The Importance of ‘Getting Your Eye-In’
One of the most well-known cricket clichés is that a batsman is most vulnerable when they first come to the crease and the second is that batting becomes easier the more runs you have made.
To test these theories, I had a look at some of the game’s greatest batsmen as well as some current-day players to compare how well they batted at different stages in their innings.
Measuring the Distribution of Scores
Firstly, let’s have a look at common cricket statistics and find a better way to measure a player’s true ability. The fact that a batting average is virtually the only statistic talked about when comparing batsmen is odd because dividing the total amount of runs a batsmen has made in their career by the number of times they have been dismissed doesn’t really tell us much about what is likely to happen each time they go out to bat.
For example, someone with an average of 50 isn’t expected to make 50 every time they bat — in fact, they are expected to make less than 50 most of the time, but then once they get their eye in they are expected to go well past 50. A batsman’s average doesn’t really tell us much by itself. We could use a player’s ‘middle’ score (the median) but as can be seen by the following table, these numbers are equally meaningless.
While it is interesting that Steve Waugh’s median is quite a bit lower than that of the other players of his ilk, it doesn’t really tell us much about the vast majority of his actual batting performances.
Basically, it just tells us that half his scores are above 25.5 and half are below it, but it doesn’t tell us by how much or how far away from this median they get. We need to look at a player’s full distribution to get a better idea of this.
The graph below shows the distribution of scores of all batsmen past and present.
As can be seen, the vast majority of scores are below 15 and the mean is greater than the median because of the potential for big scores which increases the average. This proves the point that a player’s average is far greater than where most of their scores lie, and explains why there is such a large difference between their ‘average’ and their median scores.
The Exponential Distribution
Fellow maths nerds may notice a similar pattern of this distribution — known as an exponential distribution.
Exponential distributions have some very interesting properties, which if cricket scores follow could make us think about the game quite differently. It’s main property is that the rate of change is constant, and if it applies in this situation then the chances of being dismissed would remain the same no matter what score the batsman is on. If this is the case, then the theory of getting your eye in would be proven wrong.
The following chart shows just how closely the distribution of test scores follows this distribution, in this case the y-axis has been changed from a frequency to a probability of making at least a certain score (so obviously 100% of innings are at least 0, whereas less than 1% are at least 300).
Although the actual distribution (black line) very closely mirrors the exponential distribution (yellow line), we can see an obvious divergence: the actual distribution is much steeper for the first 15–20 runs, confirming what we already know about cricket — that people are most vulnerable early in their innings.
Some degree of flattening out also occurs, although it appears that the actual distribution pretty much follows the exponential distribution after the first 20 runs or so of an innings.
This suggests that once a batsman has reached this mark (aka — is ‘in’), they are just as likely to be dismissed at any later time in their innings, meaning a batsman is just as likely to go out when they are 30 as they are when they are on 100 (if they get there).
Comparing GOATs
Now that we have shown that it is true that players are generally more vulnerable early in their innings, let’s have a look at some of the all-time greats and how their ability changed as they became settled at the crease.
The players chosen were some greats of living memory, as well as the true GOAT, and the iconic Viv Richards. Firstly, let’s just look at the importance of getting off the mark.
There is quite a spread in duck percentage and surprisingly it was Bradman who scored the most ducks as a percentage of total innings of all these players (perhaps he was human after all.)
Bradman however, also improved his average the most by scoring a run, averaging almost 10 runs more when on one compared to when on zero.
(Note: This average on one doesn’t include the run he made already made. For example, if Bradman got to one, on average he would make another 109.89 runs — otherwise the averages would obviously keep increasing as the batsmen’s scores increased.)
All players improve their average after getting off the mark, which tells us that even the greatest players of all time started relatively poorly, and shows that their ability to bat when off the mark was already better than when they started their innings.
While unquestionably the greatest player of all time, Bradman is not ideal to analyse because he is so far away from anyone else to have ever played the game. This is shown by my first attempt at plotting these players together.
