Win Probability

Dave Wilson | 6:06am gmt 14 May 2013

Brett Lee - how important was his batting at Edgbaston?
Batting Impact

I've been trying for some time to determine if it's possible to assess the contribution of individual players to the changing state of matches - my first attempt can be found here. I had hoped to automate this from my database but for various reasons this has not been done.

Simplistically, what I've been doing is assessing the win probability of a player's team at the start of his innings and comparing it with the win probability at the end, either through dismissal or some other reason for termination (e.g. declaration or end of match). The difference can then be assigned to the batsman based on his proportion of the runs scored while he was at the crease.

In the first article I looked at Bradman and Lara, and since that time I've added Headley, Pollock and Tendulkar (like I said, it takes a long time to do this manually, though admittedly it took a lot longer to determine Tendulkar's values than it did Headley's). As an example of the method, let's take Graham Pollock's 175 against Australia at Adelaide in Jan 1964. When Pollock came into bat, South Africa were 275 runs behind Australia's first innings total and had lost two wickets, the win probability at that time being 40.3%. When he was out, he and Eddie Barlow had put on 341 such that South Africa were 66 runs ahead and only one further wicket down; their win probability at that time was then 83.3%, such that Pollock's share inimproving the win probability was (83.3-40.3)*(175/341), or 43.1%.

We can do this for all of the batsman's innings and find his career impact in terms of win contributions. As mentined above, I've now completed this for Don Bradman, Brian Lara, George Headley, Graeme Pollock and Sachin Tendulkar. Their cumulative career impact totals are as follows:-

 Player Inns Impact Bradman 80 490.1 Tendulkar 327 442.6 Lara 230 357.1 Pollock 41 102.1 Headley 40 66.4

Bradman, despite his low career total of 80 innings still tops the list; that percentage number represents the equivalent of him single-handedly taken almost ten games from a position of fifty-fifty to outright victory. However, Pollock and Headley graced the game with even fewer innings so here is the same list on a per-innings basis:-

 Player Impact per Innings Bradman 6.13% Pollock 2.49% Headley 1.66% Lara 1.55% Tendulkar 1.35%

Bradman is miles ahead now, but isn't he always? Pollock and Headley have moved up, as expected. There are other interesting facts I was able to glean from this, but I won't post them here.

That's mainly because, after quite some time looking into this it occurred to me that the system wasn't fair. Yes, it assesses the player's contribution to wins in terms of the change in win probability at the start and end of his innings, but it doesn't take into account anything that went on in between. To illustrate the unfairness of this I'd like to use as an example the the Edgbaston Test from the 2005 Ashes.

Impact and the Greatest Ever Test

Kevin Pietersen crafted an innings of 71 in what was his second Test, steering England through from 170/3, having just lost two wickets for only six runs, through to 348/8. If we compare the win probability differential between his entrance and exit, that would be only 2.17%; again there had been two wickets just lost for six runs. By comparison, Andrew Strauss's 43 would be worth 9.37% using this measure - obviously that's not right.

So what I've done is to try and take into account everything that happens. In Pietersen's case, this would be assessed as follows:-

 EVENT WP-PRE WP-POST KP SHARE KP in 62.65% MV out 65.00% 52.76% +1.80% AF out 83.08% 74.39% +8.83% GJ out 80.00% 62.12% +1.87% AG out 81.82% 80.33% +9.25% KP out 84.21% 68.09% +0.41%, -5.32%

When KP came in, the England win probability (WP-Post dismissal) was 62.65%. Pietersen's partnership with Vaughan amounted to 17 runs, during which the WP increased slightly to 65.00% - KP's share of that amounted to +1.80%. The KP share column shows his share of the WP increases for each of the partnerships in which he was involved, and when he was out, the cost of his wickets is shared between the batsman (for getting himself out), the fielder (if applicable) and the bowler - the batsman is always debited a third of the cost of his wicket. Different wickets are assessed a different cost as they occur at different match situations.

When we total KP's positive shares from his batting, offset by the negative share of his dismissal, we arrive at a total win contribution for England's first innings of 19.01%; this contrasts sharply to the figure derived just from his entrance and exit (2.17%). Strauss meanwhile is assessed a win contrbution of 9.50%, to which Pietersen's contribution comparesmore favourably.

Impact on the Other Side of the Ball

We then do the same for the fielders and bowlers. For each dismissal, fielders receive a third of the differential between pre- and post-dismissal WP, while bowlers get the remaining third; if no fielder is involved, i.e. lbw or bowled, the bowler gets the fielders share as well. The Australian fielding team then receives the following contributions for England's first innings:-

 SHARE PLAYER +13.40 Warne +11.27 Kasprowicz +5.73 Gillespie +7.94 Lee +15.26 Gilchrist +5.38 Katich

We then do this for each innings and total each players contributions. The final totals look like this:-

ENGLAND

 SHARE PLAYER +24.43 Trescothick +15.95 Strauss +13.59 Vaughan +7.36 Bell +25.45 Pietersen +107.06 Flintoff +16.93 Jones, GO +28.94 Giles -1.97 Hoggard -3.56 Harmison 25.71 Jones SP

AUSTRALIA

 SHARE PLAYER +22.13 Langer +9.88 Hayden +22.15 Ponting -2.49 Martyn +16.52 Clarke -0.16 Katich +32.24 Gilchrist +50.22 Warne +81.69 Lee +11.17 Gillespie +9.34 Kasprowicz

Real or Imagined?

For Edgbaston, Andrew Flintoff is correctly identified as the man of the match, and was England's prominent player by a significant margin. For Australia, Brett Lee comes out tops rather than Shane Warne, and this is largely because of Lee's performance with the bat in Australia's second innings. When Australia lost their penultimate wicket with 62 still to get, their win probability was then basically zero. However, once Lee and Kasprowicz had taken Australia to within two runs, their win probability was then virtually 100%, i.e. in virtually every other case when a side had two runs to make and one wicket to give they won. Once Kasprowicz was out he then of course was debited his share of the huge swing of win probability on his dismissal, whereas Lee, who was not out, did not lose anything, so he ends up with quite a large batting share.

So, has this method correctly measured Lee's impact in helping to take Australia to within two runs? The system is of course objective, as it uses the results from other Test matches which saw the same situations. Of course, the situation we had at Edgbaston has hardly ever been reproduced in 2000+ Tests, so this is an extreme example.

However, if the sight of Lee famously being consoled by Flintoff at the end of the match is anything to go by, I would have to say yes.

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