The folks at Basketball Prospectus recently found that three-balls were undervalued. Does that mean that there's been an inefficiency in the accepted market inefficiency? I don't know. Commenter Guy also had ideas for how to study three-ball strategies.
Some batters never swing on 3-0 counts. Take the difference between the average 3-0 swing zone and strike zone.
Overall, only 6% of those pitches are swung at. Of those 6%, I estimate 17% would be called balls. If batters never swung at 3-0, that means they would walk about 36% of the time on that pitch, as opposed to the current rate of 35%. Sounds negligible, and it's likely that if batters are able to do damage on 3-0, then they're right to swing at times.
Upon swinging, batters hit .390 with a .760 slugging average. That does not include the 54% of swings that either miss or result in fouls, thereby bringing the count to 3-1. Using linear weights, I estimate that batters currently add about a run per 100 pitches by swinging on 3-0 rather than always taking. I don't think the pure strategy "always take 3-0" is correct. That said, I also think that there are some pitchers who are so bad at throwing strikes or hitters so bad at hitting that such a strategy would be viable.
Along similar lines, batters are more likely to swing at full-count pitches than 2-2 pitches. What if we were to map out 2-2 strategies on 3-2 pitches? Well, I'm not entirely sure this makes sense, but I tried to do it.
I made the payoffs on 2-2 counts equal to those on 3-2 counts, then predicted run value while controlling for batter/pitcher handedness and pitch type. Mapping both predictions onto the 3-2 distribution, I found the overall difference in expected output to be similar to the difference I found between never swinging on 3-0 and the current strategy. Again, the current strategy proved more optimal. Unfortunately, graphing the differences didn't produce anything intelligible.
Decades of baseball evolution have brought us to the point where radical changes to current strategies can mostly be ruled out. But achieving equilibrium is a complicated process, and we would be doing the game of baseball and baseball players a disservice to think that there is no room for improvement. I'm more comfortable saying that batters might swing too often on three-ball counts than I am suggesting what their strategy should be.