Pappus' plane - cricket stats

This is a bit different from my usual fare, but I thought it deserved its own post, rather than just being in a couple of comments threads around the place. Thanks to AGB commenter Professor Rosseforp for bringing my attention to the Ferdinands and Kersting paper.

For a long time, the definition of an illegal delivery action was that the ball couldn't be thrown or jerked. (Stuart gave us details here and here.)

A recent paper suggests that we might be able to return to a sort of 'jerkiness' definition, only this time backed up by some science. I'll go through a bit of background first. The key goal that we want is for science to come up with a criterion whereby bowlers who look like chuckers are chuckers. An exception to this is Murali, who can bowl in a brace (so he can't possibly chuck) and still look bad. But the problem of a chucking definition is much bigger than just Murali, and it should be possible to get science to agree with the naked eye, at least most of the time, for bowlers with 'normal' arms.

The ICC's current tolerance of 15 degree elbow straightening (or 'extension'? not really sure of the difference) was based on a study done by Porter, Elliott, and Hurrion during the 2004 Champions Trophy. Unfortunately, the full details of the study haven't been released to the general public. The reason given by the ICC is confidentiality issues: "We do not think it would be correct to release the figures publicly without the prior consent of the individual bowlers and the researchers themselves. This consent has not been obtained."

I don't understand why the researchers, who have published many biomechanics studies publicly, should care. I can see why the ICC might not want to give names and elbow straightenings, because there'd be a torrent of allegations of chucking all over the place.

Nevertheless, the ICC's secrecy over the matter means that we don't really know much about elbow straightenings, except that Sarwan's was zero, and Pollock and McGrath up to 12 degrees or so.

But luckily there was a paper published (in Sports Biomechanics, 'Fast Bowling Arm Actions and the Illegal Delivery Law in Men's High Performance Cricket Matches') by Portus, Rosemond, and Rath in 2006 which does give us some numbers. They also don't name names, but they did study thirty-four deliveries by twenty-one fast bowlers, from Test, ODI, and tour matches. None of the bowlers had had any questions raised over their actions. These sorts of analyses take a long time, which is why so few balls were studied.

The errors in the measurements are +/- 1 degree.

Of the thirty-four balls bowled, three were by two bowlers with hyperextended elbows, so we'll ignore them. Of the remaining thirty-one, six had elbow straightenings larger than 15 degrees. These were spread across four bowlers out of nineteen. If you go by the 15-degree rule, then those are chucks. Many of the bowlers only had one ball recorded, so it's not clear if there were any more chuckers-under-the-15-degree-rule in the sample. Looking at the numbers in the table, you'd guess that at least a couple of them go past 15 degrees sometimes.

So, to summarise: Under the 15-degree rule, one in four or five fast bowlers sometimes chuck, often more than once per over.

These are, remember, bowlers whose actions haven't been questioned.

So here we have the first problem of the 15-degree rule: many bowlers who should be deemed legitimate are breaking the rule.

Now we get onto the other problem of the 15-degree rule: you can chuck without straightening your elbow 15 degrees.

This takes us to the paper by Ferdinands and Kersting, also published in Sports Biomechanics, in 2007 ('An evaluation of biomechanical measures of bowling action legality in cricket'). The technical details are a bit over my head, but this is what they say:

If bowlers adopted a similar action to throwing, where the elbow remains flexed at release, then it may be possible to utilize effective humeral internal rotation in bowling while satisfying the current 15° elbow extension angle limit. For instance, if in bowling the elbow can be flexed 26° at release, which has been achieved in professional Cuban baseball pitchers (Escamilla et al., 2001), then a bowler can theoretically have an elbow flexion angle of 41° and extend 15° before ball release. Any amount of elbow extension is allowed after release. Such a bowling technique would use a bowling arm with a lower absolute elbow angle about the flexion-extension axis (more flexed), which would extend rapidly before and after release. This technique would share some of the characteristics of a throwing-type action, but still remain legal according to the current elbow extension angle limit.

But it's not just speculation about new 'bowling' techniques that would be blatant chucks without breaking 15 degrees. Ferdinands and Kersting studied bowlers (in the lab, not in match conditions) from club level in New Zealand to international level, some of whom had had their actions reported. There were 'fast' bowlers and spinners. One of the limitations of the study is that their 'fast' bowlers weren't fast by international standards, and this is the obvious place where the next bit of research should go.

There were six bowlers studied with suspect actions. Five of these had mean elbow extensions less than 15 degrees, and indeed at least 75% of the balls bowled by those with suspect actions passed the 15 degree test (it's not clear precisely how many from the graphs).

Let's have a look at the box-and-whisker plot for the various groups considered:



The boxes represent the middle 50% of deliveries, in terms of how much elbow extension there is. The horizontal lines in them show the medians.

The suspect box starts higher and finishes higher than the others (so there is some correlation between elbow straightening and apparent chucking), but there's a big overlap with spinners and fast bowlers. So just going by the elbow straightening isn't very good at distinguishing those with bad-looking actions from those with clean actions.

Now (at last!) here comes the key point. In addition to just measuring the total straightening, they also measured the rate of the elbow extension, the 'elbow extension angular velocity'. Now the box-and-whisker plot clearly shows up the chuckers:



The bottom of the suspect box is at around 200 degrees per second, and the top of any of the other boxes is around 100 degrees per second.

The implication is clear: measuring the elbow extension angular velocity gives much, much better agreement with the naked eye than just going by the total straughtening. It's not perfect, and there were some deliveries in the non-suspect groups that went above their suggested threshold of 200 degrees per second, but it's a lot better than what we currently do. And importantly, it gives us an objective definition that generally agrees with what our eyes tell us is a clean action and what is not.

As I said earlier, we need to see this research done on a large group of international-class bowlers before applying it to international cricket. But the results are very promising. At the very least, the 200-degree-per-second cutoff is better than the 15-degree cutoff, which clearly doesn't work.

I'll finish by noting that this gets back to the old 'jerk' definition. A gradual straightening caused by general stress on the elbow during the bowling action isn't jerky, but a rapid bit of straightening just before release is jerky.