When to Steal?

Some recent discussion on a list of the SABR statistical analysis committee inspired me to take a quick a look at how stolen base attempts are distributed throughout a game. The results for 2004...

Inning PerInn  SB2 CS2   PCT SB3 CS3   PCT SB4 CS4   PCT
1  4857 0.129  400 151 0.726  60  15 0.800   2   0 1.000
2  4858 0.074  200 118 0.629  26  11 0.703   1   5 0.167
3  4856 0.098  280 133 0.678  38  22 0.633   0   5 0.000
4  4857 0.081  243 101 0.706  27  16 0.628   2   4 0.333
5  4856 0.086  237 119 0.666  42  14 0.750   1   6 0.143
6  4853 0.078  221 106 0.676  38  10 0.792   0   3 0.000
7  4851 0.081  255  80 0.761  43  10 0.811   1   2 0.333
8  4850 0.070  219  79 0.735  26  13 0.667   1   3 0.250
9  3771 0.055  130  50 0.722  24   3 0.889   0   2 0.000
10+ 946 0.096   65  17 0.793   7   1 0.875   0   1 0.000

What first caught my attention was that there were more stolen bases attempts per inning (.129) in the first inning than in any other. As you might imagine, this is mostly the case because the leadoff hitter, who is typically more of a stolen base threat, is guaranteed to bat in the first inning. In fact, in all innings in which the leadoff batter hit first (9,308 half innings) there were .119 attempts per half inning.

What most surprised me, however, is that there was not a general trend towards more attempts in later innings. One would think that later in the game teams would tend to gravitate towards strategies that produced single runs when those runs were more valuable. I then wrote a similar query that looked at the distribution of sacrifice hits that showed largely the same thing with the exception of extra innings where sacrifice hits are employed much more often.

Inning SH Per Inning
1  129  0.027
2  187  0.038
3  225  0.046
4  170  0.035
5  223  0.046
6  172  0.035
7  178  0.037
8  185  0.038
9  139  0.037
10 123  0.130

However, at second thought it occurred to me that the spread of the score would tend to increase during the game which may offset this effect. To check this I ran one more query which showed...

Diff  PA Att/PA
0  48766 0.024
1  43536 0.022
2  32214 0.020
3  21834 0.020
4  14750 0.019
5   9807 0.011
6   6573 0.007
7   3996 0.001
8   2711 0.001
9   1890 0.001
10  1071 0.001
11   672 0.000
12   292 0.000
13   162 0.000
14    82 0.000
15    92 0.000
16    48 0.000
17     2 0.000
18     1 0.000
19     4 0.000
20     5 0.000
21    23 0.000
22     8 0.000

Here you can see that as the spread of the score increases the number of stolen base attempts per plate appearance decreases. However, given that the stolen base is a tactical weapon that typically increases the odds of scoring a single run at the cost of the big inning I'm surprised that the difference in attempts per half-inning between a one-run game (.022) and a four-run game (.019) is so small (I also checked to see if the frequency was significantly different when, for example, a team was trailing by three runs as opposed to winning by three - there wasn't). Although not shown the stolen base percentage from 0 to +-4 runs is roughly the same and then jumps up over 80% at +-5.

My conclusion is that this is another situation where major league managers don't really understand the value of stolen bases and therefore employ them too often, especially when down by two or more runs.