Clearly Bradman is in a class of his own, which is remarkable in itself but makes it difficult to compare the other players and look for trends. However, for Bradman, it appears that his average is constantly around 110–120 once he is off the mark.
The other problem with this graph is that the players all have different starting points and so its hard to compare how quickly it takes to get their eye in and how much better they are once settled.
To solve this problem, we can change the y-axis from overall average to percentage improvement from their average on zero (their batting average.) This normalises all the scores to a starting point of zero and will make it easier to see how much each player improves over time .
It is also a better judge of how big the improvement is, as an improvement of 10 runs is much more substantial for a player with a low average. For example, a player who averages 10 on zero but 20 on 1 increases their performance 100% compared to a player who goes from 50 to 60 who improves just 20%.
This may appear confusing and crowded, but if you follow each line individually, you can start to get a picture as to how each batsman operated.
When looking at this graph remember:
- A steeper curve means greater improvement after being on a certain score.
Waugh dramatically improves over his first two runs, whereas Tendulkar climbs more slowly. This means both that Waugh was comparatively more vulnerable early in his innings but improved considerably after only a few runs. Compared to Tendulkar who took longer to show the same improvement - The point where a line becomes relatively ‘flat’ (it may continue to vary up and down by 5%, but this is due to natural variation and small sample sizes) is when a batsman has their ‘eye in’.
The fact that the line is basically flat means that batting does not get easier or harder once they reach this point. The lines all become more variable if the graph is extended beyond 40. This is probably due to the smaller sample sizes (less innings) rather than actual variation but there are exceptions, which we will get to later. - The level at which the line flattens tells us how good a batsman is when set compared to their baseline.
A high level means they are much harder to get out once settled than when new to the crease, whereas a low level means they are susceptible to dismissal throughout there innings. - The black line is the baseline average of all the batsmen I analysed (not just these six legends) as a comparison to the ‘average’ batsmen.
If the distribution was truly exponential, then this black line would be horizontally flat for the whole graph. It levels off at around the 17–18% mark, so on average, players improve by 17–18% once their eye is in and it takes about 20 runs to get to this point.
Genius Takes Many Forms…
Let’s start by looking at the most unique approach from our list of GOATs, Steve Waugh.
His initial jump is virtually the same as Bradman’s, showing the he too was a very nervous starter, but the differences here are that it takes him a lot longer for his average to level out, and that his peak batting ability was substantially higher than when he started his innings — he averaged around 35–40% (15-20 runs) more when set compared to the start of his innings. This is vastly more than any others on the list and shows two things: he was very vulnerable early in his innings, but once set he was willing to bat a long time without giving up his wicket easily.
Brian Lara is another batsman of this ilk, as can be seen with the sharp, high rise early in his innings. Lara is a bit different to Waugh in that he appears to have two plateaus, his first is probably reached after around 8–10 runs, and this is already a marked improvement from his nervous start. However, his average rises another 10 runs once he gets to 50, showing that once he made ‘a start’ he really set himself for a massive score, averaging roughly another 70 runs.
It also shows that Lara was not truly comfortable to bat to the best of his ability until he got to 50. This confirms the common theory surrounding Lara that he could be scratchy and vulnerable early but once in he could bat all day, as attested by his triple and quadruple centuries in Test cricket.
His average rises again as it approaches 100, which may again show that he wasn’t content with just 100, but wanted a massive score, however caution should be used when interpreting the averages at those scores due to the smaller sample sizes.
In sharp contrast to aforementioned batsmen’s approach, the great Viv Richards reaches a peak batting ability much earlier and with much less difference to his baseline than Waugh or Lara.
Richards improved his average by 10% after just 3 runs and that is about as high as the improvement gets until much later in his innings. This means that Richards was just as good when on 3 as when he was on any score up to 70. This may be because of his aggressive approach, which meant he continued to give chances as his innings progressed but as a result was a more fluent starter than the other batsmen analysed.
