Do Hundreds Matter?

Ambivalence: having two opposing feelings at the same time, or being uncertain about how you feel.

Cambridge Dictionary (Cambridge University Press)

Yesterday (2nd August 2019) Rory Burns scored his first Test century.  It was a struggle. It was error strewn. But he got there. In the evening the twitter consensus was that the important thing was that he did it, not how he did it.

Fig 1 – Twitter Screenshot.

What didn’t I like about Butcher’s point*? I’ve always thought that you can learn more from a lucky long innings than a duck. Someone gives a chance first ball, gets out – so what? Another player hacks their way to thirty, regularly playing and missing or chopping the ball past the stumps – well there you have some useful data – the bowler is dominating the batsman with a decent sample size.

But a hundred? I’m conflicted. You can’t use a hundred as evidence that a player is no good. Can you?

You are surprisingly unlikely to get more than a hundred if you average under 25

Fig 2 – Theoretical Probability of scoring a century in a single innings vs average.
Fig 3 – Theoretical Probability of scoring at least one century over fifteen innings

Over his first seven Tests, Burns averaged 22. A batsman with that ability only has a 1% chance of getting a hundred in any innings. Does that mean that Burns was lucky? That depends what you believe: either he is a twenty-something averaging batsman who had some fortune, or a thirty-something averaging player who is performing as expected. County data says he’s the latter.

One can get lots of runs at a decent average without a hundred.

In the appendix I’ve listed the top run scorers in Test Cricket who didn’t get a century. Was Chetan Chauhan any less of a batsman because he scored 2,000 runs averaging 32 but never made more than 97? No, the data says there’s a 5% probability that it was just chance that meant he didn’t get a hundred, with no psychological flaws or lack of stamina at play.

That’s all lovely – but DO HUNDREDS MATTER?

Joe Root’s hundreds don’t matter. He has played a lot of innings, so his average is the one metric you need. 49.03.

Rory Burns’ hundred doesn’t matter to me (other than to say there’s no reason to over-rule my analysis– expect him to average 39 over the long term in Test Cricket). Burns scoring a century matters only if Test scores are all you use to appraise batsmen. You would rate him significantly more highly after scoring a hundred than before (though, knowing it was an ugly hundred, you would probably rank his expected average somewhere from 25-35).

One example where I think hundreds matter is when there’s very little to go on. Dan Douthwaite scored a hundred against Sussex when playing for Cardiff University. As he wasn’t on my radar at that point, that 100* meant that I could safely assume he would average more than 25 in Division 2.

I’m thus ambivalent about rating players based on scoring hundreds: most of the time I’ll take averages over hundreds. When there’s noting else to go on, a big score can tell you that someone’s not bad.

Appendix:

Fig 4 – Test records of batsmen with no hundreds. Final column shows the probability of a player with that average not scoring a hundred in the number of innings they played.

*I should add that Control Percentage isn’t a metric I value as highly as False Shot Percentage. To my embarrassment, I’ll admit I misread Butcher’s original tweet as criticising False Shot Percentages. Still, serendipity – if I could read, I’d never have worked out whether I care about hundreds.

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