# Bettering your average- how standard deviation can be used to enhance the way we look at cricket performance.

What are the shortcomings with averages as a performance measure?

If, like me, you are a keen cricket player, you might find yourself having a cheeky check of your average on the Play Cricket website on a Saturday night after getting a decent score or, perhaps more likely, surveying the damage to it, after spooning a catch up for not very many earlier on in the day. You may even find yourself slyly looking at the averages of next week’s opposition and who their dangerman might be, during your lunch break at work. After doing just this, I loaded up my ‘Flaws of Averages’ powerpoint ready to teach my Year 11 GCSE Maths class and thought “hang on a sec, why are we so obsessed with averages in cricket then?!”

Over the next hour, I went into the shortcomings of each of the different types of average. The mean, what we all refer to as an average in everyday and cricketing terms, I told my class, has the problem that it doesn’t take account of the distribution of values. For example, if we took Player A and Player B who both had a dreamy average of 50 after the first two games of the season we would initially think that perhaps they are both very similar players. On further inspection though, we would see that Player A had scored 50 in both innings and Player B 0 and 100, giving us a completely different picture that just looking at the average wouldn’t have shown us.

This flaw in using averages as a measure is highlighted when looking at the averages of England’s two openers across the test matches this winter. Cook averaged 33.25 compared to Stoneman just behind on 30.23. For somebody purely looking at these averages to judge performance, there is little to distinguish between the two. However, those who have followed the tests would know that both players scored very differently, with Cook having a succession of low scores and one extremely high scoring innings in Melbourne (I was lucky enough to witness this and have put my video of the celebrations when he reached 200 below) and Stoneman regularly getting into double-figures and failing to kick-on further.

Hopefully, this illustrates the problem with just looking at averages when judging player performance. Fortunately, there is a measure called ‘standard deviation’, which can be easily calculated and I believe could provide us with some valuable insight for cricket that purely looking at averages would not give.

What is standard deviation?

Standard deviation is used to tell us how far away the values are on average from the mean, giving a concrete reference about the distribution of values and making up for the main shortcoming of the mean. In cricketing terms, this would be the typical difference between a batter’s average and what they have scored in each innings. For the normal punter, this is what we might call consistency, the lower a player’s standard deviation then the more consistent they are (good or bad). Going back to our earlier example, the consistent Player A would have a standard deviation of 0, this is because there is no difference between each of Player A’s two scores and their average. Conversely, the inconsistent Player B would have a standard deviation of 50, because we expect that they will either score 50 below their average or 50 above. If we look at Cook and Stoneman’s standard deviations from their scores across the winter they had values of 72 and 20 respectively, showing that although their averages were similar, Stoneman scored more consistently than Cook. Visually you can see this on the graphs below, the standard deviation for each batter is the average distance of the blue points (each score) away from the orange points (average across the winter), it is clear that Stoneman’s scores are closer to his average than Cook’s, illustrating his lower standard deviation and more consistent performance.

*Note for ease of calculation and I added Cook’s not out score to his next complete innings.

What has been written in the past about standard deviation and cricket?

I’m not claiming to be the first person to have thought about calculating standard deviation for cricket. Some very interesting blog posts by Anantha Narayanan and Ric Finlay extol the virtues of Jack Hobbs and Sachin Tendulkar’s performances through using standard deviation to create a consistency index for test players who have scored over 5000 runs. I find the insight into past player performance extremely interesting and these calculations involving standard deviation certainly offers a valuable perspective on the history books. What I think is missed, however, is how standard deviation may be used in the future to improve a team’s results.

How can we use standard deviation?

I would suggest that there could be a few ways to use standard deviation values that might be useful for any coach or captain when selecting a team or deciding upon the batting order.

Firstly, let us go back to Players A and B, who we are now told also both open the batting. Who would you prefer as an opener, reliable Player A or the occasionally brilliant Player B? If I was batting at number 3, I know that I’d prefer the steadiness of Player A, I could put my feet up for the first 10 overs knowing that it’s unlikely I’ll be in and by the time that I am the ball should have stopped swinging. This could seem like an obvious choice, we all know that a big part of opening the batting is to see off the new ball and if you have an opener that can regularly do this then it will probably boost the total of the whole team by giving the rest of the order a chance to play more freely.

