Speed variation is not sufficient

But it's a necessary tool for elite spinners

In a recent Cricinfo article, Andrew Fidel Fernando notes about India legspinner Kuldeep Yadav, "He varies the pace, but that is the most boring observation. All the really good spinners do that." My feelings upon reading this were so mixed that I decided to take a look at what actually happens when slow bowlers vary their pace.

Within my circle of cricket nerds, we have converged at the position that different spinners have different styles of pace variation. Some, like Kuldeep, have a wide pace range to circle through, but they seldom choose to show all their cards, instead selecting a range of 5 to 10kmph depending on pitch conditions and sticking to this bin. Others, like Gudakesh Motie, engage in more of what I like to call "big" pace variation—going straight from bowling 95kmph darts to slipping one in at 78kmph.

But which style is better?

Frankly, no one knows. It is an uncomfortable truth acknowledged by many cricket analysts that the benefits to speed variation don't show up in the data. This fact is universally appreciated in the case of fast bowlers, whose slower variations usually yield a higher economy rate than their stock balls. Nevertheless, the slower ball must come useful in highly specific use cases - such as when they see a batter setting up to use the pace, or on a pitch that has been ragging sideways for spinners - lest they wouldn't be so beloved by pacers. The problem is that such high-specificity cases cannot be summoned in cricket data without raising concerns of overfitting or small sample sizes.

This familiar problem shows up in Table 1. These charts display batting outcomes off balls grouped by different speed variation bins. A quick note on how to interpret the main variable of interest: when speed variation is negative, it means that a bowler has slipped in a slower one, when it is positive a faster one has been chucked out. These charts consider two-ball sequences - this means a sequence of balls in which a bowler has gone slow then fast or vice versa - not sequences where multiple slower balls have been followed up by a fast dart. The results observed are contradictory to what everyday cricketing intuition tells us: the higher the pace variation, the better the batting outcome.

Though this paradox has been known to me for a while, I have typically assumed that this must be a reflection of the absent surprise factor implicit in a simple two-ball sequence. After all, one would hardly call a single outswinger followed by an inswinger a set-up. So this time as I was running the numbers, I decided to look at longer sequences. Off the last ball of a sequence of three balls, in which the first two have witnessed pace variation of less than 5kmph and the last one upwards of 10kmph, batters average 42 and strike at 128. I also looked at four-ball sequences: here the strike-rate jumps to 149 and the average drops to 27. Either the data is spitting out noisy gunk or there is no discernible impact of speed variation on batting outcomes.

But perhaps this effect is simply not visible at the level of the ball because we have zoomed in way too much. Maybe, if we take a step back and look at outcomes at the level of the over, we would have achieved the nice compromise of there being enough variation within each unit to return sensible outputs and every unit being sizable enough to be an accurate representation of the population parameter. Table 2 plots various batting outcomes split by the number of balls in an over which have varied by more than 5kmph. Alas, the conclusion remains unchanged. As the frequency of variation rises, so do the strike-rate and average. (This trend is also replicated when one considers "big" pace variation at the over-level.)

What if we zoom out even more and look at things from the level of each individual bowler? A simple way of testing this is by looking at raw correlations—if we can plot the percentage of balls that each bowler varies his pace off of and then see how well the resultant rankings predict their success over the last three IPL editions. Table 3 gives the correlation coefficient between various measures of speed variation and bowling outcomes for all bowlers with at least 100 balls in the last three seasons. You may have guessed by now that the correlations are weak, but there’s more. The estimated coefficients are never statistically significant, and not even the sign of the correlation stays consistent.

This seemingly irresolvable puzzle has its answer in what Fidel Fernando points out in his article. Almost every spinner who is good enough to play at the international level can vary his pace, as the below scatterplot shows. There is barely a pattern characterizing the distribution of the world’s best tweakers on this plot. Some like Rashid Khan engage in a good deal of it, while others like Akeal Hosein nail down the same bin over and over again. What we forget so often in our conversations about this mystical quantity is that for every Mitchell Santner there is a Nitish Rana (who engages in big pace variation more often than any other bowler in the database), and for every Ravindra Jadeja there is a Murugan Ashwin (who in 34 overs has not once altered his speed by more than 10kmph).

In short, pace variation is a necessary skillset, but it's hardly sufficient.

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This raises a question of existential importance for me: was I mistaken in assigning so much weightage to the ability of new bowlers to vary pace while determining their potential? I must admit that crunching these numbers has caused me to update my priors a bit - I will no longer look towards the bottom of the screen as my only metric of proficiency in this department but a bowler's ability to take a batter by surprise with pace variation - but having said that, it is vital to remember that good pace variation is not all pace variation.

This is best illustrated using an example. One question that analysis of the above vein does not tackle is the following: do good bowlers vary their pace in combination with other attributes, or do they keep variation of different attributes independent of one another? There are arguments in favour of both tactics—maybe it is the case that combining change of pace with change in trajectory discombobulates the batter by giving him more than one source of variation to contend with, or maybe it is that a bowler shows his hand by giving two streams of informational cues.

Tables 5 and 6 reveal that the former effect dominates the latter. Since spin is largely a one-length art, I concentrate on line as the main constituent of trajectory. When bowlers pair a change in speed with a change in line, batting outcomes dip considerably—the fact that this dip is observed even for two-ball sequences suggests that the actual effect must be even greater. An even stronger effect is observed when speed variation is coupled with a different direction of turn, with strike-rate falling by 12 points and average by 12%.

What this shows us is essentially that there is a nonnegligible “interaction effect” between pace variation and the variation of other attributes that we must take into account when judging bowlers. We can't tell how strong this effect is in total because we don't have a complete record of all the attributes bowlers vary before release. For this could include aspects as closely related to pace as run-up speed, to those as remotely linked as whether the bowler has been distracting the batter by making a funny face. At the end of the day, we are constrained by the fact that cricket is a game so complicated that even the best kind of data we have available at present allows us to understand it only so well.

But what we do see in the data is this: change of pace alone does little to trouble international-quality batters. Pairing it with variation of other attributes could be the way to go.