Let’s do some back of the envelope math. Whom would you rather have at the plate? Miguel Cabrera in all of his 2013 glory, or David Ortiz … bunting?  After doing some very extensive mathematical research, talking to several GMs who do not wish to be named, watching hours of film footage, and taking a brief glance at Mr. Cabrera’s player page, I can say with confidence that Cabrera was a very good hitter in 2013. Can we make the case that Big Papi could be more productive than Miggy by bunting more?  You can probably figure out that Ortiz is a stand-in for “left-handed pull-happy guy against whom teams often play an infield shift.” In fact, for years, Ortiz was the one guy against whom teams employed the shift, putting three infielders on the right side of the infield because that’s where he hit most of his ground balls. When a team is shifting, the third baseman often plays halfway between second and third base, more like the classic positioning of the shortstop. Some teams leave the actual shortstop on the left side and make the third baseman into the third infielder on the right side. Either way, it leaves a lot of empty space down the third-base line, perfect for a bunt.  This leads to one of the great mysteries of the universe: Why doesn’t the batter just bunt toward third base? If he keeps it fair and gets it past the pitcher, then he’s got a free base hit. A recent survey found that this question has been muttered by every single person who has ever watched a baseball game either in person or on TV.  It seems like a feat of undeniable foolishness that players do not bunt much more often than they do now. Yes, there’s always a reason for everything, and no, it’s not always a good reason. We’ll talk about what that reason is in a minute.  Ortiz approaches home plate and sees that the other team is putting on “The Shift.” Let’s simplify his choices here to “his usual swing-away approach” vs. “bunt toward third” and look at his options in terms of expected value. To make things easier, let’s assume no one is on base and no one is out (the calculations come out roughly the same no matter what suite of assumptions you make).  If Ortiz bunts, the two most likely outcomes are a single and an out. (Let’s leave out the idea that the pitcher or catcher or 3B/SS might get to the bunt and throw it into the first-base dugout, or that the bunt might go down the line for a double, although those things do happen.) Using 2013 numbers, if Ortiz is safe at first, the Red Sox’ run expectancy has gone from 0.4672 (no outs, no one on) to 0.8262, for a net increase of .359 runs. If he is out, the Red Sox drop to a run expectancy of 0.2489, for a net loss of .2183 runs.  If Ortiz does what he usually does, then there are a number of outcomes that could occur as a result. He might strike out. He might hit a home run. He might hit a ball right at the guy playing in short right field because of the shift. There’s plenty of evidence that shifting actually works, at least as teams are implementing it now, in that it robs players of some of their hitting mojo. But even with the shift, Ortiz had a pretty good year last year. The stat RE24 uses the same run expectancy framework as I used above. In his 600 (exactly) plate appearances last year, Ortiz increased Boston’s run expectancy by a total of 43.26 runs, or .0721 runs per plate appearance. (Careful readers will note that RE24 takes into account his performance in all situations, not just no runners, no outs. Back of the envelope, people…back of the envelope.)  So, how often would Ortiz have to be successful in getting a hit on a bunt toward third to make it worth his while?  Warning! Gory Mathematical Details Ahead! This is simple algebra (and it’s been done before). If we assume two outcomes (single or out), and we have the cost/benefit for both of them, we can figure out at what value of p (for probability) Ortiz would break even with his usual “hit away” approach.  .359 * p - .2183 * (1 –p) = .0721  If you solve for p on that one, it’s 50.1 percent. If Ortiz thinks that he has more than a 50/50 chance of getting a bunt down, to his left, in fair territory, and hard enough for the ball to evade the pitcher, then he should bunt. At least that’s what the math says.  Even if we give Ortiz an upgrade to being Cabrera (75.19 RE24 in 652 plate appearances, for an average of .1153 runs per PA), his break-even point is now 57.8 percent. If Ortiz (or anyone else) can pull off the bunt more than 60 percent of the time (roughly) when teams shift against him, he will be a more valuable hitter than Cabrera was in 2013, at least during those plate appearances. If a hitter doesn’t happen to be Cabrera, the break-even point compared to his own talents (and that’s the real point of comparison) is even lower.  Now of course, bunting isn’t easy, but this doesn’t need to be a perfect bunt either. Normally, bunts come when the defense is expecting it, and so you have to place the ball in the Bermuda triangle between the pitcher, catcher and charging third baseman. Here, the third baseman is miles away. In some sense, if the ball is fair (and you get three shots at that) you can smack it rather hard and you’ll be fine. No, not everyone has much practice or skill in bunting, but a) pitchers do it and b) did I mention that this is a perfectly legal way to produce more value than Cabrera? Maybe there’s a little incentive there to take bunting practice, as Brandon Moss did this spring?  So, why on earth don’t more hitters bunt against a shift? I’m sure the answer begins with “I’m not being paid to bunt. I’m being paid to hit home runs ...” Ah yes, the testosterone factor. If our player bunts, he gives up the chance to hit a home run, or at least a double or triple, all of which are more valuable than some dinky little bunt single. Plus, his bunt single will not be shown on the 11 p.m. news. His potential home run will. And bunting is often what you ask of the guy who can’t really do anything else.  Of course, it’s wishful thinking to assume that you’ll hit a home run or even a double. Last year’s most prodigious extra-base hitter, Chris Davis, registered 42 doubles, one triple — Chris Davis hit a triple? — and 53 home runs for a total of 96 extra-base hits in 673 plate appearances, or one for every seven plate appearances (14 percent). Expressed a little more mathematically, our reluctant bunter is saying that he prefers a higher-variance strategy despite its lower expected value, because he might come out ahead. It’s sort of like saying that investing all of your money in lottery tickets is a good investment strategy because you could win 20 million dollars. The lottery is still a really bad investment strategy when there’s a much safer, much better expected rate of return available.  