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Wednesday, April 14, 2004

The Small Ball Fallacy, or Why Buck Was Right To Let Laird Swing Away 

Last night's game was incredibly frustrating, on a lot of levels. Mickey Callaway getting shelled (and promptly being put on the D.L.) wasn't as troublesome as Joaquin Benoit's failure to shut down the A's in his newly anointed position as the designated long man.

Still, the Rangers got to Barry Zito early and often, and when Eric Young doubled to lead off the bottom of the ninth, putting the tying run in scoring position, the Rangers had a golden opportunity to at least tie the score. Playing at home, with none out and a rookie catcher coming up, the book would say to bunt, in order to get the tying run to third so that a fly ball could score the runner. Buck Showalter let Laird swing away, and...well, you know the rest. Laird got out, Nix hit a fly ball that would have probably would have brought Young home, and Michael Young grounded out to end the game.

Buck's decision resulted in a fair amount of second-guessing. And while I'm someone who is not terribly impressed with Buck as an in-game manager, and am more than happy to second-guess his decisions (*cough* David Dellucci *cough*), in this case, the book was wrong, and Buck was right. Gerald Laird should not have bunted.

Quick review of the situation -- Eric Young was on second base, none out, 10-9 A's lead in the bottom of the ninth. Arthur Rhodes was on the mound, and Gerald Laird, Laynce Nix, and Michael Young were due up. With Mark Teixeira sidelined because of an oblique muscle problem, only Rod Barajas and David Dellucci were available off the bench.

In evaluating whether or not to bunt, you have to determine whether Young is more likely to score from third, with one out and Nix coming up, than he is from second, with none out and Laird and Nix coming up. According to Nichols' Expected Run Table, a runner on 2nd with none out has a 63.3% chance of scoring, versus a 66.7% chance of a runner on third with one out scoring.

That gives a slight edge to bunting (if we ignore the possibility of the bunt not advancing the runner or, even worse, getting the runner thrown out at third on the attempted sacrifice). Yes, a 3.4% advantage isn't great, but it is on those small advantages that winning teams are built, right?

But let's look at this particular situation more closely, and examine whether the participants involved might narrow the gap.

Ultimately, the decision on whether to bunt comes down to whether the likelihood of Young being able to score from third, but not from second, is greater than the chance of Laird driving him home from second. While there are circumstances, such as with a wild pitch or an infield single, where Young might score from third when he couldn't otherwise, the determination basically boils down to whether Nix is more likely to drive Young home with a sacrifice fly or a ground out than Laird is to get a hit.

The Rhodes-Nix matchup is very unfavorable for the Rangers, in this case. For one, you have the lefty/lefty matchup. Rhodes, throughout his career, has been tough on both lefties and righties, but has been especially tough on lefthanders. Lefties, from 2001 through 2003, put up a line of .206/.243/.281 against him, versus a .210/.266/.329 line for righthanders. Moreover, since Buck has benched Nix against lefthanded starters, both last year and this year, it is makes it that much more difficult for Nix when he does face off against a lefty, since he almost never sees them.

Let's assume, for the sake of discussion, that Nix is a .200 hitter against Rhodes (which may be slightly overstating his expected average, but makes the math easier). That means that 80% of the time, Nix is going to make an out. So how often is that out going to advance a runner from third?

We know that Rhodes is a strikeout pitcher, and Nix has been, during his stints in the majors, prone to strikeouts. Over the course of Rhodes' career, he has faced 3,742 batters, and struck out 872 of them, meaning he strikes out 23.3% of the hitters he faces. Nix, in 215 major league plate appearances, has struck out 58 times, or 27% of his plate appearances, which, once again, is a very high percentage. In contrast, the 2003 Minnesota Twins, who were #15 out of 30 teams last season in strikeouts, struck out in 16.2% of their total plate appearances.

So Rhodes strikes out batters about 44% more often than the average, and Nix strikes out 69% more often than average. As a result, you would expect Nix to strike out in approximately 39% of his plate appearances against Rhodes.

So if Nix gets a hit 20% of the time, and strikes out 39% of the time, that leaves 41% of plate appearances where he will put the ball into play for an out. One would hope, of course, for a sacrifice fly. Rhodes, however, has been a very groundball-oriented pitcher the last several years, putting up groundball/flyball ratios of 1.22, 1.40, and 1.27 from 2001 through 2003. As a result, that means that Nix would be hitting a fly ball out against Rhodes approximately 16% of the time, and a groundball out against Rhodes approximately 25% of the time.

Now, with a collection of outfielders with pretty good arms, what are the chances that Young will be able to score on a fly ball out? One in two, maybe? That gives us 8% on the flyballs. With a drawn in infield, and a ground ball from Nix, what are the chances of Young scoring? Closer to one in three or one in four. Say it is one in three...that gives us an 8% for groundballs.

That gives us a 16% chance that Nix would drive in Young from third with a "productive out", where Young wouldn't be able to score from second.

However, that 16% chance is gained at the expense of taking the bat out of Gerald Laird's hands. And unless the chance of Laird getting a hit against Rhodes is less than 16%, bunting Young from second to third reduces the chances of the Rangers scoring in that situation. Plus, giving up the out with the sacrifice bunt significantly reduces the chances of scoring two runs and ending the game once and for all...the expected total runs scored with a runner on second and none out is 1.13, versus .96 runs expected with a runner on third and one out.

So, by foregoing the bunt, Showalter, at the very least, did not reduce the Rangers' chances of scoring a run in the bottom of the 9th, and increased their chances of plating two runners and getting the win.


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