Toss decisions: it's complicated

Recently, I wrote about how the toss-decisions made by captains before games were probably sub-optimal. I stand by everything said within that article (which concluded with me claiming that I would have a better record than the average T20 captain were I the one making decisions) but there were complications that I chose not include. This post exists to demonstrate that interpreting even the simplest data is often far from straightforward - and the capacity to confuse cause and effect is always present

Let's start with what I said in the previous article:

  • IPL captains who win the toss and bat first lose more than 50% of the time
  • One explanation for this trend is that captains are resistant to the idea that their ability to read the conditions is often irrelevant
  • Another explanation is that the human brain struggles with probabilities and prefers to classify things: bat first pitch vs. bat second pitch
  • Although T20 teams are choosing to bat second far more often in recent years, they have not yet reached an equilibrium and bat second captains are still more successful than bat first captains
  • This is probably because the realisation that batting second is advantageous arrived in tandem with a greater appreciation for how to manage resources in a chase

I still believe all of that...

... but I was never under the impression that my data proved that the decisions were sub-optimal. And Ian Popplestone sent me a superb email which demonstrates why I would wrong to have that impression. After reading what I had written, he outlined a scenario in which my analysis would fail to recognise perfect decision-making from an experienced captain...

The Piddling T20 League (PTL) has just two teams - Over Piddling and Under Piddling. The 'Overs', as they're called, are clearly the better team. In normal conditions on the Piddling Village Green, where all matches are played, the Overs will win 70% of the time when batting first and 80% of the time when batting second
Piddling weather though, as locals are aware, is occasionally (on say one in five match days) subject to a strange condition known as boggling. When the weather boggles the team that bats first can chance its arm: by doing so, 40% of the time it will post an unbeatable score and 60% of the time be skittled out for a score that will never win. If it chooses not to chance its arm then the usual odds, as noted in the paragraph above, still stand
The catch is that boggling weather is difficult to identify. Strangers to the village often cannot perceive it at all. Indeed, the 'Overs' captain, Darcy Strongman, can never spot it: his guesses are no better than chance. Old Jack Hasbin is the captain of the 'Unders' and his best cricketing days are long behind him. He is a shrewd captain, though, and a great reader of boggling weather. He has a 100% success rate in identifying it
Clearly... if the 'Overs' win the toss they should always choose to bat second. They'd only be guessing on weather conditions and most of the time would be conceding 10% of their advantage by batting first
And if the 'Unders' win the toss they always know exactly what they should do. They bat second, except when the weather boggles, when they bat first and chance their arm
Martha Hasbin, Jack's aunt, has scored the matches since she was a young girl. She has produced a simple spreadsheet that shows the upshot of all of this to be: a 56% chance that the team batting second wins the match, a 54% chance that the toss winner wins the match, a 72% chance that the Overs will win. This justifies the Strongman tactics of batting second, given that he can't read the conditions
Needless to say, this is all very confusing for outsiders or newcomers to the village. Even the reporter for the NewTown Chronicle, who visited Piddling to write up this year's PTL, having cast his eye over the stats noted in his column that he "would bat second every time. And history would judge me more successful than the average Piddling T20 captain"
Jack Hasbin is at this very moment writing his first letter to the Chronicle to offer up his thoughts on this

Presumably, I play the role of the NewTown Chronicle reporter in this fantasy. The data that this scenario produces would fit wholly within my argument in the first post on toss decisions. And in this case, I would obviously be wrong

The point is that underdogs should often adopt a high variance strategy whilst favourites are best to stick to convention. The high variance strategy in the world of making T20 decisions might be to take a gamble on pitch conditions helping to cause an upset. And this is exactly what happens in real life... using a model that uses the aggregate strength of the players on each team to decide a favourite, I found that underdog captains are much more like to chose bat-first than the captains of stronger teams

Underdog captains are more likely than their counterparts to adopt a high risk strategy - chosing to bat first in T20 games after winning the toss

With all that said, the percentages and probabilities that Ian uses in his email are extreme. And hopefully, in real life, astute captains who can read the conditions do not solely captain underdog teams. It would be preposterous to conclude that the underdog/favourite dynamic completely explains why toss-winning captains seem to make poor decisions. I am certain that those psychological biases play a large role. And there are surely other factors that I haven't considered

What this does show is that even when you have the most simple data to interpret - which team is at home, which team won the toss, and which team won the match - making conclusions is not equally simple. So when trying to decipher strike rates and averages in a high-variance game, among different match situations, against different opposition, and on different pitches... all compounded by very small sample sizes... even the best analyst will struggle to identify truth