When a pitcher starts a batter off with two consecutive strikes, he's clearly ahead in the count and has a range of options available. He can take the efficient route, again throwing the pitch in the strike zone and forcing the hitter to take a defensive swing or head back to the bench. Alternatively, he can "waste a pitch", throwing it out of the strike zone and hoping that the hitter goes after it, either completing the strikeout or managing weak contact for an easy out.
Which is generally the better strategy?
We can consult the 24 States Matrix for the answer. The 24 States Matrix tells us how many runs, on average, we can expect a team to score from the current situation until the end of the inning. For example, with nobody on and zero outs, the average team last season scored .49 runs. If the first batter reaches base (now a runner on first with no outs), the "Run Expectancy" moves up to .86, based on the league's average number of runs scored in those situations. We can credit the first play (whether it was a single, a walk, an error, etc.) for an increase of .86 - .49 = .37 runs.
We calculated the Run Expectancy change for each 0-2 count in MLB in 2010. Utilizing the 24 States Matrix, we found that a batter falling behind 0-2 knocks off .10 runs from the team's run expectancy, almost as bad as sending your pitcher up to bat with a 0-0 count.
As it turns out, pitchers ahead 0-2 threw the next pitch outside the strike zone 72 percent of the time. The average change in Run Expectancy in those at bats remained exactly the same, -.10. On the other hand, if a pitcher challenged the hitter with an 0-2 pitch in the strike zone, the result was ever-so-slightly better for the hitter, at -.09.