the new rescaled distributions maintain their consistency across years. Unlike the original distributions, skewness has been reduced to close to zero and the percentiles also appear at consistent ratings even on an year-by-year basis.

Let us now look at how the percentiles are distributed, similar to figure 2.4. Here, we will plot the percentiles on both the original and rescaled normal versions of the yearly average rating distributions for comparison.

Take a look at figure 6.3 below.

Note that we are still looking at Test bowlers’ ratings between 1952 and 1992.

About this Figure

This graph is similar to figure 2.4, except that we include three versions of the graph.

• The first graph shows the distribution of percentiles on the original yearly average rating distributions during 1952-1992.
• The second shows the distibution of percentiles on the their rescaled normal versions.
• The intervals for these graphs are 50 wide each, similar to previous graphs.
• The third graph shows percentiles on the same rescaled normal distribution as the second graph, but shows a different set of percentiles that better showcase properties of the normal distribution.
  • The intervals in the third graph have been made smaller to better show the tighter spread of percentiles. They are now only 20 wide each.

    Intervals are 1-20, 21-40, 41-60, ... 981-1000.

Show Figure 6.3

• Test Bowlers: 1952-1992

  
  
• Test Bowlers: 1952-1992 (Rescaled)

  
  
• Test Bowlers: 1952-1992 (Rescaled) (More Percentiles)

  
  

Figure 6.3: Distribution of regular and rescaled versions of average yearly ratings at 50th, 75th and 90th percentiles for Test Bowlers during 1952-1992. Overall average rating at each percentile and one standard deviation interval are also shown.

We note that the percentiles have significantly tighter confidence intervals on the rescaled normal distribution (the second graph).

This means that we can now accurately predict what percentage of players are above certain ratings, not just at p50 like we did in Section 2 earlier but at every percentile.

Looking at the third graph, we notice the following:

• Every percentile plotted has a tight confidence interval between +/-10 and +/-16.
• The median (p50) is at 490 +/ 12, or ~500
• The middle two quartiles (p25 and p75) are at 306 +/12 and 668 +/ 16, or ~310 and ~670 respectively.

  We note that these aren’t spaced equally around the median.

• The one-sigma intervals (p16 and p84) are at 254 +/ 10 and 735 +/- 11, or ~260 and ~740 respectively.

  We note that unlike the middle quartiles these are spaced equally around the mean, thereby conforming to the normal distribution.

  We can also say that a rating above 750 might be in the top ~15% of players, and a rating below 250 might be in the bottom ~15% of players.

• p97 (two-sigma positive interval) is at 828 +/- 15, or ~830.

  We note that this isn’t spaced equally vs the one-sigma positive interval, indicating that only the mean and one-sigma ratings conform to the normal distribution.

• Finally, while we had scaled the standard normal distribution to (500, 200), the resulting yearly rescaled distributions seem to have a slightly higher standard deviation at ~240 on average.

  We don't know why this happens, but it doesn't bother us as long as the distribution is normal-like and we have rescaled it from a standard normal distribution anyway.

In summary, we have shown that the rescaled distribution of ratings, while normally distributed at the mean and one-sigma ratings, still maintains its variance at other ratings. At the same time, it can produce tight bounds on all percentiles, allowing us to estimate with confidence what top or bottom percentage of players a rating might fall into.

We now look at how rescaled ratings map to the top percentage of players, similar to the interval graphs we saw in figures 2.5 and 3.2.

Figure 6.4 below shows three graphs, one each for the regular and rescaled normal distributions of Test bowling ratings during 1952-1992, and a third that zooms into the 500+ rating range of the rescaled normal distribution.

About this Figure

• The first graph is the same interval graph as figure 2.5.
• The second graph has all the same parameters but with the underlying distribution rescaled to a normal distribution like in figure 6.2 above.
• The third graph zooms into the top-left corner (500-1000 rating range and 0% ~ 50% range of players) of the second graph, with rating thresholds at steps of 20 each similar to the interval graphs that we saw in figure 3.2.
• The statistics represented by various intervals in all three graphs are the same as in earlier sections, and are also shown in the legend on the upper right.

Show Figure 6.4

• Test Bowlers: 1952-1992

  
  
• Test Bowlers: 1952-1992 (Rescaled)

  
  
• Test Bowlers: 1952-1992 (Rescaled)(Zoomed)

  
  

Figure 6.4: Regular and rescaled versions of average yearly no. of players above rating thresholds for Test Bowlers between 1952 and 1992. An additional graph zooms into the top-left quarter of the second graph. Only players with rescaled ratings above 500 are included in the third graph.

