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August 5, 2009

Red Light, Green Light

Hack or Hold Up?

by Dan Malkiel

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Conventional wisdom dictates that a hitter take a pitch on a 3-0 count. The pitcher has thrown three straight balls, so why not make him throw a few strikes in a row? On the other hand, the 3-0 pitch is probably the easiest to hit, as the pitcher has no margin for error and can't afford to try anything fancy. Which is the more compelling argument?

Let's begin with some descriptive analysis: who swings on 3-0 and who doesn't? I looked at all 3-0 counts between 2003 and 2008, excluding intentional walks; below are the 20 players who swung most often (minimum 50 PA).

Player             PA  Swing     %
Sammy Sosa         57   25     43.9%
Jeff Kent         127   46     36.2%
Victor Martinez   144   50     34.7%
Vladimir Guerrero  50   16     32.0%
Matt Stairs       109   33     30.3%
Jeff Bagwell       52   15     28.8%
Ryan Howard       111   32     28.8%
Luke Scott         63   18     28.6%
Alfonso Soriano    89   25     28.1%
Ben Broussard      80   21     26.3%
David Ortiz       208   51     24.5%
Jacque Jones       86   21     24.4%
Torii Hunter      128   31     24.2%
Jose Guillen       89   21     23.6%
Mike Sweeney       65   15     23.1%
Hank Blalock      112   25     22.3%
Pedro Feliz        81   18     22.2%
Craig Monroe       59   13     22.0%
Matt Holliday     129   28     21.7%
Jim Thome         180   38     21.1%

Here we find some of the usual suspects when it comes to hacking: Soriano, Jones, Guillen, et al. Surprisingly, though, we also find some very patient hitters such as Bagwell, Ortiz, and Thome. On the other end of the spectrum, there were 53 players who never swung at the 3-0 pitch. Here are the 20 with the most PA:

Player           PA w/o a 3-0 swing
Luis Castillo      153
Omar Vizquel       149
David Eckstein     141
Jason Kendall      140
Kevin Youkilis     136
Jose Reyes         132
Bobby Crosby       123
Scott Podsednik    123
Ray Durham         121
Mark Kotsay        117
Dave Roberts       105
David DeJesus      104
Frank Catalanotto  104
Juan Pierre        102
Mark Ellis         101
Kazuo Matsui       101
Darin Erstad        98
Ryan Freel          96
Curtis Granderson   95
Craig Biggio        90

Note that both groups feature some very good hitters, particularly the first. This is because a hitter needs to stay in a lineup and command a minimum of respect from pitchers in order to accumulate 50 PA with 3-0 counts.

Next, let's look at 3-0 swing rates on the team level over that 2003-2008 period:

Team    3-0 Swing %
Astros   14.5%
Angels   14.1%
Rangers  10.2%
Indians   9.6%
Royals    9.3%
Mariners  9.3%
Phillies  8.9%
Rockies   8.5%
Cardinals 7.9%
Dodgers   7.8%
Red Sox   7.7%
Rays      7.7%
Tigers    7.4%
Cubs      7.1%
Twins     7.0%
Braves    6.8%
Orioles   6.8%
Marlins   6.5%
D'backs   6.3%
Expos     6.0%
Yankees   5.8%
Brewers   5.7%
Reds      5.7%
Padres    5.7%
Giants    5.2%
White Sox 5.1%
Blue Jays 4.5%
Mets      3.5%
Pirates   3.4%
Nationals 3.1%
Athletics 1.7%

As you can see, there is considerable variation in swing percentage. Is this variation due to directives from the manager or front office, or because the teams with higher percentages just happen to have more 3-0 swingers on their rosters, as a matter of coincidence or design? I can't say for sure, but my guess would be a mixture of both.

On to the normative question: should hitters be swinging 3-0? For starters, here are the overall batting lines for all 3-0 plate appearances from 2003-2008:

Swing?   PA     AVG/ OBP/ SLG   HR/PA   HR   BB     wOBA
Yes      2826  .347/.505/.685   .059   166   708   0.500
No      37666  .289/.742/.498   .016   603  23806  0.582
Total   40492  .297/.726/.523   .019   769  24514  0.577

First of all, it is clear that just getting to a 3-0 count is a huge win for a hitter; you really can't go wrong with either approach. That said, taking on 3-0 resulted in more production as measured by wOBA; a t-test confirms this increase as statistically significant. Most of this advantage, however, is due to the walks that are the result of 63.2 percent of PA with a take on 3-0. In other respects, swinging on 3-0 is advantageous; note the large increases in average, slugging, and home run rate. This suggests that there are many instances when giving the batter the green light makes sense.

For a final perspective on this issue, let's return to the first group, our "rakers." Though taking is more productive on the whole, could it be that a free swinger does better with an approach on 3-0 that is consistent with his general approach at the plate? That is, should the rakers be raking? Here are the top 20 swingers, along with their wOBA when taking and swinging:

Player         Take wOBA  Swing wOBA   Difference
Sammy Sosa        0.725      0.808      -0.083
Jeff Kent         0.664      0.498       0.166
Victor Martinez   0.541      0.468       0.073
Vladimir Guerrero 0.656      0.682      -0.026
Matt Stairs       0.618      0.490       0.128
Jeff Bagwell      0.637      0.501       0.136
Ryan Howard       0.677      0.565       0.113
Luke Scott        0.576      0.358       0.218
Alfonso Soriano   0.709      0.438       0.271
Ben Broussard     0.565      0.710      -0.144
David Ortiz       0.681      0.659       0.023
Jacque Jones      0.556      0.499       0.057
Torii Hunter      0.600      0.673      -0.073
Jose Guillen      0.607      0.773      -0.166
Mike Sweeney      0.528      0.442       0.086
Hank Blalock      0.674      0.403       0.271
Pedro Feliz       0.582      0.475       0.107
Craig Monroe      0.512      0.740      -0.228
Matt Holliday     0.553      0.507       0.045
Jim Thome         0.620      0.598       0.022

Only five of the 20 rakers benefited from doing so; the other 15 saw their performance suffer, in many cases dramatically. Perhaps the get-me-over fastball isn't quite as juicy as some of these hitters seem to think.

This analysis seems to support the conventional wisdom: overall, it is better to take on 3-0. The difference, however, is not as big as I expected; indeed, one can think of many situations where giving a hitter the green light will increase run expectation. There's also a game-theoretic argument for the green light: if a hitter commits to taking on 3-0, then the pitcher has an incentive to lob a meatball over the plate. This, in turn, gives the hitter an incentive to swing away. Then the pitcher has an incentive to throw the ball a bit off the plate…and so on. By adopting the mixed strategy of swinging on occasion, a hitter might get the best of both worlds: more walks and some easy extra-base hits.

Dan Malkiel is an intern with Baseball Prospectus.

Dan Malkiel is an author of Baseball Prospectus. 
Click here to see Dan's other articles. You can contact Dan by clicking here

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