The impossible run chase

I should start this post with a warning to about 98% of the world’s population, just in case they happen past and think they might have a quick read. It will involve cricket, statistics and not much else. There’s every possibility that you should guard against splitting sides from an excess of hilarity. Don’t say I didn’t make you aware, that’s all.

Now I’m a decidedly amateur statistician. Please don’t tell my boss, because it’s actually what he pays me for. But I have a very limited – let’s say statistically insignificant – understanding of terms such as “standard deviation”. As far as I know, “poisson distribution” was instigated by Jesus of Nazareth when Galilee Burgers let him down at the last minute. My employment comes mainly from the ability to remember in what order Microsoft Excel processes odd words like “concatenate” and “sumif” to produce a pretty line graph or something.

But what I DO always tell the MD, before he starts firing people on the basis that one of my lines is angled downwards, is what he can and can’t read into the numbers I give him. A 75% drop in instructions from a particular client may be Armageddon, but it may simply mean that last year they sent us four and this year only one. Similarly, a 200% rise does not mean we should buy that new office building if it comes from a source which only accounted for 1% of our work last year. If he just looked at the lines, he wouldn’t necessarily know this – they have to be read in conjunction with the axes and the other graphs.

And this is where the cricket thing comes in. Statistics in cricket CAN be very useful. At the moment, Middlesex and England bowler Steven Finn takes, on average, one wicket for every 39 balls he bowls in Test matches. The same figure for his colleague Chris Tremlett is 66 balls, and for England’s top fast bowler James Anderson is 57 balls. This figure provides a useful comparison between Finn and Tremlett, who have fewer than 20 Test innings between them, and tells the pair of them what they need to aim for, as Anderson has around 100 under his belt.

Batting averages are also useful, although they can be misleading for bowlers who come in at number 11 and never get out, because of the way cricket statisticians calculate the average. For those who aren’t asleep, it’s “number of runs scored divided by number of times out”. So a hypothetical number 11 who has scored two runs in 30 consecutive innings, but only got out once, has an average of 60, which is much higher than any of England’s real batsmen, who all average less than 50 in Test matches.

And one of the more fascinating ones is batsmen who score 50 or more loads of times, but very rarely make it to 100. Commentators call this the “conversion rate”, and used well I suspect it could isolate certain personality traits surrounding complacency and hot-headedness, although obviously I’m not thinking of anybody in particular. Kevin.

But the one that really winds me up is the one about how many teams “can” score to win a match in the fourth innings. This is trotted out on every single occasion a “run chase” appears to be on the cards, when the team batting first has completed both its innings with a score which may just be reachable by its opponents.

As I write this, England are just concluding their opening session of “how not to chase nearly 400” in Perth. Losing your top four batsmen for 81 runs is an almost textbook example of how not to do it, in fact. But there is absolutely nothing to say that they couldn’t do it, simply on the statistical history.

The argument goes like this. England have NEVER scored more than 332 runs in the fourth innings to win a match. In this match, they are required to score 391, and therefore the likelihood of them doing it is tiny. History weighs against them. Only four times has any team ever scored 391 or more to win. It would be a simply monumental achievement.

Would it? Really? The anorak’s site to end ALL anorak’s sites, Cricinfo, has this page on highest fourth innings totals in Test matches.

The first thing to do is ignore the 654/5 that England scored in Durban in 1939. This is known throughout cricket as the “Timeless Test”, when some bright spark decided that rather than everybody shaking hands on a drawn series they should play the deciding match to a finish, resulting in a ten day match which still ended in a draw, as England had to catch the boat home. No Timeless Tests have been played since then, although ICC chief executive Haroon Lorgat has raised the possibility that they could be revived to decide a putative World Test Championship.

So leaving that aside, how likely is it that a team can score 391 in the fourth innings? The thing is, the stat quoted above is always “to win”. Even a brief look at the table shows that there have been 19 occasions since the war when a team has scored 391 or more in the fourth innings regardless of the result. England themselves posted 350 in defeat on the same ground the last time they were there. Restricting the number of runs that “can” be scored in the fourth innings on the basis of whether the team scoring them ended up winning or not doesn’t seem like statistical sense to me.

Then there’s the time available. All but two of those post-war scores have come in well under 1000 balls, with special mention going to New Zealand’s heroically futile 451 off 561. With 1128 balls to play with, India managed 445 at the Adelaide Oval, and the Kiwis hit 440 at Trent Bridge. At the start of their innings today, England had a theoretical 1290 balls available. The required run rate, on a pitch known for improving as the match goes on, was just 1.82 runs per over.

And finally there’s the clinching nonsense. All of the facts and all of the debunking above fail to take one thing into account: run chases stop when the chasing team wins! Let’s say that England’s target today was significantly lower than 391. Let’s say they’d bowled Australia out really cheaply in their second innings, for about 100, and the chase was just 180 or so. That wouldn’t figure in the Cricinfo table – it probably wouldn’t get in the top few hundred. But it’s entirely realistic to suggest they could have done it with maybe one or two wickets down, in 60 overs, so the game would have been over by mid-afternoon on the third day. Who knows how many they could have scored, had they been allowed to continue? In the region of 800 wouldn’t be outlandish if Australia simply couldn’t take wickets.

This fact, that teams could score many many more runs in the fourth innings if only they didn’t have to stop when they won, must account for a large chunk of run chases around the world, which then simply don’t appear in the stats chucked out by the commentators on days like today.

Is there a point to all this tedious rambling? Well, yes. To commentators and journalists – historical statistics are all very well, but not necessarily as predictors of performance. To England’s cricketers – ignore historical fourth innings run chase figures completely, and concentrate on your abilities in the number of overs you’ve got left!

Update: a commenter elsewhere makes a good point, that if a team is chasing 300+ in the fourth innings then it is likely that that team has made a pretty bad fist of the rest of the match, and therefore is on the defensive or at the very least “fighting an uphill battle”, whereas one needing 180 with three days to spare has all the momentum in the match. This is an interesting comment on sporting psychology, but it’s a bit of a circular argument in that part of the defensiveness might be a belief that the stats are against them!

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2 Responses to The impossible run chase

  1. Afrikaner says:

    Good post..but afraid to say your boys are now 81/5 and though not a statistically impossible chase it is looking increasingly difficult. What about if we looked at the final chase as per the batting teams ave?? So in that scenario, we could look at the averages of the remaining not out batsmen and try and conclude some sort of expected value for Englands final score??

  2. Another interesting thought – not so much for this one game, but in general: how close is a team’s score to the aggregate of its batting averages? My guess would be “nowhere near” but I know for an absolute fact I don’t have time to do the research!

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