It is also true that batting in different positions can be more suitable to varying techniques and styles of batting; a captain is unlikely to promote their high-scoring number 5 batter, that plays spin well, but is horribly exposed to swing, to the top of the order. Such a situation might seem like a no-brainer to somebody who knows a bit about cricket and snippets of knowledge like this are why we love the intricacies of the game and certainly shouldn’t be overlooked.

I would argue that, on top of these intricate details and the opinions of the coaches and captains, standard deviation should be thrown into the mix, when deciding who to promote to the top of the order. It offers some concrete evidence for a player’s consistency and could just give a team the edge over another by reducing their chance of losing an early wicket.

Secondly, let’s pretend that you are the captain of the 1^{st} XI of a club. Next Saturday, you know that your regular number 5 can’t play, because they must go to yet another wedding. The choice of who to call up from the 2^{nd} XI has a couple of obvious candidates who are averaging well above the rest of their team, yes, you guessed it, its Player A and Player B again. But who do you call up? You know that they are both averaging 50 this season and so are ‘really’ as good as each other. Well, of course you now know that maybe looking at the standard deviation of each player could offer further insight, but how would you use this information?

I would like to claim that this depends on the opposition. Let’s again imagine that your team is mid-table and top of the table is your next fixture on the list. You know that they are a good team and think that you can only beat them on a good day. If this was the case, I think that it would be worth ‘rolling the dice’ and plumping for the occasionally brilliant Player B. Suppose you call up Player B, who has a higher chance of scoring a magnificent hundred and guiding your team to victory compared to Player A, who scores another solid 50, which isn’t quite enough to overcome the top of the league.

Of course, Player B has a considerable chance of also getting a duck, but you’re playing against top of the league so what have you got to lose? On the other hand, if you were playing against bottom of the league and know that Player A’s consistent 50 scoring prowess is more than likely to be enough to guarantee you the win then it probably would be the sensible choice over the erratic scoring of Player B.

Say you did instead pick Player B who half of the time smashed a big score and heaped the misery of the bottom of the league team sending them to a huge defeat and the other half of the time getting out cheaply and sending your side to an unlikely loss. If you’re the type of person that likes to win then maybe getting a steady, but not huge, win each time through picking Player A is the way to go.

What further ideas does this prompt?

The potential uses of standard deviation stretch well beyond the couple of applications that have been discussed above. It would be extremely interesting to calculate confidence intervals for projected innings scores when batting or runs conceded when bowling and this could have strong influencing factors for coaches and captains when looking at their team as a unit. I’ve discussed the importance of a consistent opener for the rest of the team when seeing off the new ball, but it would be interesting to confirm this common piece of cricketing knowledge that is taken for granted with some concrete evidence.

This could be pursued by analysing the affect that consistent vs. inconsistent openers have on overall team scores or even considering if any value is gained by seeing off the new ball at all. Using standard deviation to create a consistency index (as done in the blogs I mentioned earlier) could also add value if incorporated into to a new measure of performance, rather than just looking at averages and strike rates of batters and bowlers.

What could we take away from this?

The scope for use of standard deviation seems to be vast and now I think that it would be great for international, county and even the most avid of club team selectors to start to use this measure when choosing their teams. We are lucky to have such a wealth of statistics collected in cricket and it would be a shame not to utilise them.

When selecting Cook’s successor as an opening batsman, whenever in the future that may be, we should use standard deviation on top of the regular criteria to scour the county game for a consistent player that can get us off to the start we need regularly and let our big-hitting middle order have free reign.

County coaches looking for a reliable opener or someone to shore up the middle-order should delve into the Play Cricket database to analyse the top club players and with a quick standard deviation calculation they could ensure a low-risk acquisition on the cheap for their team. For the club selectors and captains, it could be an interesting discussion point to calculate their teams’ consistency through standard deviation.

By Rory Mathews