Cricket is a confusing game, full of traditions and customs that have aged to the point where they are not even questioned. For example, why do players raise their bat at 50 and 100, not 30 or 62? Why is three wickets in a row a special celebration, not two, or three in an over? Why do players need a 40 minute break for lunch but then only a 20 minute break for tea? The mere suggestion at altering many of these time-honoured traditions would be considered sacrilege by many cricket tragics. I probably consider myself in that ‘traditionalist’ view of cricket in that it is enhanced by its quirks and its inconsistencies more than it is degraded by them. The fact that a game has remained so steadfast for almost 150 years adds significance to each match.

There is, however, one long-standing quirk that I think could be improved upon. It is a statistic that is about as fundamental as any in sport, in fact one player’s statistic was considered to be a part of Australian citizenship testing and is burned into the brain of any cricket lover worldwide. I, of course, am talking about the batting average (and Bradman’s outlandish 99.94).

This simple measurement of a player’s batting ability is the one number that a player has associated to their name. Sure, other stats such as number of total runs, 100s, 50s and strike rate are also measured, but the average is the ‘gold-standard’ way that is currently used to compare players.

#### To unravel the batting average statistic, we first need to understand what it is measuring.

Alert: Stats deep-dive impending, look away now if numbers scare you

A player’s batting average is calculated by simply dividing the number of runs they have made by the number of times they have been dismissed. To first understand what the batting average is measuring, we should look at all the scores that players make and notice the distribution. If a batting average is attempting to tell us what a batsman is expected to score in any innings, then is it truly an accurate estimation? The histogram below shows that clearly if you guess a player will score their average every time they bat then you will overestimate for the majority of their innings, however, some innings will be far greater than their average — these could be considered outliers and are what drags a player’s average away from the median and gives the distribution this positive skewing.

Whilst an average is one of (and probably the most used) measurements of central tendency, it is not the only, and arguably in the case of a skewed distribution such as batting scores, it is not the most accurate. Other measurements of the centre of a distribution include the mode and the median.

The mode is the most common score and is not helpful in cricket — almost all players’ mode would be a duck for a few reasons: players all start at 0 and hence it is the only score that every player is on in every innings they play and secondly, players are more likely to be dismissed on zero than on any other score (attributed to getting their eye in — see my earlier piece for further details). The median is a player’s ‘middle’ score — i.e. 50% of their innings are higher and 50% are lower than their median score. It can be of some use, but it also lacks information on the range of scores the batsman makes.

The lack of information provided by any one of these measures can be noticed by the extreme example of comparing hypothetical players Mr Consistent and Mr AllOrNothing. Let’s say both players have 5 innings, Mr Consistent makes 50, 40, 50, 60 and 50, whereas Mr AllOrNothing makes 140, 0, 100, 0 and 10. Both players have made 250 runs from 5 innings and both average 50, but it is pretty obvious that they are vastly different players. Comparing the medians doesn’t help with Mr Consistent’s median of 50 and Mr AllOrNothing having a median of just 10, suggesting Mr Consistent is a far better player, the mode also says that Mr Consistent’s mode is 50 and Mr AllOrNothing’s is 0. Clearly, these statistics are insufficient to describe the individual skills of each player and whilst in the real world there won’t be examples this extreme, it illustrates that two players with similar averages are not necessarily similar players.

It is common knowledge that there are many different ways to be a successful test batsman. For example, Joe Root is considered one of the best current batsmen in the world but is flawed in his ability to convert 50s into 100s. If you simply look at his batting average next to Kohli’s or Williamson’s you can see that they are quite similarly rated. However, looking at the conversion rate tells us some more information that clearly Williamson, Smith and Kohli are more likely to make 100s and bigger scores if they get their eye in.

However, the missing other piece of information that can be inferred, but is often forgotten, is that if Root has made less hundreds but has still maintained a great average, he must get more starts than other players. Currently there is no clear way to measure this ability, but surely the ability to avoid failure more often than not can be vital — especially for a top order player whose job (other than scoring runs) is to see off the new ball and make batting conditions easier for players coming in later on in the innings.

This brings me to my recent creation, which aims to solve the problem of measuring players with a single number and instead breaks down different aspects of an innings and rates each skillset a player has. Taking a leaf out of other sports rating systems, I have chosen to give it the backronym LARA, which retroactively applies to mean ‘Likely Approximation of Run Attributes’.

The LARA rating system can be viewed here: https://ocfitz1.shinyapps.io/TestBatsmen/

The ‘Guide’ tab in the app explains how to use the LARA ratings. The app aims to show more information about the qualities of a batsman rather than simply their batting average. It works best when used in landscape orientation and using on a computer allows easier interaction but it is also mobile friendly.

