## Monday, June 21, 2010

### Are doubles and home runs disproportionately valuable in high scoring environments?

This issue came up in a recent NY Times blog entry. It was A Labor Market (and Baseball) Mystery. The issue had to do with the pay of middle infielders. One economist said:
"Doubles and home runs are disproportionately valuable in high scoring environments than low scoring environments, because their runner-advancing potential is greater when there are more runners on base. In a high-scoring, a home run is more likely to score other runners, and someone who hits a double is less likely to be stranded on second base."
I wondered if this were true. So I looked at the run values of various events from Tom Ruane's article called The Value Added Approach to Evaluating Performance. Tom used Markov Chains to find the run values of various events in each league, year-by-year, from 1960-2004. For example, in 1960, in the AL, a single had a run value on average of .464 while a HR had 1.419.

What I did next was find the following ratios, by run value, for 2B/1B, 2B/BB, HR/1B, and HR/BB. Then I found the correlation of those ratios with the runs per game for each year. Here are those correlations for each ratio.

2B/1B) -.14
2B/BB) -.49
HR/1B) -.84
HR/BB) -.83

The negative correlations indicate that as scoring goes up, the value of HRs and 2Bs, relative to other events, falls. I checked the scatter plot for the first one to see if there was any sort of non-linear pattern like a parabola, but there was not.

Here were the top 5 years in terms of HR/1B ratio. The numbers in parantheses are the runs per game in that environment. Walks were non-intentional walks.

1972AL) 3.43 (3.47)
1968AL) 3.32 (3.41)
1968NL) 3.29 (3.43)
1978NL) 3.29 (3.99)
1963NL) 3.29 (3.81)

Most fans probably know that these were low scoring seasons. In the 1972AL, the run value of a HR was 1.444 while the value of a 1B was .421. 1.444/.421 = 3.43.

Here were the bottom 5 years in terms of HR/1B ratio. Notice how these are much higher scoring seasons.

1994AL) 2.86 (5.23)
1996AL) 2.85 (5.38)
1995AL) 2.84 (5.06)
2000AL) 2.84 (5.30)
2002AL) 2.80 (4.81)

In the 1994AL, the value of a HR was 1.399 while it was .489 for a 1B.

Tom Tango (tangotiger) came up with run values for various events using Baseruns. This is at Custom Linear Weights Values by Team Generated using the BaseRuns system. He looked at all teams from 1919-2000. I ran the same correlations as mentioned above but did not include 1919. Here they are. They show about the same pattern as above. HRs and 2Bs have less relative value in higher scoring environments.

2B/1B) -0.649
2B/BB) -0.650
HR/1B) -0.878
HR/BB) -0.862

Tom Tango had a good discussion of this issue at Reader Mail of the Day: Environment impacting events .