Does Sachin Tendulkar exhibit form?

Can we identify patterns in Sachin Tendulkar’s test match innings?

If there’s a list of phrases and terms used universally across all sports, it would probably feature ‘form’. Always discussed but never formally defined, it’s often a starting point for debate on a range of topics.

This post is inspired by this debate, and also the techniques used by sports bloggers* to quantify regression to the mean. In short, what is a better predictor of an athlete’s next performance: his most recent performance(s) or his average performance?

The former would support the view that players go through peaks and troughs of form, the latter that results randomly fluctuate around a specific skill level. This may vary from sport to sport, but I’ve focused on cricket’s Sachin Tendulkar as a case study.

Innings to innings

Can we predict how Sachin Tendulkar will do in his next innings, based on his previous innings? In a word, no, as the chart below shows. The virtually horizontal line of best fit tells us that the best prediction of his next innings is his innings average (51, after imposing some conditions). High scores are randomly followed by high or low scores, and vice versa. A ‘form player’ would likely see high scores followed largely by high scores, and the same for low scores.

Innings where Tendulkar finished not out from less than 100 balls are excluded, on the basis that there was insufficient opportunity to maximise his scoring. Innings separated by more than 30 days are also excluded, as it seems improbable that form would persist over such a long stretch without a test match innings in between.

There are multiple factors ignored – opposition, match situation, location and innings (first or second). However, even accounting for some of these factors, it seems unlikely that this would explain all of the variation we see in the chart above.

The following chart looks at the relationship of first innings scores only, to remove the effect of second innings-bats generally being more difficult. The same conditions are imposed.

Again, a horizontal line tells us that if you want to hazard a guess at Tendulkar’s next first innings score, you’re better off using his first innings average of 58 (after conditions) than his last first-innings score.

Recent innings to innings

Perhaps this is too simplistic. As suggested, there are a number of factors at play, and a good ball can get a batsman out at any time.

If Tendulkar is in or out of form, then it’s likely to be a collection of recent innings that best describes this state, rather than his last innings. Under this basis, I’ve looked at his average innings score in the previous 90 days, with a maximum of 5 innings played – an arbitrary definition of his ‘recent form’.

Again, however, there is no significant effect. Tendulkar’s recent scores have next to no bearing on his next performance.

This evidence suggests Sachin Tendulkar is not a form player, which probably wouldn’t concern a player who averages over 50 in test match cricket. You know what you’ll get when he comes to the crease – his exceptionally high average – and the variation around that comes through a number of factors, not least luck.

The question is whether this is a universal trait for cricketers, or whether some do exhibit more predictable, streaky behaviour. Suggestions for case studies are welcome, as well as an application to other sports.

*Both James Grayson’s blog and this post in particular.