Confirmation Bias and Ball Four

Imagine the following scenario:

A pitcher has been pitching a relatively decent game, showing decent control throughout the game. The pitcher has just thrown three balls to a hitter to reach a three balls no strikes count. These three pitches were all relatively close to the plate, not extremely wild. Assume that the pitcher has no desire to walk the batter and would like to throw a strike.

What do you expect the result of the next pitch to be?

Most astute baseball fans would guess a strike, as the pitcher took a little off and did his best to guarantee he did not walk the hitter.

Next imagine the following scenario:

A pitcher has a hitter in an 0-2 count. The pitcher would obviously like a strikeout and would love to get the hitter to chase a pitch. The hitter doesn't want to strike out and will likely swing at not only a strike, but anything that he thinks is close to being a strike. The hitter sees a pitch and does not swing.

Do you think the pitch was probably a strike or a ball?

This one seems even easier. It seems borderline near certain that the pitch was an obvious ball.

What these two thought experiments show is the following: in a 3-0 count, we expect pitchers to throw strikes and on 0-2 counts where the hitter doesn't swing, we expect that the pitcher threw a ball. It's reasonable to believe that umpires, who observe a LOT of baseball, have these same sorts of observations. They know that in general those tendencies hold true. They actually can't unknow this, even if they wanted to.

Which brings me to the new-ish book Scorecasting by Moskowitz and Wertheim, and particularly the first chapter on omission bias.

Amongst other claims, the two authors attribute the fact that umpires are more likely to call a 3-0 pitch a strike and an 0-2 a ball to omission bias. For the unitiated, omission bias is the idea that we view it as worse to do something bad than to not do something equally good. That an action leading to a bad result is worse than an inaction leading to the same bad result. Wikipedia has a more thorough explanation here.

Now omission bias obviously exists and has been proven to be something our brains do in a myriad of psychological studies. However, I think Moskowitz and Wertheim are a little cavalier in their ascription in at least the case with umpires calling balls and strikes.

There is another type of cognitive bias, that is very well known and is believed to be amongst our strongest and most difficult to overcome cognitive biases: confirmation bias and a sort of subranch of confirmation bias, selective perception.

Confirmation bias has been well understood for a long time. We tend to interpret things in accordance to the current understanding we have of the world around us. Confirmation bias isn't so much about seeing what you want to see, as much as it's about seeing what you expect to see. Some people in fact refer to the phenomenon as expectations bias. When an observed event doesn't conform to our beliefs, we either twist it in such a way that it does or discard it entirely as a mere aberration. We see what we expect to see, for the most part.

The strange thing about this sort of bias is that in many cases, it can actually make our perceptions more accurate, unlike most cognitive biases. Say for instance that you see a bird shooting by and you really didn't see enough of it to know what color it was, but you know that a lot of crows live near by and often fly by your window. Without you actually thinking about it, you will likely have "seen" the bird as being black. Now this is obviously going to much more accurate than if your brain picked random colors to see the bird as. However, it makes you biased against seeing blue birds.

It is my belief that this type of bias is the primary reason behind an umpire's actions when calling balls and strikes. The umpire knows that on 3-0 counts a pitcher is substantially more likely than normal to throw a strike and that hitters often "take all the way" on 3-0 counts, regardless of where the pitch is, hoping to eventually draw a walk. Likewise, umpires know that pitchers are more likely to "try to get a hitter to chase" a ball on an 0-2 count and that hitters will usually swing at anything close.

So what would this theory of the explanation predict? Well, one thing to notice is that on 0-2 counts, the umpire has two pieces of information when a hitter doesn't swing: 1) that it's an 0-2 count and 2) that the hitter didn't swing. This is in opposition to a 3-0 count where the hitter probably won't swing unless he's Jeff Francouer or it's the one pitch in the one tiny area the hitter is looking for. There the umpire only has one piece of information, that it is a 3-0 count. Therefore we would expect the "bias" to be much more magnified for 0-2 counts than for 3-0 counts. The umpire has twice as many reasons to think the pitch was a ball on an 0-2 count where the hitter failed to swing than he has reasons to think a pitch was a strike on a 3-0 pitch where the hitter failed to swing.

Luckily Moskowitz and Wertheim provide us with these probabilities and this prediction turns out to be wildly correct. On an 0-2 pitch that a hitter doesn't swing at, that is in the strike zone, the umpire calls the pitch a strike just 57.7% of the time. This is in comparison with 80% accuracy calling a strike a strike in all cases. That's a whopping 22.3% difference in accuracy. Compare this to the opposite situation, a 3-0 count where the pitch is actually a ball and the hitter doesn't swing. Here the umpire calls a ball a ball 80% of the time on 3-0 counts, in comparison to getting the call right 87% of the time on all counts. A mere 7% difference. While Omission bias wouldn't really explain why this difference in differences should be so stark, 22.3% v. 7%, confirmation/expectations bias does.

There are a lot of other studies that could be done with ball and strike data combined with pitch f/x data to figure out which effect is more likely driving the phenomena. For instance, we could study the correlation effect of whether or not a pitcher throwing a lot of strikes on a given day makes an umpire more likely to call a given pitch a strike. Expectation bias would seem to predict that the old baseball observation that you've got to establish that you can throw strikes before an umpire will give you a borderline call might have some truth to it. Omission bias would say nothing about this effect. Likewise we could examine whether or not hitters that are known to have a "good eye for the strike zone" get more borderline pitches called balls. Again, this would go along with traditional baseball observations and beliefs, but it needs to be studied more thoroughly than simply trusting traditional beliefs. Stepping away from balls and strikes, we could study whether or not an umpire is likely to call a good basestealer safe incorrectly on stolen base attempts. Expectation bias would say that since the umpire expects that the runner will likely be safe, he's more likely to call him safe in borderline cases.

I'm not saying that omission bias plays no role in this phenomenon. What I am saying is that we should really look at confirmation/expectation bias more closely, because there is at least some evidence that it could play a role, if not the major role in explaining this phenomenon.