It sounds like testosterone running crazy. Or is it?  As my Baseball Prospectus colleague Ben Lindbergh has been chronicling, it appears that more hitters are taking a stab at bunting against the shift this year. Maybe they did the math. The numbers show that hitters, even those who don’t bunt often, aren’t bad at getting a fair bunt down. From 2009 to 2013, I found all players who had at least 400 PA in a season, but who attempted to bunt only once or twice during that season. During those plate appearances where they attempted to bunt, they were successful in getting a fair bunt down 48.2 percent of the time (105 for 218). Imagine what would happen if they actually practiced a bit. They could easily break even. (And as Ben’s early season numbers reveal, they’ve been even more successful with the shift on, at least in a small sample size.)  Now that we know that hitters could take huge advantage of the shift, if they wanted to, why on earth are fielding teams setting up their defense in a way that would allow hitters such a huge advantage? Surely, someone on at least one of the 30 teams has noticed the obvious. (Trust me, they have. All of them.) But then, if no one shows any signs of bunting, why defend against it? At that point, playing the fourth infielder in the shortstop spot is the most reasonable alignment on the off chance that the batter does hit one to the left of second.  At some point, bunting against the shift will become more common and teams will have a decision to make. If they want to play three on the right side of the infield, then that means they can either defend the space between second and third or they can have someone on the third-base line. At that point, taking away the bunt makes more sense, mostly because the reason the team is shifting in the first place is that they don’t think the batter will it to the left side of the infield when he swings away. If bunting against the shift does become more common, it’s likely that teams will re-arrange their defense.  But wait a minute. Maybe there’s a rational explanation for all of this, albeit one that involves some crazy mental judo (or a basic understanding of game theory) being played. Maybe hitters don’t bunt specifically because they know that once they start doing so on a regular basis, teams will start to cover the third-base line and take away their “free base hit” option. Maybe hitters are thinking that they’d rather save that free base hit for a time when they really need it, maybe in the ninth inning of a close game. The shift is not an all-you-can-eat buffet of free base hits, or at least it shouldn’t be. Bunting against the shift is a trick that you can pull only a couple of times before the option gets taken away. Logically, the hitters want to save that limited resource for a situation where it will have the most impact. This is called “picking your spots.”  I’d argue that up until this point, hitters have been far too conservative in picking spots, maybe giving in to the fear that the next plate appearance might be even more important. Maybe it’s male pride. Maybe it’s just a lack of understanding of the game being played, but the fact that defenses still seem largely uninterested in preventing the bunt tells you all you need to know about that. The calculation for the defense is simple. Is it more likely that the batter will swing away and hit one toward the shortstop area – something that some analysis of his spray chart can tell you – or is he more likely to bunt? Right now, teams have clearly decided to play for the swing away option, because hitters so rarely bunt.  *By clicking "SUBSCRIBE", you have read and agreed to the Fox Sports Privacy Policy and Terms of Use.  It seems that now, it’s becoming a bit more common for hitters to test the limits of that tolerance by bunting a bit more. Once teams believe that they will bunt more often than they will swing away and hit the ball toward the traditional shortstop spot, they’ll start taking away the bunt. It’s not that hitters can push too far. They’re being shifted because they don’t often hit the ball to the left side, so the threshold at which defenses will start taking away the bunt is low. Hitters also can’t be too predictable in the spots that they pick. If defenses notice that they bunt only in the eighth or ninth inning, then they’ll only shift the fourth infielder over to take away the bunt only in the eighth or ninth inning. But eventually we might start to see a few teams start to change their fielding ways as well.  So, we enter an odd state where the fielding team seems to be giving away an obvious advantage to the hitter -- one that the hitter is politely declining - and it makes some sense. If hitters are playing the game correctly, they should actually bunt at random times, and at a rate slightly below the rate at which they would otherwise hit a ground ball to the left of second base when they swing away – which isn’t that often. Anything more and the defense will (or at least should) adjust and take away the free base hit buffet. This object of the game is to have your bunting tendencies fly enough under the radar that the fielding team doesn’t take it away.  It leaves us with an interesting case study in human behavior. Putting three infielders on the right side makes sense for some hitters, including Ortiz. Maybe some of the reluctance to bunt is just macho pride, but I’d argue that ignoring those acres of space down the third-base line, except for a few rare and random cases, is completely justifiable. If you look at the problem in a vacuum, it’s easy to blame the testosterone, but a good chess master thinks two moves ahead. If Ortiz bunts here, he might not be able to later. Now we’ve changed the question from “What is the best outcome for this plate appearance?” to “How will this plate appearance affect one down the road that might be more important?” That calculus keeps the number of bunts below where it makes sense to guard the line, and you end up with an arrangement that makes no sense on the surface, but complete sense with a little bit of deep thought. The reason that David Ortiz doesn’t bunt (very often) is that if he does it too much, his chance at free base hits will simply be taken away from him. He wants to at least preserve the couple of times that he might be able to take advantage of it.
The third base line is wide open ... a free base hit for the taking. It seems so simple, right?