Toss decisions: worse than random

Sometimes even the simplest predictive models can be revealing. I am currently starting my own mini project to predict match outcomes based on team form and individual player ratings. My first step was to understand the importance of (1) being at home, (2) batting second, and (3) winning the toss. The expectation was that all three would increase a team's chances of winning... but I was wrong

Before going any further, I should note that all the stats used in this post are from the IPL (all 10 seasons). I have also excluded matches where the overs were cut short for some reason (e.g. rain). There are obviously many other T20 competitions and the percentages do vary depending on competition. But the overall story is largely consistent. Numbers from the Big Bash and the Caribbean Premier league match the IPL closely. I have included the the relevant numbers from each league at the end of this article

IPL toss bias.PNG

Being at home in the IPL gives the team a 1% advantage. Batting second gives the team a 5% advantage. And winning the toss gives the team a 2% advantage. That may all seem to conform to common sense but a closer examination of those figures reveals an inconsistency: how can winning the toss possibly be less advantageous than batting second?

There have been 151 occasions where the home captain has won the toss and opted to bat first. I'm sure there are many reasons for doing this, relating to weather, lighting, grass, dew, or whatever else cricket experts know more about than I do. Having made their expert judgement and opted to bat first, they have gone on to win the match 49% of the time

This might be obvious... but that is worse than a coin flip. Despite having two apparent advantages - being at home and winning the toss - their teams were less successful than if the captains had just agreed to decide the match on the toss of another coin

The illusion of control is the tendency for humans to overestimate their ability to control events. There is a deep-seated psychological need for coaches and captains to believe that their knowledge of pitch conditions is important. The following is copied and pasted from the pertinent Wikipedia article:

Ellen Langer, who first demonstrated the illusion of control, proposed that people base their judgments of control on "skill cues". These are features of a situation that are usually associated with games of skill, such as competitiveness, familiarity and individual choice. When more of these skill cues are present, the illusion is stronger

In other words, even if it were true that the captain should always chose to bat second in T20 - and I am not saying that it is - it would be a difficult reality for cricket insiders to accept. They may even prefer to lose the toss and watch the opposing captain make an informed choice, rather than simply relinquish control to the whims of a coin. At least then you are being defeated by skill, not random chance. Even if a coin toss actually makes winning more likely

We humans are also very poor at dealing with probabilities and this plays an important role here too. Let's imagine that we are all omniscient pitch-evaluating gods who are assessing conditions before a coin toss. We conclude that batting second would give us a 53% chance of winning and that batting first would give us a 52% chance of winning. Normally, the difference between these two probabilities would be greater - more like 56% to 51% - but on this day the conditions are bat-first friendly and reduce that disparity. But we would still obviously choose to bat second: 52% is still better than 48%

This is not how a human brain reads the situation. A human brain finds such fine gradations in probability hard to process. I would not be surprised if some readers had to reread that last paragraph to make sense of it. A human brain wants things to be binary: good pitch / bad pitch. My belief is that captains are likely to interpret the situation as, "This is a bad pitch for batting second and so we should bat first." The assessment - bad pitch - is correct... but the conclusion is wrong

During the Ashes, Joe Root made the controversial decision to bat second at Adelaide. It feels like that was a more extreme version of T20 captains choosing to bat first. Former Australia captain Ian Chappell once said: "At Adelaide, 99 per cent of the time, if you win the toss, you bat first and the other one per cent, you think about bowling and then you bat anyway."

Joe Root understood that the overhead cloud and the cool forecast meant that batting second was a reasonable option. He had analysed the situation using 61 matches previous Test experience as his guide and made a shrewd assessment. He was within Chappell's 'one per cent'. If there were ever an occasion to bat second then maybe this was it, but the reality is that the advantages of batting first at the Adelaide Oval are so great that he should have batted first anyway

With almost no understanding of cricket pitches whatsoever, I would bat second every time. And history would judge me more successful than the average T20 captain (assuming that I don't have to actually play)

Reassuringly, the rest of the cricketing world seems to be catching up. The last two seasons of the IPL saw 84% of toss-winning captains chose to bat first vs. 53% during the first eight seasons. The same trend exists in the Big Bash


Unfortunately, captains who chose to bat first are still winning less often (40%) than captains who chose to bat second (63%). Just as teams are starting to realise the benefits of batting second (primarily the ability to better manage resource) they are also becoming better at it. Which perhaps isn't so surprising

Basic principles of game theory tell us that captains may still be batting first too often. We have not reached the Nash Equilibrium. Only when teams are just as likely to win after choosing to bat as they are choosing to bowl will we have reached something close to optimal decision-making. At that point, winning the toss should proffer a greater advantage than simply batting second every single time

All leagues choice bias.PNG