Martin’s Blog

Dave’s got more graphs

In case anybody is following these graphs via my blog and not checking out Pappus’ plane here are some more form graphs.

The interesting one is this one for all batsman who have averaged over 40 in test match cricket.

This shows that form probably is useful for predicting your next innings. But it’s not a huge factor. I guess this is what I would have predicted before any graphs were made. But it is pretty interesting to see all the individual batsman’s graphs and the varying correlations.

The natural conclusion of one day cricket

 I was looking for some cricket to watch on the internet and found a highlights video of that famous game where the world record ODI score was broken twice on the same day. It’s definitely worth a watch.

For my American audience you should keep in mind that this is the highlights of perhaps the most manic game of cricket ever played. It will teach you almost nothing about the rhythm of the game, fielding, running between the wickets or even bowling. But it will show you what can be achieved by destructive batsmanship on a good pitch with a fast outfield, at altitude.

A description from my new favourite cricket writer (He’s like Roebuck on acid or something): “It was a game without a people, there were no players, no personality, no heroes – just a ground violently expelling balls into a crowd.”

The myth of form?

A while back I asked the question of whether form has predictive value for test match cricket batting. Dave took up the challenge and produced some very interesting graphs. (Dave’s a physicist in real life as well as playing one on the internet so he’s good at this kind of stuff).

Here’s the Ponting graph. Each dot represents a completed innings with the x (horizontal) value being the player’s average in their previous five innings and the y (vertical) value being the score in that innings.

The blue line is the straight line that best fits the data and the red line is the straight line that we would expect to get if the data was arranged horizontally randomly. So since the blue line is above the red line for large x values we would expect that for Ponting being in form means that he is more likely to score runs. It doesn’t look a particularly big factor but I’d believe that it’s there.

But when you look at other players sometimes this is reversed. Justin Langer’s graph shows why he was always struggling for his place in the side despite averaging 45: he only scored big scores when he was out of form!

The black curve is the average score for the batsman when their average for the last 5 innings is greater than the x value. So if you go across to x=80 and then go up to the black curve you will find the average that Ponting has when he has averaged at least 80 in his previous 5 innings. It looks to be 60 odd: slightly higher than his career average.

At first it seems interesting that for everybody except Greg Chappell this number decreases for large x values. But I think that this is just a result of the smaller sample size as you go to the right: Big scores contribute a lot to averages but are rare events so if you select only a few innings you would expect the average of those innings to be less than the overall average. (Think about picking 2 scores out of {0,10,20,30,40,140}. The average of these is 40 but the average of two of them is less than 40 for 10 of the possible 15 pairs.) If a batsman had a large number of innings (in the thousands rather than hundreds) we might expect the black curve to look more like what it does for middling x – some kind of oscillation about the blue line.

I do agree with Dave that the black line shows the inconsistency of Blewett – most player’s dropoff occurs at x=80 or so, his is at about x=48.

I am amused that Damian Martyn seems to have no correlation at all. This backs up a quote from Nick Whittock, a writer of some interesting cricket poetry:

“Form is a concept that largely escapes me in terms of poetry. In cricket on the other hand, and Damien Martyn is a prime example here, it is clear that it barely exists at all. I understand form, or perhaps the myth of form, perfectly when I watch cricket.”

Some questions that Dave might want to think about:
- Do we have the same kinds of patterns for tailenders? What do the graphs look like for Warne, Gillespie, Lee, McGrath for example?
- If we did a graph for all the batsman (ever/the ones he’s looked at so far) what would it look like? From the graphs so far it seems it would be fairly flat. So then the question is: does form exist? Do these graphs represent some real difference between Ponting and Langer or is it all just statistical noise?