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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.

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Other than the team stats, which just sort of seem thrown in there, this is a very good and well put together article. Thanks. Instead of the team splits, it might be more interesting to see it by manager/year. It would be interesting if this is a management philosophy thing, or if you just make a decision based on the player at hand.

I'm a bit stunned that Howard has gotten to 3-0 111 though. That would require him to not swing at 3 bad pitches in a row. Stunning.
I think you missed a big point you could've made in one of your charts. The HR/PA for a hitter that swings at a 3-0 count is 0.59 but drops to 0.16 if the hitter takes (and presumably swings later). Thus, that would suggest that a player should definitely swing 3-0 in situations where a home run is important, such as the home team in an extra inning game or with runners on base.

As an addendum, your third chart was kind of interesting but you did nothing with it... so why include it if you can't analyze or synthesize it beyond "I can’t say for sure, but my guess would be a mixture of both."
I'm going to say that in the situation where the batting team *needs* a home run, the pitching team knows it, and that the pitching approach is thereby altered. Thus, I'd doubt that the difference in home run percentages in that particular situation is nearly as large as it is generally.
In pretty much any situation where there's a close game and a home run can tie it or win it, you hear the cliches about "Don't give him anything good to hit", "A walk is as good as a hit", etc. In other words, even if a pitching approach is altered, it might not be executed well.
>Thus, that would suggest that a player should definitely swing 3-0 in situations where a home run is important, such as the home team in an extra inning game or with runners on base.

Correlation, not causation. He is swinging at only a pitch he absolutely loves, which is why he is likely to hit a home run. You can't then say that everyone should be swinging at 3-0 pitches because they'll hit 0.059 hr/pa. At most you can suggest to give the batter the green light to go for a hr if he likes the pitch, but that seems pretty obvious.
Besides "defensive swings", many swings are taken on pitches that players "absolutely love".

I'm definitely not saying that everyone should swing at 3-0 pitches.. if a player has no or little power, then it makes little sense to swing. But if a player has a good chance at hitting for power, then it's probably worth giving the green light to.
The HR/PA gap is not quite as significant as it seems due to the PA with four consecutive balls, during which a hitter never has a chance to homer. Even so, the implication you draw is correct: players should not try to work a walk when more is called for.

Regarding the team chart, I was simply interested in whether there were organizational philosophies on this matter. Had the rates all been roughly the same, we could have concluded that there probably weren't. Since they are different, it seems likely that there are.
"players should not try to work a walk when more is called for"

I don't think you can say that. A walk is always a positive, except in situations where a double play is essential (in which case the other team isn't going to give you anything to hit anyway).

One of the big cultural barriers in baseball is the feeling that a player who draws a walk is passing the buck, where a player who takes his cuts is shouldering the load, manning up, etc. Unless you're Barry Bonds on the otherwise impotent Giants, leaving it to the next guy with no more outs and another man on is never the worst alternative.
Yes, but a large reason for the differential in HR/PA rates is that, if the batter takes on the 3-0 pitch, 63% of the time he's taking a ball, and therefore doesn't get another chance to swing. The HR/PA rate from a subsequent 3-1 count is .0435.
You could have taken this one step further and answered your game theory question posed at the end of the article.

Do the hitters that always take on 3-0 see more strikes than the hitters that are willing to swing on 3-0? If the walk rate is similar then the batters gain nothing from mixing it up and swinging every now and then.
This is a difficult question to answer. I suspect that players who _never_ swing on 3-0 do get more strikes, since these players are likely identified as "takers" by scouting reports. I doubt, however, that scouting is fine-grained enough to distinguish between player X who swings 15% of the time and player Y who swings 20% of the time. I may try to confirm this speculation in a later article.
Good analysis, but I think there is somewhat of a hole in there: you are category those by batters' action, not their intend.

What if a hitter plan to swing at a 3-0 pitch, but saw it drifting out of zone or just to a spot where he is not comfortable swing at? Or more unlikely, a batter decided to take but saw a absolute meatball and changes his mind, which might or might not result in solid contact due to late start.

If you could do this study by intend (which of course you cannot), I would not be surprised to see a "Green Light" would generate a better result than to take regardless. And I think that would offer more insight.
I agree that this is definitely the whole in the approach. No one (except perhaps a player determined to avoid walks at all costs, of which a few probably exist) goes up at a 3-0 count determined to swing no matter what. Rather they will swing if it is the pitch they are looking for and lay off if it is not, or if it is clearly a ball. If you could give hitters choosing that strategy credit for the walks they take when a pitch isn't what they were looking for, in addition to all the hits they get when it is, I strongly suspect that this is clearly the better strategy. I also suspect that especially for those hitters with a reasonable probablity of doing more than getting a single if they do manage to hit the ball. Of course, the best strategy is also very dependant on the number of outs and the baserunners. Taking makes little sense as a strategy if you are the number 8 hitter with the pitcher on deck, and there are two outs and runners on second and third, it makes a lot more sense if there is a runner on first or the bases are empty and you are a singles hitter.
Not quite. Jim Thome will swing 3-0 if the pitch is exactly the one he's looking for. Alfonso Soriano will swing 3-0 if the pitch is one he would have swung at on a 0-0 count. That's why Soriano needs a red light, and Thome doesn't.

