Wednesday, July 23, 2008

Saving runs for tomorrow

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 2003-2007 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 5.2% of the time, held to one run 9.3% of the time, etc. We can see that teams rarely scored 12+ runs in a game - only 3.5% of the time - so that seems like a good cut off.

Table 1: Distribution of runs scored in all games (2003-2007)

Runs Scored

Percent of Games

Cumulative Percent

0

5.2

5.2

1

9.3

14.5

2

12.0

26.5

3

13.3

39.8

4

13.1

52.9

5

11.6

64.5

6

9.8

74.3

7

7.6

81.9

8

5.5

87.4

9

4.2

91.7

10

2.8

94.5

11

2.0

96.5

12+

3.5

100.00



In Table 2, we can see that there were 848 games between 2003-2007 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 = (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 is 4.88. The actual average is also 4.88. Suppose we choose a more extreme cutoff such as 15+ runs. Once again , the average of the expected runs (4.88) is almost identical to the actual average (4.86). It appears, in general, that scoring a lot of runs in one game has little effect on what happens in the next game.


Table 2: Expected runs versus actual runs in follow-up game

Runs in game 1

Games

Expected avg. runs in game 2

Actual avg. runs in game 2

0-2

6,399

4.71

4.63

3-5

9,170

4.74

4.71

6-8

5,542

4.79

4.87

9-11

2,189

4.82

4.99

12+

848

4.88

4.88

15+

200

4.88

4.86



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 26.9% of the time in follow-ups to high scoring games as compared to 26.5% 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.

So, the next time you see the Tigers score 19 runs in a game, don't fret about the next game. Just enjoy it.


Table 3: Runs scored in game following a 12+ run game

Runs Scored in game 2

Percent of Games

Cumulative Percent

0

6.2

6.2

1

8.5

14.7

2

12.2

26.9

3

11.9

38.8

4

13.4

52.2

5

9.7

61.9

6

9.8

71.7

7

7.3

79.0

8

6.0

85.0

9

5.7

90.7

10

3.7

94.3

11

1.9

96.2

12+

3.8

100.0


The information used here was obtained free of charge from and is copyrighted by
Retrosheet. Interested parties may contact Retrosheet at "www.retrosheet.org"

3 comments:

  1. This seems to be the one instance where fans recognize regression to the mean. Of course regression doesn't happen instantly.

    ReplyDelete
  2. Justin (jj04)July 23, 2008

    Lee, thank you for disproving my assumption (that teams that score a lot of runs in one game more often than not tend to be a dud the following game).

    ReplyDelete
  3. No problem Justin. I like disproving assumptions. :-)

    Lee

    ReplyDelete

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