Tuesday, 7 June 2011

England v Sri Lanka, 2nd Test at Lord's: Day 4

The fourth day of the Test began with yet more bad weather, leaving us to wonder what could have been had we had a full four days' play. Despite this, Swann and the quicks actually did quite a good job of restraining the Sri Lankans, leaving them all out on 479. The draw probability took an early blow in England's second innings whan Strauss was dismissed for a duck, but soon rebounded as Trott and Cook began to build a healthy lead.

Here's how much each player has altered his team's chances of winning the Test match, as of the end of the fourth day:

Eng win
SL win
Tremlett 10.6% -7.3% -3.4%
Morgan 8.3% -9.6% 1.3%
Strauss -8.2% 21.5% -13.4%
Finn 5.2% 2.4% -7.6%
Trott -2.1% 0.0% 2.1%
Cook 11.3% -26.6% 15.4%
Bell 1.3% -1.3% -0.1%
Pietersen -11.4% 8.1% 3.3%
Broad -16.4% 10.5% 6.0%
Prior 14.3% -17.7% 3.5%
Swann -19.4% 11.6% 7.8%

SL win
Eng win
Maharoof -19.2% 16.8% 2.4%
Weleg'ara 6.3% 3.8% -10.1%
P.Jay'dene 2.3% -3.3% 0.9%
Sang'ara -3.1% 0.2% 2.9%
Parav'ana 0.0% -5.2% 5.2%
Sam'eera -3.0% 7.2% -4.2%
M.Jay'dene 4.2% -4.4% 0.3%
Herath -6.7% 3.3% 3.4%
Lakmal -4.0% 0.2% 3.8%
Fernando -13.4% 12.0% 1.5%
Dilshan 19.4% -29.3% 9.8%

Dilshan remains the most influential player of the match so far, having contributed 19.4% of a win for Sri Lanka, and taken away almost 30% of a win from England. Cook now stands out as England's top performer with 11.3% of an England win added and 26.6% of a Sri Lanka win taken away. Strauss's poor run of form continues, and he may be on the verge of a WPA 'wooden spoon', scoring only 4 runs in the match and contributing 21.5% to Sri Lanka's chances of winning.

Here is the match so far, in graphical form:

Geeks' note:

Please take our estimates of 'unlikely outcomes' with a pinch of salt (eg in this case the likelihood of a SL win). The model is very good at dealing with most regular situations but it is not yet equipped to deal with 'fat tails'. For the mathematically inclined, it's because we currently base our projections on binomial distributions for each potential future batsman. This generally is a good approximation, particularly early in the game looking forward, but in reality the probability distribution function should not be binomial. Unsurprisingly, (say in the case of a recognised batsman) there is a greater chance of dismissal for under ca. 15 runs than the binomial predicts, and a lower than predicted chance of dismissal for 15-40 runs or so... So basically, we tend to underwight the probability of a dramatic collapse.

We have always been aware of this and have been working towards sorting it out, but suffice to say, SL's win probability is very small, but not as small as the graph implies. This doesn't actually affect the players' WPA numbers very much, and that really is our main concern, the graph is something of an illustrative sideshow... However we still believe SL's collapse in 24 overs at the end of the last Test was truly extraordinary. We will also write more about how the model works in the future and look forward to hearing your thoughts!

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