If you are an NL #8 hitter, with the pitcher on deck, a walk is a FANTASTIC outcome. In the early innings, it means you avoid having the pitcher lead off (and kill) an inning. (With 2 outs and runners on 2nd and 3rd, you won't get a hittable pitch anyway.) In the late innings, either you're getting a (semi-)intentional walk anyway, or you're setting up for a pinch hitter to have a high-leverage PA. Both of those are much more valuable than what a #8 hitter will generally do at the plate, and should be praised.
Interesting. You sort of allude to the impact of walks but it would be nice if you could take into account that in your "take" stats you have instances where the hitter had the green light but the ball was well off the plate.
This would be more informative if PA were restricted to either swinging or taking strike 1. Not much strategy involved if the pitcher threw up three poor pitches immediately followed by a fourth. You'll lose lots of data for individual batters, but it'd be interesting to see "team philosophies" emerge from this cross-section.
It would also add to the quality of the analysis if the table of Take vs Swing performance was done relative to the batters' average. For example, if the swingers average a HR every 15 PA, then .059 is not very good. Another perhaps interesting benchmark, similar to what CESTILP1 suggests, is the performance on 3-0 compared to that on 3-1 (however they got there).
I give this article the thumbs up.
I think the problem with this analysis is that the interesting question is not is it better to swing or take 3-0 because certainly noone decides before the pitch to swing. The interesting question might be: if the pitch is a strike is it better to take or swing, b/c the way the analysis is done now it's essentially inevitable that you're going to find that taking is better.
Assume that if the pitch were "hittable" its equal to take or swing. The presumably large number of out of the strike-zone pitches on 3-0 which pump up the OBP of the "take" option but don't truly get to the heart of the question because even a hitter looking to hit will probably take that pitch. Basically you treat every case of a 3-0 walk as a case where the hitter has decided to take, a tremendously false assumption.
The analysis doesn't really do much to answer the question you set out to examine for this reason. I think in the absence of the ability to actually see when the hitter was taking all the way you should redo it using only at-bats with a 3-0 pitch which is a strike.
This is a very good point. Most takes on 3-0 are the result of the hitter "taking all the way," a fact that somewhat mitigates your concern. It remains a concern, however, and I hope to address it in a follow-up article.
Detail: wOBA is not defined in your article.

Solid piece.
As a primer, this will help:
Overall I agree with thenamestsam,

but wasn't there a rule about being worked inside, really close inside, by the pitcher next time he sees you if swing at his 3-0 pitch? There should be.
Interesting stuff.

I think the people complaining about your way of breaking the problem down are missing the point. You can't say "only swing at strikes" because batters don't have that skill. They can only decide in advance to not swing at ANYTHING, or to be willing to swing. Once they are willing to swing, they can be fooled, or get overanxious, or just plain miss.

As follow-on work, it might be interesting to see if it's possible to characterize the type of hitter who gets the biggest wOBA boost from swinging at 3-0 pitches. It looks like it's the already-selective power hitters, but quantifying that difference might be fun.
I thought this was a very interesting article, is a common question for anyone who's played baseball, and I'm surprised it hasn't been taken before. I too think I'd rather see it broken down by manager than team, and I'd be curious to see the splits on when a team is winning vs losing to see if that changes anything.
One point I noticed that doesn't seem to have been mentioned yet: the guys who never swung at a 3-0 pitch are almost all really fast (Kendall and Youkilis excepted, and Kendall once was fast) and almost all have below average extra-base power (Youkilis, Biggio and Granderson excepted). The guys who frequently swung are almost all really slow middle of the order hitters (Soriano excepted).

I wonder if there's a tendency for players to swing at the 3-0 more with someone on base. With men on base already, trading a little bit of on base percentage for a bit of slugging percentage can be a good deal for the team. Also, walks are more valuable for faster players, especially if first base is open.
Interesting analysis. The biggest hole that I see is that it doesn't consider runners on base. Especially for free swingers, seeing one or two runners in scoring position and a 3-0 count may increase his temptation to swing away. OTOH, he may be more reluctant to swing if there were no runners on or only a runner on 1B (in that case because taking a walk puts a runner into scoring position).

In addition, swinging away may depend on what inning it is, how many outs there are, what the score is.

So, although you have a relatively small number of cases to deal with, you should do the full analysis of the potential risks and payoffs of swinging away, not just using a general wOBA calculation but one that takes the base-out situation into account as well as the inniner and score.
Great article.

I'm not sure how to articulate this, but I think we need a tripartite analysis: looking at wOBA on a take vs. a swing lumps together the two kinds of takes (those leading to a walk and those to a 3-1 count) as well as the two kinds of swings (those leading to a 3-1 count and those leading to a ball in play.)

Imagine an ideal hitter who swings only when, if he does not, the will become 3-1. Then what we want is wOBA(swing in 3-0)-wOBA(in 3-1). And that, I'm guessing, will favor swinging in 3-0.
Most important thing here is the type of hitter. Why would David Eckstein ever swing on 3-0 when he has no chance of hitting a home run and his best case scenario is 9 times out of ten the same as a walk. Whereas Adam Dunn has a good chance of doing damage on a 3-0 count.

I think a good study would be to see how "power hitters" and non-power hitters" fare when they take or swing on a 3-0 count. Since the advantage in swinging is increased power and the advantage of taking is increased obp.