Several years ago I took my older daughter on a fossil hunting trip in the Cretaceous Badlands of western Kansas, in what was then the Western Interior Seaway. After just a few minutes of struggling to see the bits of fossilized bone, shell, and teeth that our guide could see so well, the concept of "search image" had become crystal clear for both my daughter and myself. The basic idea is that we see what we're trained to see. Our minds interpret the data coming from our eyes using predefined patterns that have been influenced and built up from experience. So to our guide, what was clearly a shark tooth of the species Cretoxyrhina literally right in front of our noses, was for us simply another piece of jagged rock. I'm happy to report that we eventually caught on and made a contribution or two as the day wore on.
I was reflecting on this experience as I examined the called ball and strike accuracy of umpires when broken down by count. To understand why this happened examine the following table, keeping in mind that the mean CSAgree% is 81.4 percent and the mean CBAgree% is 94.6 percent:
Count Pitches CS CSAgree% CB CBAgree% Agree%
1-0 6653 2690 .803 3963 .945 .887
2-0 2349 1078 .828 1271 .943 .891
3-0 1155 710 .883 445 .948 .908
1-1 5066 1199 .772 3867 .950 .908
1-2 3871 400 .670 3471 .962 .932
2-1 2359 616 .756 1743 .952 .901
2-2 2637 336 .732 2301 .969 .939
3-1 1048 388 .799 660 .952 .895
3-2 1168 184 .788 984 .966 .938
0-0 20415 8960 .837 11455 .928 .888
0-1 6971 1450 .790 5521 .944 .912
0-2 3078 233 .695 2845 .968 .947
Now, take a look at the bolded numbers. They differ in a statistically significant way from the overall mean at the 95 percent confidence level. Notice how far they deviate from the means--at 3-0, over 88 percent of called strikes are actually strikes, while at 1-2 and 0-2 the percentages drop to 67 percent and 69.5 percent, respectively. In other words, at 3-0 (and 2-0 to a lesser extent), umpires are more likely to see the pitch as a ball, and with two strikes (likewise at 2-2), they're more likely to see the pitch as a strike.
Note that in the cases where there are two strikes this is exactly the opposite of the intent of the pitcher, where experience tells us they typically try and get hitters to chase, and therefore should result in more thrown balls. One possible explanation is that umpires, even in the short span of several pitches, have their search image modified, and as a result tend to model their calls on the prevailing trend.
What this indicates is that while umpires may, in the words of George Will, be "natural republicans–dead to human feelings," they are prone to at least some of the same biases and perceptions as the rest of us.