Sunday, February 15, 2015

Saving Runs For Another Game

Should the Rangers have saved some runs for the next game?
(Photo credit: MLB.COM)

Does it seem as if a team that explodes for 12 or 15 or 20 runs one day inevitably gets shut out or held to one run the next day? Is this a real effect? Does a team become too relaxed after a big game and thus get shut down in the following game? Or perhaps the opposing team gets embarrassed and plays for revenge the next day? Should we really wish that out favorite team saves some runs for the next game?

In order to determine whether a team that scores a large number of runs in one game tends to get held down in the next one, I looked at all games from 2005-2014 using the retrosheet databases. First, I needed to determine a cut off to be used for an unusually high score. Table 1 below looks at the distribution of runs scored in all games during the period: Teams were shut out 6.1% of the time, held to one run 10.3% of the time, etc. We can see that teams rarely scored 12+ runs in a game - only 2.9% of the time - so that seems like a good cut off.

Table 1: Distribution of Runs Scored in All Games, 2005-2014
RS
%
Cum %
0
6.1
6.1
1
10.3
16.3
2
13.0
29.4
3
14.1
43.5
4
13.3
56.8
5
11.2
68.0
6
9.4
77.4
7
6.9
84.3
8
5.0
89.3
9
3.7
93.0
10
2.4
95.4
11
1.7
97.1
12+
2.9
100.0
Data source: Retrosheet.org

In Table 2, we can see that there were 1,386 games between 2005-2014 where a team scored 12 or more runs. I calculated the expected runs in the next game as follows: Suppose the Tigers scored 14 runs in a game. The expected runs in the next game would be the team average runs scored for that season with that game removed. That is:

Expected Runs Scored = (Team total runs scored for the year -14)/161

Table 2 shows that the average of the expected runs in the follow-up game to a 12+ run game was 4.6. The actual average was also 4.8. So, teams scored slightly more than their average in the next game after a high-run scoring game. Suppose we choose a more extreme cutoff such as 15+ runs. In this case, the expected runs (4.7) was almost identical to the actual average (4.8). It appears, in general, that scoring a lot of runs in one game did not depress scoring in the next game.

Table 2: Expected runs versus actual runs in follow-up game
RS
Game 1
Games
Expected RS Game 2
Actual RS Game 2
0-2
14,185
4.4
4.3
3-5
18,666
4.5
4.5
6-8
10,296
4.5
4.5
9-11
3,765
4.6
4.7
12+
1,386
4.6
4.8
15+
313
4.7
4.8
Data source: Retrosheet.org

The point is further illustrated in Table 3 which shows the distribution of runs scored in games following 12+ run games. We can see that it is very similar to the distribution for all games in Table 1. For example, teams scored two runs or fewer 26.1% of the time in follow-ups to high scoring games as compared to 29.4% in all games. It certainly does not look as if teams have a tendency to get shut down the next game after an offensive explosion. If anything, they appear a little more likely to exceed their average output in the next game.

So, the next time you see the Tigers score 17 runs in a game, don't fret about the next game. Just enjoy it. 

Table 3: Distribution of Runs Scored in All Games following 12+Run Game, 2005-2014
RS
%
Cum %
0
5.3
5.3
1
9.0
14.4
2
11.8
26.1
3
14.1
40.3
4
13.4
53.9
5
10.7
64.4
6
9.8
74.2
7
7.7
81.9
8
5.7
87.6
9
4.5
92.1
10
2.4
94.4
11
1.5
96.0
12+
4.0
100.0
Data source: Retrosheet.org

3 comments:

  1. Liked reading this, Lee. I tried to tackle a similar question last season but didn't really know how to do it. (https://aldland.wordpress.com/2014/07/31/flying-tigers-where-are-the-bats/) As usual, your approach makes sense and is clearly explained.

    ReplyDelete
  2. AD, you might be interested in this article at hardballtimes:

    http://www.hardballtimes.com/runs-per-game/

    ReplyDelete

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