Rationality and the sportsman - an introduction

Sport is all about making the right decision. It is Wimbledon. The sportsman is up 5-4 in the fifth. It is 40-30. Championship Point, second serve. Does he go for the big one out wide and close it out? Does he put the second serve in and play it out? He is dead tired after two weeks of gruelling tennis. He does the former. He serves a double fault. He goes on to lose the game and the Championship. People will say that he made the wrong decision.

It is the final of the world cup. One run to win. One ball. The field is up. The sensible thing to do would be to play it along the ground and make a dash for it. The batsman, however, sees it as a chance to hit above the infield, reasoning that he has a better chance of clearing the infield. The trade-off, in this case, is that with it comes a greater risk of an edge going through to the keeper of the slip. The batsman decides to take the risk. The ball is pitched up. It just clears the infield. He has won the world cup.

In both the above scenarios, there were two choices that the sportsman was faced with. One of those choices involved risk; the other – a certain degree of risk, albeit a much smaller one. In the first, the sportsman decided to go for glory. He copped out. In the second, the sportsman decided to go for glory. He scraped through. The former is vilified; the later, glorified. This is what sport is all about. Decisions.

There is a branch of science that deals with decision making. Aptly, it is named Decision theory. However, decisions are not made purely on a scientific basis alone. If they were, they would be purely logical, machine made. Man made decisions, however, tend to involve a fair bit of art that goes with the calculated science.

The premise of decision theory is that it considers human beings to be rational; to be more precise, boundedly rational. To be rational, the decision maker is to exhibit certain characteristics. First, there must a consistency in his choice making. The choices, in other words, are to be transitive. Simply put, if he prefers Option A to Option B and Option B to Option C, he must choose Option A to Option C. Simple, really.

The second is that if he has a set of choices, he must rank them in an order that is based on what he defines his utility function to be. By utility function, one means that everyone has a certain utility or, to put it in simpler terms, usefulness for a set of choices. It is only when one can rank his choices based on this utility function that one can be deemed rational.

How does this apply to sport? Well, let’s look at cricket. In a T20 game, a batsman has the propensity to hit it in the air and play more attacking cricket. Now, in this form of the game, his utility function is such that a six or a four has a higher pay-off than if he loses his wicket. However, if the same scenario were a Test match, the batsman is more circumspect. This is because even if he misses out on one ball, he has plenty of more opportunities to make amends. There, preservation of his wicket has a greater utility for him.

The third, and perhaps the most important aspect, is that of bounded rationality. The meaning is simple: Human beings, even if they have complete information, have only a limited processing power. In the first place, it is almost impossible to have complete information about any situation and even if it is available, human beings only have a capacity to process a part of it. Thus, the rationality in human beings is bounded.

It is the last minute of the Champions League final. The sportsman’s team has the ball at the edge of the opposition box. The sportsman seemingly has two choices: shoot or pass. He looks up. He sees a team mate making a run into the box. He thinks about the pass. He looks up. The goalkeeper is slightly off where he ought to be. He thinks. He takes a shot. It flies into the top corner; he is a hero. It flies into the fifth tier of the stand; he is a villain. What does he do? There is quite simply too much information to be processed. That is where the heuristic comes in. His gut tells him something. Muscle memory tells him something. He does that.

Decisions make sport. Thus, looking at sport through the eyes of rationality could be an interesting exercise, one I hope to take up in slightly more depth in a few subsequent articles. Until then, I leave you with a simple exercise. Think of the greatest sporting moment that you have witnessed. Now look at the sportsman in question. Look at the single most important decision that he made that led to that moment. Think about it. What would’ve happened if he’d taken an alternative that was not the one he did take? How would history have been different?