The Bradman Class and Sabermetrics

My link in yesterday's blog, which was to a discussion on the validity of sabermetric methods for cricket, was itself generated by the publication of this paper in The Journal of Quantitative Analysis in Sports.

The authors propose a new method of evaluating Test batsmen, which tries to incorporate the consistency of a batsman's innings. Someone like Alistair Cook has a high average this year, but it's a consequence of a couple of big innings, rather than consistency. His median score is quite low. The question the paper's authors don't address, however, is whether a consistent batsman is more likely to produce Test match wins. What they do look at is the relative importance of a batsman's average to that of his team-mates, but this isn't the same thing.

This is where most of what passes for sabermetric research in cricket misses the point. Ranking batsmen is jolly good fun for a discussion down the pub. What I want to know, however, is the relationship between runs and wins.

And that's what I still regard as my key discovery: it is more important to stop your wicket from being taken than to score masses of runs. This means it is more important to have bowlers who take wickets than to have batsmen who score runs. The secret to success in Test cricket is the right balance between how quickly you take wickets, and how slowly you lose them. The first building block in this is to find bowlers, not batsmen. And that raises an interesting question about the relationship between bowlers' overuse and injuries or declines in effectiveness.

Runs/Wickets State 3

As stated in the last post, the problem with looking at a single innings in isolation is that it does not take into account the match situation. Mitchell Johnson may have been improving Australia's chances of winning the match, but did they have much chance to begin with? For that, we need to look briefly at South Africa's second innings.

When the ninth wicket fell, the chances of South Africa winning, based on previous results were about.667—that is, two-thirds of all matches where the team batting in the second innings stood at 637/9 ended up with that team winning. However, there had been no matches that had seen the second innings finish on 651. Thus, at that point, we go with the available data, and wait on the outcome.

When the fifth Australian wicket fell, their chances of winning were .288-.667=-.379. When the tenth Australian wicket fell, we learned that the 422 score in the second innings results in defeat 2 out of 3 times. Australia's chances of winning were .333. South Africa's chances of winning on 651 go up to 1.000. They are the only team to reach that score at the end of the second innings of a match. However, the net effect of Hilfenhaus losing his wicket took Australia from -.271 chance of success to -.667, or a swing of -.396. But it would be unfair to pin all that blame on him. We need to share it out among all eleven players. Cricket is a collective effort, Mitchell Johnson gets the same blame for falling short as Hilfenhaus. Everyone gets a reduction in their score of -.032. The table produced yesterday now looks like this:

Johnson +.109-.032=+.077
McDonald +.101-.032=+.069
McGain +.014-.032=-.018
Siddle -.007-.032=-.039
Hilfenhaus -.032

Just because Hilfenhaus' was the last wicket to fall doesn't mean he deserves all the blame. Siddle's wicket was actually more significant in leading to a defeat. McGain's performance goes from being a positive to a negative.

One could argue that we need to adjust South Africa's score for Australia's first innings. I'm not sure. We'll take a look at that another time.

Runs/Wickets State 2

So, now the match is finished, let's take another look at how we can use the Runs/Wickets State to measure a player's contribution.

When Mitchel Johnson came in, the runs/wickets state was 218/6. Teams at 218/6 had gone on to win .294 of their Test matches.

Johnson and McDonald took the score to 381/7. Teams at 381/7 went on to win .389 of their Test matches. Thus, Johnson and McDonald in this wicket managed to increase Australia's chances of victory by .095.

Siddle was out next ball, but at 381/8 we're looking at .382 wins, so Johnson's score stays the same but Siddle gets a -.007. (We'll punish the player whose wicket falls with any negative, and share the credit for any positive.)

Johnson and McGain put on 7 runs, so at 388/9 we're looking at .396 wins. Johnson's score goes up to .109, McGain gets credit for .014.

Johnson and Hilfenhaus take the score to 422. But defeat in this match transforms a score of 422 in the third innings of the match from a .500 win to a .333 win. That's a big -.063 for Hilfenhaus? Or is it a plus .104 for both?

Ah, you see, you can't just use a single innings' score. You have to remember that in the third innings of a match a team is chasing a pre-existing state.

Anyway, for the purpose of this post, let's call the scores as follows:

Johnson +.109
McDonald +.101
McGain +.014
Siddle -.007
Hilfenhaus -.063

Runs/Wickets State

Following on from yesterday's post, about Base/Out States in baseball, I thought I'd take a snapshot of the current Test Match, which will perhaps explain more plainly the direction that I'm going in.

When I checked the South Africa v Australia score, at tea Australia were 231/6. Teams at 231/6 in the third innings of the match have a cumulative record of 243 wins, 330 losses and 235 draws. That's a success rate of .301, which tells you that, even not knowing South Africa scored 651 runs, that Australia weren't in good shape to win the match.

At 365/6, the current score, the success rate is .383, still not good, but better, an improvement of .082. Thus, we can calculate that this current stand by McDonald and Johnson has increased the Australian chances of success.

Base/Out Musings

Thinking about the way sabermetrics analyses baseball, and trying to translate that to cricket, is the main area where not enough work has been done. There's a tendency, even on my part, to focus on trying to keep too close to the baseball model, and not enough on adapting the underlying principles to the very different game of cricket. The first big breakthrough I made was in recognizing that cricket is a mirror image, so some things need to be reversed. Thus, wickets in cricket are more analytically useful than runs, whereas in baseball runs are of more use than outs.

Looking at the idea of the base/out state in an inning has brought me to the realization that in order to estimate win expectancy, a cricket sabermetrics would do better to look to Duckworth-Lewis, and think about resources in a Test match. This opens up some fascinating potential in the analysis of bowling, but also some interesting perspectives on batting. I'm working on a way to deploy this so that we can follow a Test match via this blog and see if practice leads to understanding.

How to Win a Test Match 2

OK, your Test opening wicket (first wicket, first innings) stands for 100 or more runs. How often do you win the match?

According to StatsGuru:

84 Wins
27 Losses
86 Draws

So not even half the time.

How to win a Test Match 1

OK, so sabermetrics is all about evaluating players to see who contributes to winning. Here's an interesting question. How many times has a side batting first in a Test match, taken twenty wickets, lost the match?

According to CricInfo's StatsGuru, twice, both Ashes Tests. In each case Australia batted first, forced the follow-on, and then failed in the run chase.

Meanwhile, if you field first, and get the opponent all out in their 3rd innings, you can lose 247 times out of 904 matches, or only 27 percent of the time.