On all-rounders and form: what role does the mind play in cricket?

This article was inspired by Matthew Engel’s profile of Sir Ian Botham on Cricinfo, where he writes “sober judges were wondering if Botham had done more harm than good by making all England believe, as he did, that cricket matches are won by inspiration not preparation.

All-rounders in cricket are fascinating for understanding the psychological aspects of the game. A world-class all-rounder has almost no equivalent in any other sport (except baseball, where they are exceptionally rare). An all-rounder performs two independent tasks (batting and bowling) with a high degree of facility. In contrast to two-way players in other team sports like basketball and soccer playing offense and defense, batting and bowling are independent and isolated activities allowing us to treat the all-rounder as a pure batsman and pure bowler for this analysis. In particular, what they do as a batsman should, in theory, have no effect on what they do as a bowler, and vice versa, except that it is the same human being in both roles and from experience, we know that our mental and physical state has a profound influence on our actions.

To address this question, we start with a digression on form. Even casual cricket watchers are aware of the term and of a batsman or a bowler being in or out of form. But form, like the ether, is easy to attribute and hard to quantify. If we ask a set of cricket fans, the question: “do you think an all-rounder’s batting and bowling form are correlated” (i.e. if, as a batsman they are doing better than average, do we expect them to do better than average as a bowler as well or more precisely, is an all-rounder in (or out) of form simultaneously as a batsman and bowler?). Most people (like me) intuitively reply Yes but a moment’s thought should make us wonder why should this be the case and more importantly, what does this say about we think form means?

If we think of form as a mental state of being, then the Yes reply makes sense as it should apply equally well to both aspects of the game. But if form corresponds to some physical aspect, then the attribution becomes trickier. The ‘ability to see the ball as big as a balloon’ as a batsman does not really help with delivering the ball any faster or get more swing as a bowler. A casual glance of the list of the greatest batsmen and fast bowlers shows that they line up at the opposite ends of the height scales. The very fact that world-class all-rounders (people who can make the team as a pure batsman or bowler) are so rare points to the fact that batting and bowling require fundamentally different skill-sets. It could be (and most likely is) that form has both a mental and physical component, in which case the answer should again be Yes.

To address this question of form in all-rounders, we will look at the batting and bowling performances of four great all-rounders (Ian Botham, Kapil Dev, Richard Hadlee and Imran Khan) in every test series they played (courtesy of Cricinfo Statsguru). By plotting their series batting (SBa) and bowling (SBo) averages on a 2D plot, we can infer if their batting and bowling performances in a given series are correlated. If their performances are correlated, then when their series batting average exceeds their career batting (CBa) average (SBa > CBa), then their series bowling average should be below their career bowling (CBo) average (SBo < CBo, in-form simultaneously). The converse should also be true, i.e. if SBa < CBa, then SBo > CBo (out-of-form simultaneously). The data points should thus lie mainly in quadrants 2 and 4. If the performances are uncorrelated, then the data points should be scattered roughly equally in all 4 quadrants and their batting performances have no influence on their bowling and vice-versa.

Before looking at the results, some notes about the analysis:

  1. This data is restricted to test series performance only.
  2. The performance in each test series is used as a metric to quantify form. Although performance in a given series is hugely dependent on opposition strength (for ex: batting form can only go so far against Roberts, Holding, Marshall and co.),statistically over the course of a long career (which all 4 players were fortunate to have), opposition effects tend to average out.
  3. One game test series results are discarded. A single performance, however exceptional (like Botham in the golden jubilee test), is not a trend.
  4. Test series in which the bowler did not take a wicket (leading to infinite series bowling average) are also discarded. This mainly affects Kapil, whose 1986–87 series (3 tests) against Australia is discarded.
Normalized test series batting and bowling averages for the four great cricketing all-rounders of the 80s (Sir Ian Botham, Kapil Dev, Sir Richard Hadlee and Imran Khan). The black dashed line shows the linear regression fit.

The Verdict:

The data for the four great all-rounders is plotted in the figure above. Instead of plotting raw batting and bowling averages, we instead plot the normalized averages (where normalized batting average = (series bat. avg-career bat. avg.)/career bat. avg. and similarly for bowling avg.). A normalized series batting average of 0 means the player equaled his career batting average. An average of 1, on the other hand, means the series average is twice the career average. A negative average means the player performed below his career average. Every data point in the plot is a test series with the x-coordinate the normalized series batting average and the y-coordinate the normalized series bowling average. Better than average (in-form) performance as both a batsman and bowler correspond to points in the bottom right quadrant(note: on this plot, a negative bowling average is better). Worse than average (out-of-form) data points sit in the top left quadrant with the other two quadrants pointing to the scenarios when the all-rounder exceeded career expectations in one and did not meet them in the other. Keeping this in mind, if we stare at the plots, we can conclude:

  1. There seems to be little, if any, significant correlation between the series batting and bowling performances. The linear regression fit, which is one metric for measuring correlation is shown in the dashed black lines. A positive correlation between batting and bowling performances (in-form in both) would correspond to the black line having a negative slope. Only Sir Ian Botham shows that (more on that later). Most all-rounders, best exemplified by Kapil, show flat to slightly positively sloped lines, which indicate anti-correlation (in-form as a batsman, slightly out-of-form as a bowler and vice-versa). I am not sure how any mental or physical theory of form can explain an anti-correlation.
  2. It is important to note that there is a lot of scatter in the data and the outliers (series with high batting averages like Botham’s 1982 series vs India, Imran’s 88–89 series vs New Zealand and Kapil’s 86–87 series vs SL) dominate the regression fits. Drawing concrete conclusions from this dataset will require more fine-grained Bayesian analysis, something I plan to do in the near future.
  3. Having said that, I do believe there is something very special about Sir Ian Botham. I have spent a long time staring at his data-set and it is visibly different in its distribution (clustered in quadrants 2 and 4) and the negative slope is surprisingly robust to addition and removal of series. For ex: adding all the one-off test series Sir Ian played makes the positive correlation even stronger. I think Matthew Engel, and most of the English public, were spot-on in their assessment.