Impact of “Not Outs” on Averages

A campaign will consist of many skirmishes and a handful of battles. I’m a combatant in a (meaningless) long standing disagreement with an old friend about the value of Chris Woakes. Today’s battleground is whether Woakes’ Test batting average is artificially inflated because he get a lot of “not outs” batting at eight. My opponent believes Woakes is “Bang Average” and therefore clutches any straw which supports that case.

I’d read this in Cricinfo back in 2013 and drew the conclusion that if not outs do make a difference, it’s so small I could ignore it for modelling/gambling purposes. As an aside, generally I like to look at things myself before concluding – for some reason the Cricinfo piece sufficed. Possibly because the author was trying and failing to make the case for adjusting averages to reflect not outs.

As counter-arguments go, I couldn’t rely on picking holes in someone else’s argument, I needed some data. Time for Statsguru!

Batting at seven vs eight

Players who have occupied both batting positions will give us the best data on the impact of those positions on average. I took players who had at least 15 completed innings in each role since 1990 and compared performance.

Fig 1 – Averages batting at seven or eight.
Fig 2 – Impact of additional not outs on average for players batting at eight rather than seven. Note the wide spread of results – there’s no clear trend. Excel’s trendline says the extra not outs from batting at eight do not boost average.

There’s no clear difference between batting at seven rather than eight.

Six versus seven is where it gets more interesting…

Batting at six vs seven

Fig 3 – Averages batting at six or seven. There seems to be a general benefit to batting at seven, but some outliers in Dhoni, Watling, Whittall.
Fig 4 – Impact of additional not outs on average for players batting at seven rather than six. Now we have something. The players with more not outs tend to get a higher average. Excel’s trendline agrees – cutting from bottom left to top right.

Discussion

Let’s take stock after that whirlwind of charts. Generally, players that batted at seven got a boost to their batting average, relative to batting at six. This benefit correlates with increased proportion of not outs when batting lower down.

There is no extra benefit from batting at eight rather than seven. But – that is not to say that there’s no overall benefit to batting at eight rather than six: it’s just that batting at eight has the same benefit as batting at seven rather than six.

I’m no fan of the proposals put forward so far for punishing players for being not out. Yet being not out is correlated with higher averages.

A suggested mechanism: Outrunning Bears

Remember the old joke: two guys, out in the forest, chance upon a bear. The bear starts wandering towards them, and one chap starts tying his shoelaces. Second guy asks “what are you doing – that won’t help you outrun the bear?” First guy answers “I don’t need to outrun the bear, I just need to outrun you”.

In nightmarish batting conditions, the top order have next to no chance of protecting their average. Only one batsman outruns the bear to be not out. There’s an advantage of being the last good batsman in the lineup – you just have to survive while the tail gets blown away, and it’s like the barrage never happened – your average is unscathed.

Fig 5 – Batting position of the not out batsman when a Test team has been bowled out for less than 100 since 1990 (top six Test teams only)

There we have it – number seven is having his average flattered because when the going gets tough, the number seven gets red ink. Well, 13% of the time anyway.

Extend that to all tricky batting situations, and there is likely to be a real impact to averages: the top six rarely get a not out in tricky conditions, that benefit belongs to numbers seven to eleven.

Conclusion

Let’s go back to the original question – is Woakes’ batting average benefiting from coming in at eight? I think so.

Can I quantify it? Not yet. All I’ve shown is that the lower batsman are more likely to survive in bad conditions, yet how often do they miss out on the best batting situations? If a team ends 400/4 declared, numbers seven and eight don’t see any of that action.

Does it matter? If comparing two players who bat in the same position then there’s no impact on their data. If comparing a seven and a six’s record, then yes – a rule of thumb would be:

Average adjustment = -70 * (additional not out % from batting at seven not six)

Which works out as about -1.5 runs in moving from seven to six.

Further reading

The Institute & Faculty of Actuaries know a thing or two about risk. Their take is here. I didn’t find it persuasive.

Appendix: Detailed Data

Fig 6 – Full list, batsmen with more than 15 completed innings batting at seven and eight in Tests since 1990.
Fig 7 – Full list, batsmen with more than 15 completed innings batting at six and seven in Tests since 1990.

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