Thursday, 13 January 2011

WPA injustice? Thoughts on Matt Prior and Mitchell Johnson...

We started writing this as a reply to George who posted some thoughts on the series totals page, but rambled so much we thought we'd post it instead...

Here was George's comment:

A very interesting means of analysis. However, I slightly take issue with the dismissal of Prior's runs at Melbourne and Sydney. 

Whilst I accept that England's innings position was already strong in both cases, as first innings runs, Prior did in fact ensure that England's bowlers had both time to recover from the first innings and also ample time to bowl Australia out again by virtue of the quantum lead that he created...

In short, from the bottom half of the batting order he effectively supplied a second innings total (with support). Had he been batting up the order in the second innings following a first innings declartaion (hypothetical) would the WPA not have given him far greater recognition?


Firstly, cheers to George for commenting on our blog! This is a very good question. Let's take the Sydney test- Prior comes in to bat when England have a hundred run lead with two recognised batsmen at the crease...

Given this game situation, we pretend we have two 'generic' teams playing each other, and have two distributions of runs we could expect to be scored (one by team A, which is in England's position and one by team B, in Australia's)... A's distribution is composed of two 'probability distribution functions': runs from the partnerships remaining in the first innings, and runs to be scored if A was to bat again. B's is just for runs B may score in the second innings. We therefore have a bunch of scenarios where team A wins (it does have a 100 run lead with an expectation of, say 100 more in the first innings) and only a few where team B wins. Some of these scenarios exceed our projected timeframe, and therefore are assigned as 'draw' scenarios. The relative number of A win, B win, and draw scenarios tells us the 'win' and 'draw probabilities'.

Our 'generic' Prior equivalent would be expected to do, well, generically, (coming off the top of my head, let's say he's expected to score 40-45 odd) so when Prior arrives, say between him, generic Bell and the generic short, jimmyless tail had a 'expected runs distribution', with an 'average expected runs' of say 100. Expected lead going into second innings is 200 runs, Team B's WPA is tiny. Some of the future game scenarios are draws, of course, so Team A isn't a sure bet. Say England declare- team B's WP goes up (it's only 100 behind now) to say 20 percent (a guess), and the draw probability goes down (without those expected 100 runs we've basically saved an expected session's worth of play). The change in DP mitigates team A's reduction in win probability, but I think in this particular situation, the model would say  that if A wants to win and no rain is forecast, you should bat on, and not forego that expected 100 runs by declaring.

As it happens, Prior did outbat team A's generic wicketkeeper batsman, and was credited with 5 or so percent of WPA. If England had declared, this is what I'd guess would happen- England's WP would have dropped with the declaration, and if Australia had performed exactly to team B's expectations, he could have earned slightly more WPA if he'd scored a century as an opener in the second innings (out of the 180 runs they'd have needed), but the prior negative impact of the 1st inns declaration would offset any team benefit. If Australia actually outperformed team B's target by a bit, say they scored 370, he could have yet more personal impact with a big knock; if Australia underperformed team B's expectation by a lot, say were all out for around 200, setting England's target at 100, He would have virtually no impact batting well in a hypothetical second innings scenario...

Anyhow, this is all getting away from the other good point George made. The model does have its drawbacks- the impact of intangibles like bowler fatigue (as well as deviations from 'generic' captaincy, fielding ability and ability to build pressure at both ends to name a few) is completely ignored and we hold our hands up to that! The fact that a bowler is the only one credited for a wicket is clearly a gross oversimplification but one that we laid down to avoid subjectivity. Clearly a team's reaction to the prospect of inclement weather (whilst the weather is recorded its historical 'prospects' are not) presents another issue (see the 'alternative analysis' section for the Adelaide test)...

But alas, poor old Prior has been treated badly by our stats, but his dismissals in the first innings both at Brisbane and in Perth (where his generic counterpart would be expected to score a much needed 40-45 or so runs on average, and, in some scenarios, match changing centuries) did far more bad to his WPA than his 50 and ton at Melbourne and Sydney did good... Who knows how much WPA he earned over a generic wicketkeeper for his glovework, but I'm sure it'd be in the positive! In general, clearly some of Anderson's and Tremlett's WPA should go the the great fielding and captaincy (eg. at Adelaide, which is clearly markedly better at the moment than the generic) and some should go to Swann's ability to keep it tight at the other end, but who knows how much? In our attempt to remain objective, we steer clear of making these kinds of judgements.

On another tack, Mitchell Johnson's ability to clock up WPA in this series despite his apparent awfulness has been noted by many, and has got some people quite upset. Indeed, none more so that I (I'm still humming that 'He bowls to the left, he bowls to the right...' song a week on with a massive smile on my face)... But, as fate would have it, he scored two half centuries at key points (well outperforming his 'generic' bowler alter ego in the batting department) and at Perth took six big, match swinging wickets (4 recognised batsmen) for 38 in the 1st, as well as two recognised batsmen in the 2nd innings. He basically won the equivalent of a whole test match (relative to generic bowler) in Perth with his bowling and batting, got a quite important 50 at Sydney (outbatting generic in this innings), and did little else for close to 3 tests (where he, like the Australian attack as a unit, leaked runs and a good deal of WPA). But net, according to WPA, his big game way outweighed his poor ones. I think he owes Matt Prior a beer (obviously assuming that they care about WPA)!

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