LARA identifies four distinct aspects of a batsman’s innings:

Starting Rating

Eye-In Rating

Cash-In Rating

Approximate Runs to Eye-In

The ratings are calculated using the standard normal distribution (i.e. the average for each rating is 0 and the standard deviation is 1). This means that players who are above average in a certain area will have a positive rating and players that are below average will receive a negative rating. The ratings can be interpreted as how many standard deviations the player is away from the ‘average’ player for each attribute. Currently the ratings include all players to have made at least 3000 test runs and a few current players.

A basic illustrative example of comparing two great Australian captains Steve Waugh and Ricky Ponting can be used to show why LARA is useful.

The joint record holders for most tests for Australia have very similar batting averages and were both amongst the best batsmen in the world at the peak of their powers. The basic statistics that are traditionally used show similar records, with Ponting probably having better numbers with a slightly better average and more hundreds, fifties and total runs. Now, using LARA, we will dive deeper into how they made their runs for a better comparison.

#### Starting Rating

Starting rating measures how good a player is at starting their innings, i.e. a positive rating means they are less likely than the average player to be dismissed early on in their innings.

The table shows an example of the output of the ratings and the final starting rating is derived from the other stats given in the table (other than approx runs to eye-in). Ponting is better than Waugh in all of the stats in the table apart from being equal on Q1 score and is rated a better than average starter, whereas Waugh has a higher than average chance of being dismissed early in his innings and his negative rating reflects that.

Waugh has a high duck percentage, he made 22 ducks in his career. Also of note is that he didn’t get his eye in until he made 19.75 runs on average. Hence, not only was he a poor starter, but it took him a long time to improve to his ‘eye-in’ ability, which compounds and extends his early vulnerability.

The Q1 score is the player’s first quartile score, i.e. 25% of that player’s innings are below this score. It should be noted that quartile scores have been calculated taking into account not out scores. So the first quartile score is actually calculated as the point where a player has a 25% chance of making this score or less at the start of their innings.

#### Eye-In Rating

Eye-in rating measures how effective a player is when their eye is in — i.e. if they make the most of their starts regularly or not. Waugh edges ahead in all the statistics used to calculate a batsman’s eye-in rating.

The ‘Average Average’ statistic used here differs from the conventional average: typically, the average for a player is just shown for when they are on zero. In contrast, this average calculates a player’s average at every point. For example, if they are on 10, then their average takes into account every innings where they made it to 10 and treats this as the new zero-point. This is a good way to see how much a player improves (or not) after a potentially shaky start. The ‘average average’ is then the average of all these averages over the batsman’s first 60 runs (60 was chosen because larger runs would have small sample sizes and skew the results).

Similarly to the Q1 score, the Q3 score is the point at which a player would be expected to have a 25% chance of making more than this at the start of their innings.

The average dismissal rates are given over different ranges to account for noise in the data that may arise due to small sample sizes.

#### Cash-In Rating

Cash-in Rating measures a player’s ability to go on and make a big score once they are set. Steve Waugh is shown to be a standard deviation better than the average player in this category.

Waugh’s ability to ‘cash-in’ is most noticeably seen by his averages at Q2 and Q3, which are both well above 60 and so it shows that once he gets to a point where he is set, he improves his batting average dramatically. Ponting also improves, but not to the same heights as Waugh.

‘% of Massive Scores’ gives the percentage of a player’s innings that would be considered ‘outliers’. The threshold used will change as more data is entered, but the idea is that an innings is considered massive if it is in the top 3–4% of all innings played — this is around the 150 mark for this data set at the moment.

#### Approximate Runs to Eye-In

The approximate runs to eye-in statistic is shown in each table and in the chart because it is important to add context.

For example, a player with a poor starting ability may not suffer too much because they get their eye in quickly, or a player may have a great eye-in rating but take a long time to reach that stage and so are vulnerable for a longer time early in their innings. So, it is important to think about the ratings in this context.

The approximate runs to eye-in is calculated by looking at the amount of runs it takes for a player to get to their ‘average average’ and their average dismissal rate across 5, 10 and 20 runs. The runs given is an approximation because obviously a player’s eye-in point changes from innings to innings and is not usually a black and white point in a player’s innings, however it is calculated to approximate the average point where a player’s likelihood of getting out stops decreasing at such a high rate, or plateaus entirely.

Using the example of Waugh and Ponting, it can be seen that LARA allows a more in-depth comparison of each player’s strengths and weaknesses than is given by traditional cricket statistics. Clearly Waugh was a nervous starter who took a long time to get comfortable, whereas Ponting was more reliable early in his innings but wasn’t as good at cashing in on his starts as Waugh was.

Whilst it can be obvious that some players play in these certain styles, LARA now allows players to be quantified and compared by using their actual test scores. I hope that you find these comparisons as interesting as I have and I will continue to update the database as regularly as I can.