Tuesday 16 June 2009

Stats life

This morning the skies were a blameless blue, but they knew what they'd done last night, oh yes... 

When the great rains swept the Oval and Duckworth-Lewis set West Indies 80 in nine overs my immediate thought was, 'that's low', and I wanted England to win not just for the obvious reason, but because questioning dear old D-L afterwards would seem less like sour grapes.

It's not. England aren't out of the tournament because of Duckworth-Lewis. The fault-lines that run through the team are all too apparent: they're a super-eights type side, nothing more and occasionally less. 

And yet... In the sharp-end super-eight games of the past few days, scores of 144, 153, 159 and 158 have all been successfully defended. D-L is a essentially a measure of worth and in the light of recent history, England's 161 felt like it was worth more than 80 from nine. Even the blunt, base-rate over-by-over comparison  shows that England were 75-2 after nine of their regular twenty.

I'm not numerate enough to understand how the D-L calculation is calibrated, but I don't think that the calibration has been adjusted since 2004 to allow for the rising primacy of the bat, and for the mindset that has accompanied it.

Perhaps the simplest way to load the calculation would be to adjust the number of available batsmen. What really swung last night's D-L figure in favour of the batting side was the 10 wickets in hand. England would have had to take more than one per over to bowl them out. A ratio of, say, seven batsmen - ie six wickets to win - would have felt fairer on the bowling team.

NB: Another delicious little titbit came to light on the radio - apparently net run rates would have been adjusted to allow for D-L if points could not separate the sides. Good luck working that one out, boys...

Update: The Guardian are reporting that Duckworth-Lewis will be revised towards the end of the year to reflect the increase in T20 data - reinforcing a point made by Dave Barry in the comments below. 


Krish said...

If West Indies had lost 5 wickets for 80 runs by the 9th over while chasing 162 and then rain started pouring, would that have qualified as a win by DL?

I think probably not.

The Old Batsman said...

That's a very interesting point... I don't know.


David Barry said...

Krishna's question is irrelevant, but using the standard DL tables, the answer is yes, the Windies would have been given the victory. With 20 overs remaining and ten wickets in hand, the DL table says that the team has 56.6% of its resources remaining. With 11.4 overs remaining and 5 wickets down, the DL table says 28.8% resources remaining.

Scaling the percentages so that you have 100% with 20 overs left (ie, a 20-over match), that's 50.88% resources left when 5 down after 8.2 overs. So the "projected score" would be a bit more than double 82, ie, certainly more than 162.

What the result would be using the professional edition of the DL method, I don't know, because the ICC in their wisdom doesn't let the general public have access to the professional edition (!!!!!).

I say that Krishna's question is irrelevant because the point of this sort of revised target is that you allow the batting side to lose more wickets - they usually have to, because they're scoring at a faster run rate.

More generally, I agree that a target of 82 in 9 overs seems low. There could well be a problem with the DL method in 20-over cricket - the tables were generated by analysing 50-over games, and there would not be much data for innings where a team hadn't lost a wicket after 30 overs, and even less data for no wickets after 41 overs.

Rob said...

I think you make a good point about available overs and wickets. Only nine overs does seem to skew it in favour of the batting side. However... WI almost went too hard and could have collapsed completely.

My recollection was that Sky said '90 off 9' and Collingwood definately said '90 from 9' in his interview afterwards ... so where did 80 come from?

Russ said...

I think, for low numbers of overs, there is a disconnect between the D/L system of anticipating how far along a chase a side should be, and the difficulty of the remaining chase.

Chasing 8 an over without risk is fairly standard these days, but sides do so by keeping their run-rate at 8 or thereabouts, rather than 5 or 6 and then trying to accelerate. So the D/L assumes (rightly) that a side would be around 0/79 after 11 overs (7 an over), chasing 162.

That's a very different thing, though, to maintaining an even probability of victory given an alternative scenario (which the D/L pointedly does not do), for a chasing side.

If the game had progressed normally, England, to win, would have needed to get the West Indies 5 or 6 wickets down so as to have batsmen at the crease incapable of scoring at 8+ an over. So although the projected runs are pretty reasonable, England incurred a penalty because they lost that opportunity to take wickets for 11 overs.

I'm not really a fan though, of taking wickets from the chasing side. A better formula would be to calculate the expected resources lost in wickets to that stage of the game (11 overs), and add the difference in resource loss to the required total.

So, if in an even game a team is normally 4 down after 11 overs, then the difference is 3% or 10 runs, meaning the West Indies would need to chase 92 (more or less).

David Barry said...

That's a very different thing, though, to maintaining an even probability of victory given an alternative scenario (which the D/L pointedly does not do), for a chasing side.
I hope you're still checking this thread Russ. I'm not sure what you're saying in the bolded bit. Are you saying that the DL method changes the probabilities of victory for each side, and if so, do you have the data to support it? Or a theoretical explanation.

Russ said...

David, having not seen the numbers I don't know, but based on this FAQ I gather that the resource change is not derived from maintaining the same probability of victory at all times. Perhaps that is an over-extrapolation of the answer to q.8.

For the reasons I mentioned in my comment, I am not sure that requirement is even possible with a single table for both adjusted targets and wash-outs. They are dealing with markedly different scenarios. Albeit with caveats for the professional edition being entirely different.

The Old Batsman said...

Chaps, I have a side question on the professional edition: does it just have some tweaked stats or does it a more comprehensive method? Why don't they release it? Is it commercially sensitive? Can you make an educated guess as to what's in it? And how come one's not been leaked?!

Okay, that's more than one question, I know...

David Barry said...

All I know about the professional edition is that it's not something you can use simply with tables - you need a computer to do all the calculations.

I have no idea why it's not generally available. My only guess is that Duckworth and Lewis figure they'll make more money by licensing it only to the ICC and national boards.

Russ said...

OB, pretty much everything I know about the professional edition I gleaned from the FAQ I linked to above. From what I can discern, there is a different table for each score in the first innings. The result seems to be that the resource curve is flattened the higher the total gets, to reflect the fact that the higher a chasing total is the closer a team needs to stay to roughly the required rate throughout the innings. Fo ODI totals over 300 the standard D/L implies run-rates of 10+ in the final few overs which are unrealistic.

The Old Batsman said...

Thanks - I'd love to see what it looks like - I suspect it's just a computer disc but in my mind the D-L method is held in a series of great leather-bound books like the full Oxford English Dictionary.