All sports, we know, are games of probabilities. What is the right thing to do in any given situation? Given enough information, math can solve the problem. There is never perfect information, of course, and this is muddied by the fact that short-term results are no indication of whether a team’s tactics or strategy are correct. Decision-making is complicated.
It is even more complicated by incentives. Sometime, a player’s interests all align in just one direction. A 100m sprinter explodes off the blocks with just one imperative in mind: run as fast as you can. But sometimes, in sports, conflicting incentives collide. The same player can have two different sets of incentives pulling them in different directions. How do you play the probabilities then?
This column looks at three situations with different levels of complexity. In all of them, the player involved needs to weigh up probabilities. In one of them, the incentives go in one clear direction, but the decisions nevertheless are complicated. In the other two, there are two rational and opposite ways to behave. Which do you choose?
In this piece, I will write about Harmanpreet Kaur and Mithali Raj. I will lay out the dilemma that Cheteshwar Pujara and Ajinkya Rahane face. But first, I want to talk about chess, and why big decisions in chess may sometimes not involve what is happening on the board.
Magnus the Misunderstood
Magnus Carlsen is the World Chess Champion, and also the No. 1 chess player in the world. Fabiano Caruana is his challenger, and the No 2. Their ratings are almost the same, the first time Carlsen has had a challenger so close to him after years of dominance. They are evenly matched.
They just played a World Championship match of 12 games. These 12 games were at what is known as classical time controls. Games can be long, and can last hours. Think of it as Test cricket.
The rules stipulate that if all games are tied, the players will play a series of rapid games. If those are tied, they will play blitz. In the first, each player gets around half an hour each for the entire game. In the second, just five minutes. Carlsen is better than Caruana at both formats. Much better – in fact, Caruana is bizarrely bad at those formats, relative to other top players. So while they are evenly matched in classical time controls, Carlsen is a huge favourite in the shorter tiebreaks.
The last time Carlsen defended his title, under identical terms, against the Russian Sergey Karjakin, he entered the 12th game with scores tied. Even though he is a better player, he opted for a quick draw in the 12th game because he was a much bigger favourite in the rapid and blitz formats. Also, there would be multiple games in the tiebreaks, and one mistake would not be finis.
The same situation came about in this match, with one exception: in the middle of that 12th game, on Monday, Carlsen had a far superior position, and Caruana was short on time. Commentators thought it a no-brainer that Carlsen, who is known for squeezing wins out of dead situations, would go for the win. Instead, he offered a draw, stunning his opponent and the rest of the chess world.
The former world champion Garry Kasparov even complained on Twitter:
In light of this shocking draw offer from Magnus in a superior position with more time, I reconsider my evaluation of him being the favorite in rapids. Tiebreaks require tremendous nerves and he seems to be losing his. — Garry Kasparov (@Kasparov63) November 26, 2018
There can be various reasons for why Carlsen offered the draw. One is that he entered the game deciding to take zero risks, since he was such a huge favourite for the tie-break. He could not snap out that mindset, and took the draw when he could.
But I don’t believe that you need to take his drawing mindset (for the game) into account. Independent of that, I can see why his decision would make sense. Let’s consider some numbers.
In the position on the board, trying to win would mean taking some chances, and opening up the small possibility of over-reaching and losing. So let’s say the game is drawn 70% of time, Carlsen wins 24% and loses 6%. So 80% of the decisive results are in his favour. Therefore, he should press for a win only when his chances in the tiebreak are less than 80%.
He is a huge favourite in the tiebreaks, and probably did think his chances of winning that were more than his chances of winning this. In that case, offering a draw even in that superior position made complete sense.
The numbers I’ve thrown out above are speculative. But whatever the actual numbers are, it is clear to me that Carlsen was in the best position to estimate them. His offering the draw, thus, may not have been a sign of fear but of confidence.
The tie-break match takes place tonight, by the way, and you can watch the live coverage here. Who knows, Carlsen may even lose. But that would not mean that he took the wrong decision.
Pujara and Rahane: Self vs Country
Virat Kohli is trying to build a modern Indian team in his image: bold, aggressive, always taking the attack to the opposition. Two of the stalwarts of his Test middle order, Cheteshwar Pujara and Ajinkya Rahane, are old-school grafters. You could say they are the Caruanas of Cricket. They are a liability to their sides in the shorter formats, and correctly no longer part of their sides in ODIs and T20s.
Even in Tests, they are often expected to bat more aggressively by their captain. But their place in the side does not depend on the captain alone, but on selectors and public opinion. They have a bunch of incentives pulling them in different directions, and they could act in the following ways.
One, do what the captain wants, and play aggro, against your own instincts. This strategy has higher variance. If you go through a prolonged bad run, you get dropped for following their captain’s instructions.
Two, ignore Kohli, and grind out enough 40s and 60s to keep your place in the side, even if the captain does not like the way you played, and your approach hurts the team. Score enough so you can’t be dropped. Self before nation.
Three, ignore Kohli and grind, but not because of selfish reasons. You genuinely believe that the captain is wrong, and that grinding is what the team needs. (Other non-Kohli batsmen are failing around you for trying to be too like Kohli.) Also, in Rahane’s case, you are the vice-captain, everyone likes you, and you could be the next captain. Hang in there.
I am not saying that the above scenario is necessarily true, or that it is the only scenario out there. Life is more, not less, complicated than this. But it is true that in a team sport where you are judged on individual performance, incentives do collide. That makes the probabilities even more complicated.
Even if you had perfect information and a mathematician’s brain, which outcome do you aim for?
Harmanpreet Kaur came under much flak recently for dropping Mithali Raj from the side in the women’s T20 World Cup semifinal. Raj had been grinding out slow 50s in previous games, and Kaur clearly felt that her pace was a liability. (Indeed, when a player whose strike rate is substantially slower than the required rate or the rest of the team, the more runs she makes, the greater the cost for her team.)
I don’t want to get into whether this is true or not, or whether the fact that this was a tough pitch justified playing Raj anyway, because resilience gained in importance against momentum. Let’s assume this is true, and then examine the decision Kaur faces.
On one hand, Kaur needs to do what is best for the team. If this requires dropping her hero and former captain, so be it.
On the other hand, this guarantees a backlash against her if she loses. If she picks Raj and loses, no one is going to be hard on her because hey, the girls tried their best. But if she drops Raj and loses, she is going to be excoriated, as indeed as has happened.
So Kaur has to balance what she believes to be good for the team against what is good for her captaincy and reputation. Let’s say she believes that dropping Raj increases India’s chances of winning by 10%. But in case the team loses, it increases Kaur’s own chance of becoming a scapegoat by 100%.
This doesn’t mean that she took the wrong decision. It means she took a brave decision. Team over self. Although I am a big fan of Mithali Raj, I give credit to Harmanpreet Kaur for courage.
An aside: from the outside, it strikes me that one possible decision would have been to play Raj, but to bat her low down at 6 or 7, where she could not bring down the team strike rate if things were going well, but could bolster the tail if there was a batting collapse, as indeed there was. But I say this in hindsight and with limited information. The captain is always best-placed to make this call.
So what’s my point of laying out these three situations? Just this: when judging the quality of a cricketing decision, we must take into account both probabilities and incentives. But too often, we do armchair commentary from a distance, taking only the result into account. Our heroes deserve better.
(Amit Varma is a writer based in Mumbai. He has been a journalist for 15 years, some of it in cricket journalism as managing editor at Cricinfo. He has won the Bastiat Prize for Journalism twice. He is currently editor of the online journal Pragati, and a columnist for the Times of India).