For the first time since I was a teenager in the 90’s, this year I followed baseball quite closely. Baseball doesn’t seem to be all that much different now than it was then, as far as I can recall. It has always been heavy on the statistics relative to other sports, and the stats themselves have gotten a bit better. The managers do more “extreme” things than when I was younger. For example, I often see an infield shift so fierce that the third baseman stands where the shortstop usually stands, and the shortstop, second baseman and first baseman all stand on the right side of the infield. Even announcers have gotten in on the game too, presenting more unusual statistics than just “batting average”. For example, if it is interesting, they often show the “spray” of a hitter, indicating the number of times they hit the ball to various areas of the diamond. Or they will break up the strike zone into various “sections”, and show hitters success rates when the pitch arrives within the various sections.

My perspective on the game has changed slightly as a result of experience (and education). I am better able to view the game statistically than when I was younger. This is a subtle change, but rather than viewing events as “successful” (for example, a player I like getting a hit) or not, I think much more globally and with “shades of grey”. As in, these are the stats, and here is what we can globally predict based on that. This is a property we are trying to minimize or maximize, and so let’s examine some reasonable strategies to see how well they achieve the objective.

Thinking of events as either “successful” or “unsuccessful” often fools humans into having silly goals. For example, this is a profile of a basketball player, Shane Battier, who is a defensive star. One strategy that only he uses is that instead of trying to block shots on defence by putting his hand in front of the ball, he always tries to stick his hands in front of the shooter’s eyes. This fascinating strategy requires a step away from a “successful” or “unsuccessful” viewpoint, and a focus more on the global, statistical viewpoint. Indeed, if he tries to stick his hand in front of their eyes, he is blocking the shot 0% of the time. If his goal is to block shots, this approach is “unsuccessful” 100% of the time! With the traditional blocking shots approach, the goal of getting the shooter to not even get the shot off is “successful” some of the time. This is a subtle idea, because if a shot is blocked, then guaranteed, they aren’t going to score on that shot. But that guarantee might really come at hidden cost.

If we remember that the strategy of blocking shots is not really the goal, then we can try other, more “shades of grey” strategies, that may not come with a guarantee. If instead, the goal is to minimize the number of points scored by the opponent, it might actually be better to sacrifice the goal of the opponent not shooting altogether. Essentially, the “blocked shot” strategy can get you trapped in a local maximum.

A very similar example of this same phenomenon is discussed in this article on the second serve in tennis. To briefly summarize, modern tennis players can serve extremely fast, and the faster they serve, the harder it is for the opponent to score. However, the harder they serve, the less accurate they are at getting the serve inbounds. And, on each point, the server gets two attempts at getting the serve inbounds before they lose the point. The general strategy has always been to use the first serve to serve as fast as possible, knowing that if they are unsuccessful at getting it inbounds, there is still a second chance. And, should the first serve fail, the server essentially always serves considerably slower, then raising the probability that they will not double fault. But at the same time, this raises the chances that the opponent will get the point. But the problem is that “getting the serve in” isn’t really the thing we should be trying to maximize. It is merely an interim strategy in the larger goal of trying to maximize your chances of getting the point. It is again very deceptive because if you don’t get the serve in on the second serve, then guaranteed, you will not win the point. But, as described in the article, it seems that they would be better off statistically to serve fast all of the time. Thus, thinking of the serve as being “successful” or “unsuccessful” could be causing a problem. Instead we should realize that the serve being inbounds is just a strategy, and not the main goal, and there might be a better strategy, without a guarantee, that maximizes the chances of getting a point. ¹

Humans do not have fine-grained control over our own motor systems. We can’t predict the precise results of our own motor systems, or of our opponents. There are a ridiculously large number of moving parts, and with such a huge number of parameters to any kind of a complex computational system, we can’t think about all of them in our own heads. The next best thing we can do is to ignore some information, establish some rough patterns and think statistically. We are stuck thinking in shades of grey.

¹ As discussed in the tennis article, the optimal strategy may not be to serve fast all the time, but something more subtle. Indeed, it could be that tennis players do not have the energy to serve fast for a whole match. But still, it seems possible to me that tennis could employ strategies which are crucial in baseball, such as deliberately altering speeds to throw off the prediction mechanisms of the opponent. Perhaps serving fast 30% of the time on the second serve would be better. It seems clear that the current strategy is not the optimal one.