Wednesday, June 15, 2011

Fun With Run Expectancy Matricies Part 1: Stolen Bases

If you've read Moneyball, you already know that attempting to steal is usually is not worth the risk associated with being thrown out. Michael Lewis didn't go into a whole lot of detail regarding Billy Beane's analysis, so let's take a deeper look. Our key reference is the Run Expectancy Matrix. This bad boy is the result of countless hours of tedious, painstaking data collection. It looks at every game for the given time period and examines all different scenarios, then calculates the average number of runs scored. Every manager should have this information with him in the dugout, but I suspect many would rather trust their "gut" and their "instincts" rather than look at a bunch of numbers calculated by nerds who have never played in the big leagues.

Now that I've completed my obligatory (albeit truncated) rant about ignoring the data, let's move on to stolen bases. Let's look at a scenario:

Runner on 1st, no outs. Great! Your lead-off hitter just got on base. Referring to the matrix, a team with a runner on 1st and no outs averages 0.941 runs in that inning. (looking at the most recent years). Now let's say this player tries to steal second. We have two potential outcomes, and here's what they look like:

Successful steal - runner on 2nd, 0 outs. Run expectancy=1.170
Thrown out - bases empty, 1 out. Run expectancy = 0.291

Yes, I know that sometimes errors are made, and the runner could end up at 3rd, etc, but let's focus on these two outcomes. Base stealing is a risk, and the more likely you are to safely steal a base, the more it's worth attempting to steal.

How often should you be successful to make it worth attempting? Let's define p as the probability of a successful stolen base, and 1-p as the probability of being thrown out. Our run expectancy right now is 0.941, and we want that to go up. Therefore:

p*1.170 + (1-p)*0.291=0.941

This will tell us how successful we need to be to keep our run expectancy at 0.941. Solving for p yields p=0.739. Our success rate has to be greater than 74% to make it worthwhile.

We can do the same for a runner on 1st base with 1 out. Referring to the matrix and setting up the equation similarly we get:

p*0.721 + (1-p)*0.112=0.562

Here p=.740, and we have essentially the same result as the previous scenario.

What about a runner on 1st with 2 outs? This is where a lot of managers look to steal. They want to get that runner in scoring position and hope for a two out hit. Let's see:

p*0.348 + 0 = 0.245

p=0.704, so you need to be successful more than 70.4% of the time to make it worthwhile.

Here is a summary of some threshold success rates:

0 out 1 out 2 out
runner on 1st 73.9% 74.0% 70.4%
runner on 2nd 77.0% 69.4% 90.4%

Ok, great, we've determined the necessary success rates. Let's compare that to how teams actually perform. Here are the rates for teams in 2010:

Team Success Rate
Team Success Rate
PHI 0.837209
MIN 0.708333
OAK 0.804124
PIT 0.707317
BOS 0.8
COL 0.707143
TBR 0.785388
KCR 0.69697
SEA 0.78453
DET 0.69697
FLA 0.779661
BAL 0.690909
NYY 0.774436
ATL 0.684783
MIL 0.757009
CIN 0.683824
NYM 0.747126
CHW 0.683761
TOR 0.74359
ARI 0.677165
HOU 0.735294
LAA 0.666667
CLE 0.733871
STL 0.658333
WSN 0.728477
LAD 0.647887
LgAvg 0.722628
CHC 0.639535
TEX 0.719298
SFG 0.632184
SDP 0.712644

It looks like a few teams benefited from stealing bases, a number of teams didn't really gain or lose runs, and a bunch of teams should just stop. The teams with the highest success rates are some of the more analytical teams in the league. Billy Beane's Oakland A's are 2nd with an 80.4% success rate, and surprisingly, they had the 3rd most stolen base attempts in the league. But doesn't Beane hate stolen bases? Not so much. In a recent interview, he said, "We never had a problem with the stolen base; we always had a problem with the caught stealing. So as long as we avoid those, we're all fine with it."

Since most attempts occur when a runner is trying to steal 2nd base, I'd say your team success rate needs to be at least 75% to make stealing bases worth the risk. It should be closer to 80% to really be a weapon for your team. As you can see, only a few teams approach this level, and many teams are killing themselves by running into outs.

Of course, these are generalities, and each individual situation is different. For example, having a good base stealer combined with a bad catcher increases your chance of success. The key is knowing when to run, and knowing that getting caught is a big deal. It looks like only a few teams have figured this out.

1 comment:

Nilesh said...

Hey, Wall Street Journal agrees: