The count is one of the most basic parts of the game of baseball. The rules have been the same for over 100 years: 4 balls for a walk, 3 strikes and you're out. The pitcher/batter interaction is also one of the most fascinating parts of the game, with each side often trying to out-think and out-guess the other. The batter may think he knows what's coming, but he can never really be sure, while the pitcher may think he can outfox a hitter, but he never really knows what the batter is looking for either.

Of course, everybody knows that the count is integral to a player's chances of success. Give even a mediocre pitcher an 0-2 count to work with and he can retire the game's greats with ease, while even the best pitcher has trouble pitching to a batter with a 3-0 count. But does the count really change the pitcher's and the batter's strategy, or do players essentially approach each pitch the same, regardless of count. Furthermore, if the strategy and approach does change, does either side gain an advantage?

Pitch Outcomes by Count

Using Retrosheet data from the 2007 season, I first looked to see how often each potential outcome of the pitch occurred. Excluding any at-bats in which there were bunt attempts or intentional balls, the results were the following:

36.8% of the time, the pitch was thrown for a ball.
26.6% of the time, the pitch was thrown for a clean strike (either called, or swinging).
16.9% of the time, the pitch was fouled off (which means 43.5% of pitches were either clean strikes OR fouls).
19.7% of the time, the pitch was hit into play

But, do these numbers stay constant no matter the count? After all, the goal remains the same. For the pitcher: get a strike past the batter. For batters: either take a ball or hit the ball hard. Perhaps strategy remains the same as well? The following table shows the same breakdown by count. If the pitcher and batter do not adjust their strategies according to the count at all, we would expect these percentages to stay the same no matter the count. Do they?

To even casual fans of baseball, it is no surprise that the rates of balls, strikes, fouls, and hits changes depending on the count. It comes as no shock that the percentage of strikes goes up in hitters counts such as 3-0 and 3-1, and the percentage of balls rises in pitchers' counts such as 0-2. Likewise, the batter is much more likely to put the ball into play in deep counts, while he is not very likely to hit it into play on the first pitch, or especially on a 3-0 count. None of this really comes as a surprise to anyone, and falls in line with conventional baseball wisdom.

It's clear then, that players do indeed change their strategy based on the count. But how does this shift in strategy change the final outcome of each plate appearance? To test this, I ran a simulation to simulate whether each at-bat turned out to be a walk, strikeout, or a ball in play, assuming that each pitch had the same ball/strike/foul/inplay probability regardless of count. I then compared this to the actual outcomes.

The following chart shows the difference between the BB/K/In-play rates in the simulation (where it is assumed both the batter and pitcher are blind to the count) and the real outcomes.

One thing to notice is that the overall walk and strikeout rates are generally slightly higher in the simulation than in real life. This is due to the fact that the batter and pitcher are more cautious on the first pitch - the pitcher is less likely to throw a strike and the batter is less likely to put the ball into play (12.6% in-play on the first pitch vs. 19.7% in-play overall). When all pitches are averaged, this lack of action carries over into other counts and decreases the in-play rate and increases the amount of K's and BB's for the simulation.

However, this effect is small and many of the simulation estimates are quite close to the real outcomes. For instance, on the 1-0 count, the simulation, which assumes that the batter and pitcher do not change their strategies, shows a strikeout occurring 14.6% of the time, while real 1-0 count data shows that the batter strikes out 13.8% of the time. Meanwhile the walk rate changed from 17.2% in the simulation, to 16.6% in real life. This indicates that there is not a major strategy shift on a 1-0 count, but in fact pitchers and batters go after each other much in the same way as they would if they did not factor the count into their approach.

Major differences occur mainly in hitters counts, such as 2-1, 3-1, and 3-2, where the true propensity to put the ball in play is higher than the simulated results, and the walk rate is much less than the simulated results. This also is no surprise, seeing that the pitcher is more likely to throw a hittable pitch when he is down in the count, and hence the batter is more likely to put it into play and less likely to walk.

A Simulation to Find Who Gains A Strategic Edge

These first two charts leave no doubt that the pitcher and batter do change their strategies, especially on more extreme counts such as 0-2, 2-0, 2-1, 3-0, 3-1, and 3-2. Of course, this shift in strategy changes the outcome of the at-bats. For instance, on a 3-0 pitch, the pitcher may change his strategy to throw a fat strike just to get one over the plate. The batter, knowing that it is a 3-0 count is more likely to try to take a pitch to draw a walk. Of course, the batter knows that the pitcher is likely to groove one, so this changes his strategy too. The pitcher in turn knows that the batter knows and he has to adjust his strategy as well. Eventually an equilibrium is reached.

Now, theoretically, If both hitters and pitchers are equally able to adjust, the equilibrium will result in neither the batter or pitcher gaining an advantage. For instance, by throwing a pitch down the middle, the pitcher may indeed avoid more walks on a 3-0 pitch, but he will have to pay for it in the form of harder hit balls and more home runs. If this trade-off becomes so extreme as to become disadvantageous to him, he will scale back this tactic and pitch more normally, varying his pitches so that the batter cannot hit him so hard, but at the expense of giving up a few more walks. The batter, likewise, is making similar adjustments. His natural inclination is to take a 3-0 pitch, but if the pitcher is consistently throwing a get-me-over fastball for a strike, he may find himself at a disadvantage, in which case he will mitigate the pitcher's change in strategy by swinging more normally. The result of all this cat-and-mouse should be theoretically that neither side gains and advantage. This final equilibrium may still be less walks and more hard hit balls, but the expected run value of the at-bat should be the same as if neither the pitcher nor the batter were paying attention to the count at all.

Of course, this is in theory. If this is not true, it indicates that the one side is gaining an advantage because the other side either cannot adjust or is playing a bad strategy and failing to adjust his thinking to the situation. We can see if this is happening by looking at the run value outcome in various counts and comparing the simulation to the real data. Below is a chart doing just that.

The chart above gives the BAV, OBP, and SLG percentages for both the simulation and the real data. It also gives the wOBA for each. The last column uses Pete Palmer's Linear Weights and shows the difference between the simulation and the real data over the course of 600 PA's at each count. This is perhaps the most useful column. Those with a positive value indicate that the batter is creating more runs than would be expected in that count via the simulation, while a negative value indicates that the batter is under-performing relative to the count.

In many counts, the simulation and the real data both produce about the same amount of runs. For instance, on the 2-0 pitch, the hitter's batting average is higher than we would expect if the players were blind to the count (.292 vs. .279 in the simulation) and the batter hits the ball much harder (.497 SLG vs. .440 SLG in the simulation), but it comes at the expense of fewer walks, with the OBP falling from .519 to .487. The overall difference in production is less than a run over 600 PA's with a 2-0 count. As we would expect, the net result is that the increased power is offset by fewer walks, and neither the pitcher nor the hitter gain an upper hand. This indicates both players are likely using an efficient strategy and not allowing the opposition to use the knowledge of the count to their advantage.

However, this offsetting does not occur at every count. The 3-0 count is obviously a hitter's count - the simulation predicts a .290/.714/.457 line from hitters with a 3-0 count. However, the true data shows hitters taking an even greater advantage of the count. The real line is .295/.720/.516 (intentional walks are removed from the data), indicating that hitters hit the ball with much greater power without sacrificing walks. The result is an advantage for the hitter above and beyond what we would expect a 3-0 count to entail if players were not strategizing about the count. This indicates that the pitcher is not able to effectively counter the batter's 3-0 strategy.

Is this true for other highly favorable hitter's counts? Looking at the 3-1 count, we see that in fact the opposite is true! In this case, the pitcher takes the strategic edge. The expected hitting line is .252/.656/.397, while the true line is .292/.590/.500. Here we again see a big increase in power, with both the slugging average and batting average increased, but it comes at a cost of fewer walks. The result is a loss of about 6 runs due to the strategizing about the count. Pitchers are more likely to throw a strike to avoid a walk, but unlike on the 3-0 count, the batters are unable to generate enough power to offset the loss of walks. The result is that the pitchers are gaining an edge.

The 0-2 count is another extreme count, in which either the pitcher or batter may take a strategic edge. In this case, it's a pitcher's count and the expected line is .192/.207/.302. This is better however, than the real line of .180/.201/.265. In this case, the batter is sacrificing power and average, without increasing his on-base percentage. The result again is a loss of 6 runs by the batter over the course of 600 PA's. The pitcher is throwing more balls dancing around the plate, and the result is less power for the hitter, but without a corresponding increase in walks. Thus the pitcher is gaining an upper-hand on the hitter.

The result of the other counts don't show either the pitcher or hitter gaining a huge edge. 3-2 and 2-2 show the batter gaining a slight strategic edge, and 2-1 and 0-1 show the pitcher taking a slight strategic edge, but the effect is small. These results don't account for the fact that potentially stronger batters are more likely to reach 3-0 counts, and weaker batters are more likely to reach 0-2 counts, which may somewhat explain the advantages seen in the real data vs. the simulation. However, this does not explain the fact that 3-1 counts seem to show the pitcher gaining an edge.

Conclusion
It's interesting to find inefficiencies in how pitchers and hitters handle the count, and it appears that the extreme counts of 3-2, 3-1, and 0-2 expose the most inefficiencies. Unfortunately, though we can see who gains an upper-hand due to knowledge of the count, it's hard to tell whether the reason is that the players are not adjusting properly due to a lack of strategy or simply have an inability to adjust. It also is difficult to see exactly how players should change their strategy to put the game back into a neutral equilibrium. Because we only have the outcome data and not how exactly the pitcher and hitters are adjusting independently, it's hard to see how hitters and pitchers could improve.

Perhaps with data such as Pitch F/X, it might be possible to tell who is adjusting in what way and recommend how hitters or pitchers can adjust differently to erase the edge that the other enjoys. For now we see that pitchers enjoy a strategic edge on 0-2 and 3-1 counts, while hitters enjoy a strategic edge on 3-0 counts. It's something to think about next time a you're watching a big at-bat.