Similarly to Lara, he has a second peak after getting to 70, which shows that when he wanted to set himself for a big score he could, but up to that point, he didn’t necessarily set himself for a hundred.
Sachin Tendulkar and Ricky Ponting on the other hand, take much longer to get set, needing at least 12 runs to plateau. They do improve early in their innings, but it is more gradual than the other batsmen, meaning both that they rely less on getting off the mark but also that they are vulnerable for longer. Both players don’t improve as much from their baseline as Lara or Waugh which shows that they were more confident starters and more consistent over the course of their innings.
None of these techniques are necessarily better or worse than others as all were great players in their own right. However, knowing when each batsman was most vulnerable tells us how important it was to bowl well at the start of their innings.
For Lara or Waugh, the team must not let them get off the mark, (or at least to 10) easily, because once there they were both significantly better bats then when on zero. For Tendulkar and Ponting, a more offensive field may be set because you know you can afford to leak a few early runs before they are settled.
Current Ashes Players
As for the upcoming Ashes series, the inexperience of both sides limits the number of players that can be analysed in a meaningful way, but here are the score distributions of batsmen who have played enough matches:
These players have far fewer innings and so we will only look at their averages up to when they are on 50 (beyond this point the averages will become meaningless as they are heavily influenced by individual innings.)
Although having vastly different batting styles, David Warner’s and Alistair Cook’s averages are very similar throughout their innings. Note the small difference (five runs) between their ‘eye-in’ average and baseline average.
This possibly shows that being a successful opener means you can’t afford to rely too heavily on getting off the mark, with the ability to see off the new ball being part of the job description. If there was a dramatic improvement at the start of their innings then it would suggest they were nervous starters and hence not suited to facing the new ball.
Jonny Bairstow’s distribution is interesting as it appears that he is as good, or possibly even better, when on zero then compared to any other time in his innings.
Clearly, an easy way for him to improve his overall average is to make the most of getting his eye in, because at the moment, it makes no difference if he gets a start or not. Australia must know that he is equally likely to go out if he is on zero, 20, 40 or 60 and so know he is less likely to punish them for not dismissing him early in his innings. This may also be in part due to his aggressive nature — as his distribution follows a similar pattern to that of Viv Richards and hence gives a lot of chances throughout his innings.
Moeen Ali shows why an overall average of 34.67 undersells his batting ability. He averages more than Bairstow after making 3 runs, and almost as much as Cook and Warner when past 15. His problem is the opposite of Bairstow in that he starts poorly, but once in he is damaging and able to bat for a relatively big score. The Australians must focus on dismissing him early in his innings when he is clearly most vulnerable, otherwise he becomes as good as a top-order batsman.
Steve Smith and Joe Root follow a similar patterns, both getting set just before the 10 run mark and showing a good ability to cash-in once there. Smith is another batsman who has the ‘double-leap.’ He improves initially and again once he gets to 20 where his average sits around 70.
Root gets his eye-in slightly earlier than Smith, but doesn’t reach the same heights once set. He is consistently an almost 10-run better batsmen once he has made at least 7 runs. If either team can dismiss the captain before getting to 10 regularly then they will be a good chance to win the Ashes, if not, then these two batsmen could dominate the series.
A New Stat For Cricket?
These statistics confirm one of cricket’s most common clichés that batsmen are at their most vulnerable when at the start of their innings.
What is somewhat surprising is the speed at which some players improve their batting ability — Steve Waugh, for example, was a 12% better batsman after scoring just 2 runs.
As such, there is a very small window where some players are less likely to succeed, and it shows that a bowler cannot afford to let a quality batsman get off the mark or hit boundaries early.
It is also interesting to see the stark differences in Bairstow and Ali’s distribution, something that the simple fact that one averages 39 and the other 34 doesn’t tell you.
The study of score distribution also confirms another cricket cliche that “one wicket brings two,” as all batsmen (except Bairstow) improve their average after making a few runs.
