The Futility Infielder

I wasted Tuesday night watching the Yanks roll over to the Anaheim Angels in Derek Jeter's return. The Angels waited out Mike Mussina, spoiling his good pitches, forcing him to labor, and then they broke the game open, winning 10-3. An uncomfortable flashback to the Halos treatment of the Bombers in last year's AL Divisional Series, or as Yogi says, déjà vu all over again.

Though the Yanks trailed all the way, the game was a close one until the top of the seventh, when things turned ugly. Leading 4-2, the Angels opened up the inning with a David Eckstein double off of Sterling Hitchcock. Adam Kennedy then laid down a sacrifice bunt to the first base side, but instead of taking the easy out, Nick Johnson threw to third base. But the throw was too late to get Eckstein, and all hands were safe.

This play drove me crazy, and it still does. It ALWAYS friggin' does. It's a bad play because the defense is acting out of desperation instead of making the smart move and taking the out. The consequence of failing to get that lead runner is that it sets up a big inning; first and third with no outs instead of third with one out.

There's a way to quantify this, using a Run Expectancy table. A Run Expectancy table tells you how often a run scores from that point on, given each of the 24 possible base-out combinations. Bill James introduced the concept to the masses in his 1987 Baseball Abstract, based on work done by Gary Skoog. Recently Baseball Primer contributer Tangotiger published one based on 1999-2002 play-by-play data, which I will reproduce below:

RE 99-02  0 Out   1 Out   2 Out 

Empty     0.555   0.297   0.117 

1st       0.953   0.573   0.251 

2nd       1.189   0.725   0.344 

3rd       1.482   0.983   0.387 

1st_2nd   1.573   0.971   0.466 

1st_3rd   1.904   1.243   0.538 

2nd_3rd   2.052   1.467   0.634 

Loaded    2.417   1.650   0.815  

What this is saying is that at the start of 1000 innings (0 on, 0 out), teams can be expected to score 555 runs. With a runner on 1st and 0 outs, that expectation rises to 953 runs per 1000 innings; with 1 out and nobody on, that expectation falls to 297 runs per 1000 innings. Pretty neat, huh? If I were a manager, I'd tattoo this data on my inner forearm.

We can use this matrix to examine the situation the Yankees faced on Tuesday night. Following Eckstein's double, the Angels had a man on 2nd and 0 outs, an expected yield of 1.189 runs. A successful sacrifice bunt would have actually lowered the run expectancy to 0.983 (man on 3rd, 1 out). A bunt with all hands safe would have left men on 1st and 3rd with no outs, an expected yield of 1.904 runs. A great defensive play to nail the lead runner would have left a man on 1st with 1 out, a run expectancy of 0.573. In fact, the Angels scored two runs in the inning, breaking the game open.

The lower run expectancy after the bunt illustrates why the sacrifice bunt has fallen out of favor among statheads. True, there is a time and a place for everything and these are just averages which don't take into account a runner's speed, a particular hitter's bunting skill, or whether the next guy up is Barry Bonds. But these averages have their uses for testing a few theories. Let's look at the Yanks' options on Kennedy's bunt. They could have played it as a sacrifice and almost certainly gotten Kennedy at first while Eckstein advanced, with a slight possiblity Kennedy would somehow end up safe -- maybe Soriano didn't reach the bag in time, maybe Johnson bobbled the ball while picking it up, maybe Kennedy morphed into Rickey Henderson on his way down the line, whatever. Let's assume that 90% of the time, Kennedy's out and 10% of the time he's safe. We can quantify all of this:

Initial State:
2nd, 0 out: 1.189 RE

Sacrifice Scenario:
90% chance (3rd, 1 out) + 10% chance (1st & 3rd, 0 out)
0.9 * 0.983 + 0.1 * 1.904 = 1.078 RE

Again this confirms that on average the Yanks would have lowered the Angels' run expectancy by taking the easy out. In fact, using a little 7th grade algebra, the hitter would have to be safe 23% of the time in order to raise the run expectancy from this sacrifice. Do you know many guys who can bunt .230?

Now let's look at what I'll call the Cutdown Scenario. Suppose it's a 50-50 shot as to whether the defense get the lead runner. This gives us the following:

Cutdown Scenario:
50% chance (1st, 1 out) + 50% chance (1st & 3rd, 0 out)
0.5 * 0.573 + 0.5 * 1.904 = 1.239 RE

Even with a 50% chance of getting the lead runner, the run expectancy is higher than the intial state. Back to Mr. Richards' 7th grade algebra class, we have a break-even point of about 54%. Now, I don't have numbers that tell me how often the defense cuts down a lead runner in a sacrifice situation, but I can tell you, it ain't 54%, hoss. Especially not with a speedy little guy like Eckstein. We've all got too many fist-sized clumps of hair lying around and too many blogged rants like this for that to be the case.

I'll admit that my analysis is an oversimplification; I could have included the possiblity the fielder throws the bunted ball into the stands for a two-base error, but then we'd be piling too many assumptions on top of each other. But even with this simple analysis, there's no escaping the conclusion that the Yankees made a stupid play Tuesday night, and it broke the game open.

• • •

Well, in the timespan I've been working on an as-promised in-depth look at the Yanks, they've lost two in a row to the Angels in less-than-impressive fashion. Since I'm headed to the ballpark Thursday, that analysis is going to need a bit of retooling before it gets posted, probably this weekend.