See https://www.nesi.org.nz/case-studies/modelling-careers-cricket-players for the full article.

]]>The three “statistical” metrics were:

**The concentration required to score hundreds**

Seems fair enough, Langer wants to see his players not just make a score, but make a big score. This is not a particularly “statistical” metric though, all we have to do is look at the percentage of scores of 100+ for each player’s first-class career. To account for not out scores, these percentages are calculated by taking the number of 100+ first-class career scores, and dividing by the number of completed/out innings in a player’s career.

Percentage of **100+** scores:

G. Maxwell = 7.7%

A. Finch = 6.3%

T. Head = 5.8%

M. Labuschagne = 5.6%

Maxwell doesn’t appear to fare too badly on this metric.

**Performance under pressure**

Again, this seems like a good performance indicator for batsman, but it is tough to measure statistically.

**The importance of 30+ scores**

Supposedly identified as a “key metric” to solve the issue of collapses, this is a metric which can be looked at from a statistical standpoint, however it has a number of shortcomings.

First of all, as pointed out by a number of people, the 30+ score metric was invented for T20 cricket and doesn’t really have any relevance to longer form first-class or Test cricket. The rationale behind this statistical rationale is fine — Justin Langer and his team of selectors want to reduce the probability of collapsing in Asian conditions by selecting batsman who are more likely to spend time at the crease and curb the momentum gained by a bowling side who have taken a couple of quick wickets. However, they haven’t explained the reasoning behind how they came up with the arbitrary number of runs scored (30 in this case) and how it is “all important”.

Again, the reasoning is more or less there, if a player is consistently scoring 30+ runs, chances are they’re spending time at the crease and absorbing a lot of pressure exerted by the bowling side.

**But why 30 runs? Would the selections have been any different if we changed this from 30 runs to some other value?**

Let’s see what happens when we change the 30+ runs threshold to some other values. The data used here are the first-class career scores for Maxwell, Finch, Head and Labuschagne. Again, to account for not out scores, these percentages are calculated by taking the number of scores greater than or equal to the threshold score and dividing by the number of completed/out innings in a player’s career.

Percentage of **20+** scores:

G. Maxwell = 60.4%

A. Finch = 55.8%

T. Head = 57.9%

M. Labuschagne = 52.4%

Percentage of **25+** scores:

G. Maxwell = 54.9%

A. Finch = 52.5%

T. Head = 50.8%

M. Labuschagne = 50.8%

Percentage of **30+** scores:

G. Maxwell = 49.5%

A. Finch = 46.7%

T. Head = 46.8%

M. Labuschagne = 41.3%

Percentage of **35+** scores:

G. Maxwell = 47.3%

A. Finch = 41.2%

T. Head = 40.5%

M. Labuschagne = 38.1%

We see that we can manipulate our argument fairly easily on which players to pick based on this metric if we change the criteria. If we use **20+** scores, the top two players are Maxwell and Head. However, increasing this to **25+** scores, the top two becomes Maxwell and Finch. Then, considering **30+** scores as our cutoff, Head moves back into second place. Finally, using **35+** scores, Maxwell and Finch again become the top choices. The only constants here are that Maxwell is consistently the top ranked batsman based on this metric and Labuschagne is the bottom ranked batsman.

**Okay, how about if Glenn Maxwell was overlooked because when he scores 30 he may have done so in an aggressive manner and therefore still may not have his “eye in”?**

If this is the case, and Cricket Australia truly wanted to take a “statistical” approach, their statistical metric should be one which considers each individuals’ playing style. A possible method of doing so would be to look at how long it takes individual players to set themselves at the crease and look at the proportion of innings each player has managed to do so. This way, selectors can pick the batsmen who manage to “get their eye in” a higher proportion of the time and therefore will be more likely to dig-in at the crease and put the pressure back onto the bowling side.

In a previous paper***,** I have developed models which predict a batsman’s ability on any given score during an innings. The three main factors calculated by the model are **(1)** a player’s initial batting ability when new to the crease, **(2)** a player’s “eye in” batting ability when set and **(3)** the speed of transition between these two states. Batting ability is measured in terms of an “effective average”, which is essentially a players ability on a given score, in terms of a batting average. For example, Justin Langer himself has an estimated Test effective average of 18.3 when on a score 0, suggesting that when on a score of 0, he batted like a player with an average of 18.3. When Langer is set, and has his eye in, his effective average increases to 49.0.

As an example, lets consider the Test careers of Justin Langer and Gary Kirsten, two opening batsmen with career batting averages of 45.27. If we had to make a choice between these two batsmen, **who would we pick based on Cricket Australia’s statistical rationale?**

Looking at each players’ effective averages, we see that Justin Langer appeared to be the better batsman at the very start of a Test innings, as suggested by his higher initial effective average. However, once scoring roughly 12-13 runs, Kirsten appears to be the superior player. Therefore, the model suggests that Langer is less likely to get out early on in his innings, however once set, Kirsten is less like to be dismissed and is the player more likely to score the most runs. Using these effective average curves we are able to calculate the probability of a player reaching a given score, while accounting for their play style. In this case, the probability of Langer making a score of **30+** is 49.0%, while for Kirsten it is 47.1%, due to him being slightly more vulnerable at the beginning of his innings — at least Langer performs well based on Cricket Australia’s own metric!

*Figure 1. Test career effective averages for Justin Langer and Gary Kirsten*

Now, lets consider the first-class career of Glenn Maxwell against the trio of Finch, Head and Labuschagne.

*Figure 2. First-class career effective averages for Maxwell, Finch, Head and Labuschange.*

Interestingly, we see that Labuschagne has the highest initial batting ability (marginally) when on a score of 0. However, after just scoring a few runs, the other three players appear to be batting at a higher ability. Again, we can calculate the probability of each player reaching a given score, based on these effective average curves.

Probability of reaching a **30+** score based on the model:

G. Maxwell = 44.7%

A. Finch = 40.9%

T. Head = 41.6%

M. Labuschagne = 38.2%

**Once again, there is little justification for not selecting Maxwell.**

I suspect the threshold of 30 runs was chosen as 20 or 25 runs didn’t quite sound right and 30 is a nice round number. Then, to justify their rationales, it seems to me that the selectors have slapped the word “statistical” in front to make it sound more convincing. Now, I’ll be the first person to admit that teams should not be selected on a purely statistical basis — there are a wide range of factors that statistics cannot measure — but statistics only strengthen Maxwell’s case for selection.

Perhaps as a statistician I’m taking issue with the fact they’ve called this a statistical rationale, instead of simply a rationale. However, its hard not to think that there is far more to this story than meets the eye, and while the Australian selectors can hide behind many different veils when it comes to overlooking Glenn Maxwell, statistics is not one of them.

*****These models provide the basis for publication for the article titled “Bayesian survival analysis of batsmen in Test cricket”, published in the Journal of Quantitative Analysis in Sports — check it out or contact me for more information regarding the mathematics behind the model discussed in this post.

See https://www.stat.auckland.ac.nz/en/about/news-and-events-5/news/news-2017/2017/06/using-statistics-to-test-cricketing-superstitions.html for the full article.

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