Last month, Ron Gardenhire made a number of headlines when he apparently asked Francisco Liriano to "pitch to contact", become more efficient with his pitches and as a result, go deeper into ball games. Of course, this drew the ire of the saber-oriented community, including SB Nation's own Rob Neyer and Aaron Gleeman. To be fair, others such as Nick Nelson have pointed out that Gardy may have misspoke, intending to convey to Liriano the value of throwing strikes, getting ahead in the count, and ultimately pitching deeper into games.

For the purposes of this analysis, I am going to take Gardy at his (apparent) word and examine the real effect that "pitching to contact" has on pitch counts relative to strikeouts. All things being equal, does "pitching to contact" really reduce pitch counts? The bottom line is, compared to strikeouts, "pitching to contact" actually increases pitch counts, for the simple reason that a strikeout (other than the rare occasion when the batter reaches base on a wild pitch or passed ball on strike three) is a guaranteed out, while a batted ball that is put in play has over a 30% chance of resulting in the batter reaching base with a hit or an error, requiring another (or another, or another, etc) at bat to record that one out. And it goes without saying that these extra potential base runners may result in additional runs allowed, making it a doubly poor tradeoff. After the jump, I'll show just how pitch counts are affected by strikeouts, walks and balls put in play, looking at Liriano in particular over the past three seasons.

Pitch Count Data: 2008-2010

In order to understand the effect that strikeouts, walks and balls in play have on pitch counts, I looked at play by play data over the last three full seasons. The table below shows the average number of pitches in at bats across MLB, overall and in at bats that result in strikeouts, walks and balls put in play.

Year Overall Strikeouts Walks Balls in Play 2010 3.820 4.818 5.528 3.376 2009 3.824 4.826 5.531 3.379 2008 3.798 4.840 5.526 3.354

As one would expect with sample sizes into the hundreds of thousands (129,431 outs recorded in 2010, for example), the averages vary little from season to season. Overall, the data clearly shows that, on average, at bats require over 1.4 fewer pitches when a ball is put in play than when a batter strikes out. On its face, it would appear that if a pitcher could simply trade strikeouts for balls in play, he could greatly reduce his pitch counts. One little problem though, there's a good chance that the pitcher will fail to record an out when the ball is put in play, and one or more additional at bats will be required to record that out.

Reaching Base When the Ball is Put Into Play

Year Balls in Play On Base Percentage 2010 133,348 43,473 32.6% 2009 134,996 44,470 32.9% 2008 136,548 44,962 32.9%

The table above shows the total number of balls put in play across all of MLB, and the number of times the at bat resulted in the pitcher failing to record an out due to the batter reaching base. For the purpose of this analysis, I include home runs since they fail to record an out, even though the ball is not technically put "in play". Last season, a batter had a 32.6% chance of reaching base if he manages to get the bat on the ball.

How Does This Affect Pitch Counts?

(caution: math ahead!)

Now that we have the data, we can calculate the expected number of pitches required to record a single out, given a strikeout versus a ball put into play. Because the data is similar from season to season, I will use 2010 data here.

For a strikeout, the calculation is simple, an average of 4.818 pitches is required to record an out.

For a ball in play, the calculation becomes a bit more difficult. I won't explain all of the math here, but we need to account for the number of pitches required for the initial at bat, as well as any additional at bats (and at bats after that...) that are required due to a batter reaching base. Ultimately we get an infinite geometric series of [a * r ^ n], where a = the average number of pitches required for an at bat where the ball is put into play, and r = the probability of the batter reaching base. This gives us a sum = a / (1 - r) = 3.376 / (1 - 0.326) = 5.009 pitches. This calculation assumes that any follow-on at bats also result in a ball put into play versus a strikeout or walk, but the calculation is similar if we consider the overall average number of pitches per at bat and the overall probability of a batter reaching base, including all strikeouts and walks.

In other words, because additional at bats may be required for the pitcher to record an out, it will on average increase pitch counts when a ball is put into play relative to a strikeout, all things being equal.

Francisco Liriano, Strikeouts and Pitch Counts

Of course, in reality, all things are not equal. It is not a simple matter of trading a strikeout for a ball put into play. As a pitcher like Liriano attempts to get a batter to chase strike three, he can run up pitch counts and open himself up to walking batters and getting into a great deal of trouble (as we've seen this season).

Year Overall Strikeouts Walks Balls in Play 2011 3.870 4.450 5.708 3.317 2010 3.735 4.930 5.931 3.069 2009 3.775 4.836 5.492 3.221

The table above shows the average number of pitches per at bat for Liriano overall, and when at bats result in strikeouts, walks or balls put into play. The most surprising aspect of this data is that, for a pitcher who had never completed a game before last week, before this season Liriano has actually run up slightly below MLB average pitch counts. His pitch counts on a per at bat basis may not be as low as Roy Halladay's (3.594 pitches per at bat), but they are not excessive either. Liriano's problem has in general been too many base runners, evidenced by his 1.30 career WHIP (still below MLB average, but not all star territory either, compared to Halladay's career 1.18 WHIP). As a pitcher allows a lot of base runners, he is going to run up pitch counts, even when he strikes out over a batter an inning.

In conclusion, could Liriano benefit from throwing more strikes, particularly early in the count? Of course. When he is up 0-1, 0-2, his slider becomes far more effective to get batters to chase strike three. But Liriano should be wary of "pitching to contact" ultimately trading a couple of strikeouts for a balls put into play. As I've shown above, this tradeoff doesn't necessarily decrease pitch counts unless walks are also reduced accordingly. I'd much rather Liriano get back to striking out over a batter an inning, giving the Twins a dominant seven innings or so, then letting the bullpen do its job. Then again, none of this will make a bit of difference unless Liriano can cut his walk rate in half.