The following statistics on yearly average percentages are shown: Average of yearly averages (blue cross), 50% and 80% middle intervals of sorted yearly averages (green and grey bars respectively) and full range of yearly averages (black lines with red dots).

We note the following in the first two graphs:

• The intervals at each rating threshold are much tighter in the rescaled distribution. Even the black lines span only 11 percentage points at most (vs 20+ in the original graph).
• The averages lie along a slight curve in the original graph, but on the rescaled graph they lie on a mostly straight line in the middle which curves along the edges.

  Interestingly, they actually curve in the opposite direction of what a cumulative distribution function for a normal distribution would in the bottom right, but it only really impacts the lower end of ratings so it doesn’t concern us much.

• All players in the rescaled graph have ratings above 150, and 98% on average have a rating above 200.

  This is similar to what we saw in the distribution in figure 6.1 above.

• On average, 49% of players have ratings above 500, with even the 80% interval confined between 47% and 51%.

  This allows us to claim that a player with rating 500 is almost guaranteed to be in the top 50% of players.

We note the following in the third graph (zoomed into 500-1000 on the second graph)

• At the top end, we see that there was at least one player with a rating above 900 in some year, which establishes 900 as a “legendary achievement”.
• On average, a player with a 860+ rating is in the top 1% of all players, with a rating of 880 guaranteeing it.
• On average, a player with a 820+ rating is in the top 5% of all players, and with 840+ in the top 5% in 9 out of 10 years.
• At 780+, a player is in the top 10% of players on average, and in the 8-12% range in 4 out of 5 years. At 800+, a player is in the top 10% in almost every year.
• At 720+, a player is in the top 19% of players on average, in the top 20% in 3 out of 4 years, and in the 15-22% range in 4 out of 5 years.
• At 700+, a player is guaranteed to be in the top 25%. The average rating threshold for the top 25% is somewhere between 660 and 680, matching the 668 rating for p75 we saw in figure 6.3 above.

In summary, we see that the rescaled distribution gives us a deterministic interpretation of players’ ratings, while allowing exceptional players to stand out.

In addition, since each years’ rating distribution is being individually rescaled, it transforms the rating scale from an absolute one to a relative one on a yearly basis. This solves three issues we saw in earlier sections:

• Players across generations are now rated in comparison to their contemporaries at all times.

  Even if the nature of the game changes over time, a 500+ rating will always put players in the top 50%, an 800+ rating will always put players in the top 10%, and similarly for other ratings.

• If there is a change in the rating algorithm (like there could have been for ODI bowlers around 2008-09), ratings are still rescaled to the full 0-1000 range and follow a normal distribution.

  This allows us to compare an ODI bowler from 1998 to one from 2018, something we cannot do now.

• Since ratings for batsmen, bowlers and all-rounders in all three formats now have the same distribution, players can be cross-compared in an objective way.

  It also now helps us identify, for example, a player-of-the-year and the best players of all time across formats.

In chapter 1, we investigated the ICC’s claims about the meanings of ratings of 500, 750 and 900. We found all of them to be inconsistent and mostly incorrect.

In this chapter we have shown that it is possible to construct a rating scale that actually guarantees such claims, and makes it much easier to compare players across formats and time.

However, we have barely scratched the surface here. We would like to point the following out:

• We have only looked at a small window of 1952-1992 and only for test bowlers.
• We only have visibility into the list of ratings on each date after the “sophisticated moving average” has been calculated. We do not have any visibility into the inning-by-inning r-scores awarded to each player.

If we can improve the ratings this much with so little data and with an off-the-shelf transformation algorithm, imagine how much better the ICC can do with all the detailed inning-by-inning data that they have.

In fact, here is a list of steps the ICC should consider taking to leverage their granular data to build an even better rating system:

1. Continue assigning r-scores to players in each inning on a scale of 0 to 1000 in the same way as now.
2. Take all the inning-by-inning r-scores from, say, the last 5 years (or last 500 matches) to create a dataset of all r-scores awarded to all players in all matches, per format and for batting and bowling each (six total).
3. Assign weights to each data point based on how recent the match was, either by time, or by match number.
4. Transform these six datasets into standard normal distributions, and create mappings of what value on the standard normal distribution each inning-by-inning r-score between 0 and 1000 translates to, interpolating where necessary.

   Let's call the mapped scores on the standard normal distributions Sigma-scores.

5. For every new inning played, calculate the r-score like you currently do and then map it to its corresponding sigma-score on the standard normal distribution.
6. Use a “sophisticated moving average” of these sigma-scores to assign each player an overall sigma-rating on the standard normal distribution.
7. To get a player's final rating, rescale this sigma-rating to the 0-1000 range with mean at 500 and an appropriate standard deviation that keeps the ratings within the 0 - 1000 range.
8. Every one year, repeat steps 2-4 to create a new baseline distribution and mapping between r-scores and sigma-scores.

