Conversion Rates, Drive And The Value of A Wicket

The value of a player's wicket is intertwined with their conversion rate and how well they perform after reaching a milestone.

Why do certain players have lower conversion rates than others, have more 50s than 100s? Why are some players less likely to reach double hundreds than others?

I stumbled upon a theory that could shed light on the question while I was investigating the issue of just how to assess the value of a wicket. The idea was prompted by a desire to find a way to properly calculate the value of a modern tailender's wicket compared to their predecessors.

The general wisdom of assessing the value of a wicket is to check a batter's average. What that means is that a batter's wicket's value is the number of his average the moment they walk onto the crease. So, if a batter who averages 45 is dismissed on 10, it means that the bowler has saved 35 runs worth of damage.

The problem with that is the fact that averages are often bolstered by not outs. The average is a player's total runs divided by their number of dismissals. Not outs are considered to be open stories that could go anywhere, incomplete innings. This unsettles me because they inflate averages. (But, that is an article for another day.)

Conversion Rate Issues

On average, most batters are susceptible to dismissal early on in their innings, as they play themselves in. As Oliver G. Stevenson and Brendon J. Brewer explained in their paper, "Bayesian survival analysis of batsmen in Test cricket," even the best batters kick off their innings with the batting ability of a player with an average of 13.2 runs.

At that point, their wickets are of low value because the batters are "walking wickets." However, after they settle in, they all have different probabilities of getting dismissed at different times. For example, take Kane Williamson and Faf du Plessis. In the bulk of his career, Faf du Plessis could score hundreds, but he did not often kick on to a big hundred, a double hundred or more. He scored "small hundreds." Therefore, the value of his wicket technically decreased once he passed the hundred mark.

The same thing can be said of Joe Root. Even though Root has a number of hundreds and a few double hundreds to his name, his conversion rate is generally poor. (40% conversion rate.) Once he reaches the 50-run mark, regardless of how good he is playing, he somehow manages to get himself dismissed.

Therefore, his average runs after 50 is a bit low. Similarly, Du Plessis' average runs after reaching a century is low. They do their most damage before these milestones.

This is different from Steve Smith or Kane Williamson. (87% and 75% conversion rates respectively.) Williamson and Smith, because of their higher conversion rates, getting to 50 is a set-up, they are just getting started. And once they get to a hundred, unlike players like Faf du Plessis, they are more likely to kick on and amass huge totals.

Therefore, the value of Smith or Williamson's wicket either remains constant or rises after a milestone. On the other hand, the value of Du Plessis or Root's wicket somewhat decreases after a certain milestone.

So, what happens?

Drive, Caution And Conversion

One of the most common things that happen as a batter is approaching a milestone is that their strike rate dips a little. The most common explanation given is that they are nervous, "nervous 90s" and "nervous 40s."

But, I have an alternative view. As players draw nearer to a milestone, they become more cautious, more motivated and more focused because of the value they place on the milestone. As statistics show, players are less likely to be dismissed in the 40s and 90s  than they are susceptible to be dismissed in the 30s or 80s. On average, players have a 22.8% chance of dismissal in the 30s and a 21.9% chance in the 40s. They also have an 18.2% likelihood of dismissal in the 80s and a 17.6% in the 90s.

The closer they are to a milestone, the lower the chances of their dismissal.

What is even more interesting is the fact that (unless they are a Brian Lara type of batter) most batters are more likely to be dismissed soon after they reach a milestone. Most batters are 9% more likely to be out for exactly 100 than they are to be out for 99. Also, they are 17% more likely to be out for 50 than 49. The reason being that most batters fall prey to the "milestone relaxation phenomenon," and lose concentration as a result.

One very telling thing that speaks loudly about the change in attitude, from focusing on a goal or reward is the rise in run-rate after a batter has just crossed a milestone threshold. For example, in ODI cricket the average batter's strike rate in the 80s is 111.9%. In the 90s that plummets to 105.5%, and then spikes to 142% between the numbers 100 and 109. In Test cricket, it is not uncommon for the run-rate to decline by more than -30% in the 90s, before spiking by +40% or more.

And there is a neurological explanation for this.

In their 2018 paper, "Drive in Sports: How Mental Fatigue Affects Endurance Performance," Lieke Schiphof-Godart, Bart Roelands and Florentina J. Hettinga discuss the factors surrounding drive in athletes.

They discuss two important things in regards to dopamine and athletes. 1.) Lower levels of dopamine deactivate facilitative brain centres (normally responsible for motivating behaviour and increased drive toward a reward), also resulting in the decreased drive. 2.) Higher levels of dopamine in the brain can ‘push’ athletes toward action and exerting effort and influence the decision ‘not to give up,’ especially under difficult circumstances.

In other words, dopamine increases athletes’ attention toward rewarding goals, and this includes milestones. Each time a batter reaches a milestone, they feel a sense of accomplishment. They have met a rewarding goal. And once that happens, the brain decreases the concentrations of dopamine it releases, which leaves them slightly mentally fatigued, less motivated and less focused.

This is the "psychological barrier" that many commentators and analysts speak of. It happens because of an unconscious goal-setting program in our brains. This goal-setting program is the result of what the sport established to be the mark of great batting. Centuries and half-centuries are highly regarded and batters are conditioned to strive for either or both to prove their worth.

One indication that most batters lose focus and get into "celebratory mode" is highlighted by the rise in their strike rate immediately after reaching a milestone. They are engulfed by a sudden sense of euphoria that they become less cautious. The goal has been achieved, so why remain acutely focused? At that point, the brain deactivates the facilitative brain centres

The batters that have higher conversion rates or manage to kick on, either have a higher milestone as the mark of accomplishment or manage to quickly recenter themselves and start a new pursuit of a bigger milestone. Either way, they do not feel a sense of accomplishment at those milestones enough for their brains to decrease the concentrations of dopamine it releases. Or they do feel it but do not spend a lot of time savouring it before setting a new goal immediately.

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