## Cricket Mythbusting: Not-Outs and Averages

The usual batting average is defined as the total number of runs scored by a batsman (both out and not-out) divided by the number of outs (total number of completed innings). Under this definition, it is possible that players who often end the innings not out may get inflated batting averages.

Really!? I’d have hoped researchers would know better. This is a popular myth about batting averages that is not just wrong but actually the opposite of the truth. Getting a lot of not outs deflates your average. I will attempt to explain why without getting too technical.

It is well known that batters “get their eye in”. When first at the crease, batting is more difficult, and once the batter gets used to the conditions (the pitch, the bowler, their technique, etc) they get better. This is not just folklore, the effect can be detected in data. If a batter is currently fresh at the crease (i.e. they are on a low score), they are less good than if they have been batting for a while.

Consider two batters. Batter 1 scores $\{40, 12, 72, 6, 38, 0\}$. Batter 2 scores $\{5^*, 13^*, 11^*, 0, 4, 12^*, 3, 17^*, 10, 3^*, 12^*, 1^*, 5, 0^*, 61, 11\}$. Both batters scored 168 runs and were dismissed 6 times, for an average of 28. But who is better? Well, it looks like Batter 1 had three fairly good innings (40, 72, and 38) where they were able to get their eye in. But Batter 2 only had one innings where they scored above 20. Batter 2 scored their runs in more difficult circumstances, while not “warmed up”. Yet they still performed as well as Batter 1. Therefore, Batter 2 is probably better.

Another way to think of this is to imagine that you are on 5 not out (say). If you were able to complete your innings, how many extra runs would you score? Since you now have your eye in a little bit, the expected amount of extra runs is greater than your actual batting average. Not outs deflate your average because they rob you of the opportunity to score an additional amount of runs that is greater than your average, because you already have your eye in.

I am a senior lecturer in the Department of Statistics at The University of Auckland. Any opinions expressed here are mine and are not endorsed by my employer.
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### 5 Responses to Cricket Mythbusting: Not-Outs and Averages

1. Matt says:

I think the perception probably occurs because lower order batsmen and bowlers do have (I think) inflated averages, so that’s assumed to be the cause. I think the real cause is facing tired bowling and older balls and having generally more attacking fields. Take the recent Ashses series and look at Australia’s batting averages over the series http://stats.espncricinfo.com/the-ashes-2013/engine/records/averages/batting_bowling_by_team.html?id=7362;team=2;type=series. Pattinson had the 5th best average and Starc the 8th, better than Warner, Haddin and Khawaja. Both Pattinson and Starc appear to benefit from 2 NOs, but I think more significantly, were batting at the end of innings against tired bowlers and old balls and batting to fields that were set to try and get them out quickly rather than saving boundaries. If Pattinson and Starc batted in the middle order they would not have such high averages, and its not because they wouldn’t have those NOs.

As far as the game goes though, a run is a run, which is why I’ve always thought that bowling alrounders are hugely valuable (and a better bet than batting allrounders, like Watson). England looked a much better side with Bresnan at 8 than they did once he was injured.

2. “I think the perception probably occurs because lower order batsmen and bowlers do have (I think) inflated averages, so that’s assumed to be the cause. I think the real cause is facing tired bowling and older balls and having generally more attacking fields.”

That seems very plausible.

• Daz Voz says:

Similarly, we may assumed openers have _deflated_ averages.
I wonder whether there is any statistically significant difference between the average at number 1 and average at number 2.

3. Nico says:

I certainly agree with what you are getting at but I don’t like your scenario – in the six completed innings both batsman had wasn’t batsman one able to better fight through his challenging period to get his eye in and then score more? The fact batter two had another nine not outs just represent him getting more opportunity than player one and with that opportunity he bumped his average up by 12 runs.

4. Nico says:

In the short format cricket I think batsman should not be rewarded for a not out when that not out comes because the team is out of deliveries to face. Personally I would move to something like what Andrew suggested but also measure the number of not outs and volume of runs in those not outs in run chases. Those are the really valuable not outs but they get the same status as a player who finishes not out in a 100 run loss!