   The lull in international cricket during the IPL every year might be the best time to do this.

We believe that this process can produce significantly better results than what we have demonstrated, and will improve the reliability of the rating system to serve as more than just a casual guide to a player’s form.

• In Chapter 1, we showed that the number of players above certain rating thresholds can vary widely across formats and time, and that it is incorrect to make interpretations about a player’s standing based on their rating. We also identified an unexplained drop in ODI bowlers’ ratings since 2008-09 that continues to present-day.
• In Chapter 2, we showed that the ratings follow a generally decreasing trend, with about 50% of all players above and below a rating of 250.
• In Chapter 3, we showed that there are large inconsistencies in rating distributions for batsmen and bowlers at the top end of the rating scale, and that these inconsistencies exist in all three formats. Limited-overs bowlers, in particular, have much lower ratings than others.
• In Chapter 4, we showed that single-day gains in ratings are generally larger than drops. We also showed that players lose rating points for all missed matches, even when they are rested. We then found out how the percentage of rating points lost per missed match is different by format, and how it has changed over the years. Finally, we identified a mysterious balance between single-day gains and drops in ratings.
• In Chapter 5, we identified shortcomings in the way all-rounders’ ratings are calculated, and proposed a new formula that addresses all of these shortcomings while maintaining the key properties of the original.
• In Chapter 6, we showed how rescaling the ratings into a normal distribution can solve almost all problems we have identified in earlier chapters, and also listed the exact process the ICC can follow to significantly improve the reliability and longevity of player ratings.

Based on these findings, we are making the following recommendations to the ICC.

These recommendations are based on our findings in this report. They are listed in decreasing order of importance in our opinion.

This is our single biggest concern with the ratings system as it exists today.

It isn’t the 1990s anymore. Today, players don’t just miss matches because they are out-of-form and dropped, but also because their workload and availability is actively managed by their boards. Consider the following examples from 2024:

• Many players, especially from associate nations, often prioritise participation in overseas leagues ahead of national duties. For example, Dutch cricketers Colin Ackermann and Roelof van der Merwe both chose to play the T20 Blast league in England instead of the 2024 T20 World Cup, and lost points for missing international games for the Netherlands.
• In July 2024, India sent its international team for a T20I series in Zimbabwe. India never intended to send the best players from their 2024 T20 World Cup winning squad on that tour, but all those players lost rating points for missing games in the Zimbabwe series nonetheless.
• Jasprit Bumrah, inarguably the best bowler in the World today, is rested regularly to prevent injury. Even as the Player of the Series in the T20 World Cup 2024, Bumrah finished the tournament at a Rating of only 640 and at Rank 12 among T20I bowlers.

The practice of penalising players 0.5 - 2% of rating points for missing a game is clearly outdated, and it needs to go away. We suggest the following alternative approach:

• Stop deducting rating points for missed games completely. Let players maintain their rating from their previous appearance when they play their next international match.
• If a player hasn’t played at least 50% of their team’s games in a moving window of the past one year (or the last 10-20 games played by the team), simply remove them from the rankings list.
• Continue updating their ratings like usual for their future innings but without including them on the rankings list.
• If and when the player meets the criteria of 50% of their team’s games in the future, start including them in the rankings list again.
• Maintain a separate “Inactive players” list where ratings for these players can be viewed. If a player hasn’t played any games for their team in the last 1-2 years, remove them from all ratings lists.

Some adjustments may need to be made to the rating algorithm to balance rating point gains and drops again (as seen in Chapter 4).

We believe that this method solves the problems created due to the challenges of the modern game, while also allowing the removal of players from the list that have been dropped from the team or have retired without announcement.

Additionally, it also removes the need for penalising players early in their careers since they won't show on the ratings list until they play at least 50% of games for their team in the moving window.

We have noticed several times during our investigation that ratings for bowlers in limited-over formats is much lower than those for batsmen and Test bowlers. ODI bowlers have had a drop in ratings since 2008-09. T20I bowlers have always had lower ratings than batsmen.

• The top-ranked ODI bowler has had an average rating of only 725 ~ 750 since 2010, while the top ODI batsman has had an average rating of 860 ~ 880 during the same period.
• The top-ranked T20I bowler has had an average rating of 750 ~ 790 since 2010, while the top T20I batsman has had an average rating of 860 ~ 880 during the same period.

