As part of a continuing series on why Australia should drop Matthew Hayden, it is worth considering the claim that his struggles represent a loss of "form", instead of something intrinsic to his game. And how is it that one could tell, statistically, rather than merely watching his increasingly frantic high-risk shot-making, and inevitable dismissal.

A moving average

The first, and most obvious way is by looking at their average. Because Hayden has played so long, and because players must be judged on recent performances, the most obvious way is to choose some time period: the past year, the past two years, or some arbitrary date that makes them look especially bad.

The less obvious, but more objective way is to take a weighted average, where recent innings carry more weight than those played in the past. The weighting should probably be done by time (R_i*0.95^M where R_i = runs scored in innings i and M = months since innings) but for technical reasons it is easiest for me to do it by innings (R_i*0.95^I where I = subsequent innings played).

Ignoring not outs. Hayden's weighted average is now down to 35.47, having been as high as 53.12 at the end of last summer. A rapid decline, but only 3 1/2 runs worse than Hussey whose decline has been even more marked.

Assessing luck

But there is another aspect to form, and that is the perception of luck. All batsmen have bad periods, because all batsmen are vulnerable to getting out for less than 20. Greg Chappell famously remarked, in the midst of a serious run of low scores, that he didn't know if he was out of form, since he hadn't batted long enough to know.

If a batsman averages 30, there may be two reasons. Firstly, it may be because they are not that good: that the distribution of their innings is that of a typical player of that average. And secondly that they are out of form: that a rash of unexpectedly low scores is not sufficiently off-set by hundreds and fifties that they typically make, and which would keep their average much higher.

Because scores are distributed unevenly, we can calculate consistency of performance by taking a weighted log average:
(2^(∑(all innings i)[log₂(R_i*0.95^I)])/W_n)
where W_n = weighted number of innings played)

If a player scored the same in each innings, their log average equals their normal average. Normally, this average is around half the normal average, thus, by dividing them, we get a consistency ratio. A normal ratio seems to be around 0.5. Players who score big hundreds amidst lower scores will have lower ratios (0.3-0.4), players scoring consistently, higher ratios (0.6-0.7).

But consistency, over short time periods, is also a measure of form. A player whose recent average is mostly the result of one big innings is obviously capable of large innings, but lacking in form. A batsman whose recent average reflects consistency of performance is likely to reproduce that form.

Combining the measures

Players' form and ability can therefore be judged against the two measures. Hussey, who last year had a recent average of 71.9, and a form ratio of 72, was clearly in rare form, that would, inevitably, end. Now, remarkably, he has regressed to the opposite end of the spectrum, averaging 39.15, with a form ratio of 39. Looking at how the form ratio tracks Hussey's recent average. Once his form regresses to the 0.5 mark, he is likely to have a career average of around 48-50. Respectable, and worth persisting with. But what of the others?

The graph is a little hard to make out, but (ignoring Haddin, who is still finding his feet), Australia's batsmen fall into three groups.

Hussey and Ponting, whose form a year ago was stellar, but who have recently struggled, both dipping into the low 40s, before Ponting's recent recovery.

Katich and Clarke, whose averages have been high this year - Katich particularly, though he is still being penalised from being dropped. But, whose form is so consistent, they are due to fail. More particularly, while their recent averages are respectable, they aren't high for players in such good form, and need to make better use of their run scoring opportunities. Tracking back to "typical" form, their averages would decline to just 40.

Symonds and Hayden, whose averages were both in the high 40s, low 50s last year, but who have recently declined to the mid 30s. More pertinently however, their form has not dipped with their average. This indicates that their recent middling scores are what you'd expect for players of their current abilities.

While Hayden's decline is of recent vintage (a year ago, you'd expect him to average in the low-40s), it is materially different to Hussey's in that it isn't luck deserting him, but his ability to make decent scores. His starts are marked by failures every bit as bad as those where he doesn't start at all. And for an ageing player, that matters.

Cricket - Analysis 1st January, 2009 23:17:35   [#] 

Comments

Distinguishing Form
Interesting stuff Russ, though I'm not sure if I'd accept the stuff about form without a deeper look at the data. So, a couple of questions. Do you have any evidence that a player who has been consistent recently is more likely to "reproduce that form" in the near future? And do you hold the stronger position that, given two players who have the same true talent, the one with more recent consistency will tend to average more in his next innings?
David Barry  2nd January, 2009 11:16:30  

Distinguishing Form
David, short answer: no, and I don't know. I would guess, a little.

I don't have a database of scores to do a proper analysis to test those propositions. If you could offer some advice on that score I'd be very appreciative.

My main purpose here, was to try and find some measure of form/consistency. That can then be used to test assumptions about selection issues: do "in form" players make more runs in the future/next innings.

I am making a proposal/assumption that given two players with similar recent averages but different form ratios, the player who has been consistent (in form/lucky), will, in general, regress to a lower average. Or to put it another way, big scores take skill (concentration/technique), but low scores are largely a matter of luck.

That may be wrong too - the consistency ratio may itself not reflect anything inherent in the player, but that goes against a lot of what we believe to be true about batsmanship.
Russ  2nd January, 2009 18:25:45  

Distinguishing Form
Fair enough. My suspicion is that there is very little predictive value in recent form, but the only studies that I know of have been done with raw averages. Charles Davis showed that using the career average is more accurate at predicting the next innings than the average of the last 10 innings. Plotting the average of the last few innings against the next for individual batsmen gives a variety of patterns, but generally the regression line is fairly shallow, one way or the other.

But I don't know of any studies using measures like yours. I think I will look into that tonight. These days I'm spending more time with chess than cricket stats, but the issue of form is a pretty important topic that could do with a bit more study, and I want to know the answer myself.
David Barry  3rd January, 2009 19:38:23  

Distinguishing Form
Blog updated.
David Barry  4th January, 2009 11:39:22