These are 100+ rating point differences between the top batsmen and bowlers. Meanwhile, both Test batsmen and bowlers have had an average top rating of ~900 during this period.

We believe that the ICC needs to make changes to the algorithm used for scoring limited-overs bowlers’ performances, to bring their ratings at par with batsmen.

The current formula for all-rounder ratings assigns very low ratings to all-rounders that do not match batting or bowling ratings. While the best batsmen and bowlers are rated around 700 ~ 900, the best all-rounders are only rated 300 ~ 400 on the same scale. These low ratings on a scale of 0-1000 are not at all intuitive and they do not highlight outstanding players like they should.

In Chapter 5 we have shown that using a geometric mean (GM) of batting and bowling ratings can produce much more intuitive ratings for all-rounders, while still maintaining the key properties of the original formula.

We understand that the current formula is simple enough to be calculated on a piece of paper, but if the rating algorithms for batting and bowling are so complex that players have to check the website for their ratings anyway, having a very simple formula for combining batting and bowling ratings serves little purpose.

We strongly recommend that the ICC adopts the GM formula that we have proposed to bring all-rounders’ ratings at-par with those for batsmen and bowlers.

During our investigation we found the following likely changes in the ratings algorithm:

• In 2021-22 the ICC changed the percentage of rating points lost per missed match from 0.5% for ODIs and 2% for T20Is to 1% for each, bringing them at par with Test cricket.
• Since 2008-09, there has been a drop in ODI bowlers’ ratings that might have been due to a change in algorithm. We have also spotted some more gradual but substantial changes in the top Test batsmen’s ratings between 1994-2008, and in ODI batsmen’s ratings during 2002-2010 that might have been due to a changes in the algorithm.

When changes are made to the algorithm, it makes all past ratings incomparable to current ratings. For example, it makes no sense to us that Joel Garner, the top ODI bowler of all time (according to ratings), had a best-ever rating of 940 when today’s top ODI bowlers barely touch the 750+ mark.

We believe that if and when changes are made to the ratings algorithm, those changes should be applied retroactively to past ratings. We understand that the nature of the game changes over time. ODI bowlers in 1984, for example, weren’t as concerned about their economy rates as bowlers in 2024 are and this might be what's causing the difference in ratings. However, if the top-rated players from different time periods have a rating difference of 200+ points it becomes pointless to know about or interpret historical ratings in the context of today's players.

We mention this last because it would require the most amount of effort.

The current ratings do not seem to follow any predictable distribution and, as we have shown in our report, are inconsistent between batting and bowling, across formats and across time. For example, a rating of 800 could indicate a top-5 ranked ODI batsman, a legendary once-in-a-decade ODI bowler (since 2008), or a mythical ODI all-rounder that cannot really exist.. And these interpretations would be different if we were looking at the same ratings during the 1990s.

In Chapter 6 we have shown that rescaling the ratings into a normal-like distribution can change the ratings from an absolute to a relative scale.

We have also shown how this rescaled rating distribution can create significantly consistent results across formats and time, while also allowing ratings to be interpreted as the top or bottom X% of players reliably.

Finally, we have suggested a step-by-step algorithm for how the ICC can go about making these changes to the rating scale using the granular inning-by-inning rating data they have.

We believe that making this change will improve the reliability and longevity of the rating system and the ICC should strongly consider moving in this direction in the future.

During our investigation, we frequently found ourselves constrained by the lack of visibility outside of the top-100 players on each date, as well as by a lack of granular data on inning-by-inning ratings assigned to players. To add to that, the rating algorithm itself is completely opaque to us. This limited our ability to produce the kind of in-depth and detailed report on the full distribution of ratings across all years and for all formats that we initially intended to.

We understand that some of the changes that we have recommended are easy to implement while others are not, and may require a lot of investigation and experimentation on the ICC’s part. There may also be time, staffing and funding constraints that can make it difficult to initiate these changes.

We humbly request the ICC to make more ratings data publicly available for download or via an API, so that data journalists and hobbyists can do more detailed investigative work on ratings and make even better data-driven suggestions on improving them. We believe that this will lead to a more fair and trustworthy ratings system for players in the long term.

With that, we wrap up our report on ICC’s player rankings.

We hope that our report will spark a constructive dialogue about the current state of the ratings system and result in long-term improvements to the ratings algorithm and to public data visibility.

If you enjoyed reading this, we recommend also checking out our companion report on the Greatest Cricket Players of all time based on ratings data.

All the code used to gather, analyse and visualise ratings data can be found right here on GitHub.

If you have questions, feedback or ideas, head over to Discussions.

This report was created by a small team of passionate cricket fans with experience in Software Engineering and Data Science.

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