Context and Hitters' Values, part 2

I originally posted this to Beyond the Box Score in 2006.

In the first part of this 

(at http://www.beyondtheboxscore.com/story/2006/3/3/11718/18810),

or (http://cyrilmorong.com/ContextandHittersvalues.htm)http://cyrilmorong.com/ContextandHittersvalues.htm

I looked at how many runs a player would add to a team if he replaced someone on that team. The example I used had Mickey Mantle of 1961 being added to a very low scoring team, the 1963 Astros, and a very high scoring team, the 1996 Indians. I assumed that all 9 hitters in each team's lineup were identical, that Mantle replaced one and got 1/9th of each team's plate appearances (PAs). Both teams were predicted to score more runs with Mantle, but the increase for the 1963 Astros was greater.

This time I am going to do something similar. But I will use the "custom linear weights" values found at this site by Tangotiger

http://www.tangotiger.net/bsrlwts.html

First, I determined how much each team's on-base percentage (OBP) would increase if Mantle replaced an average hitter on each team. The Astros would go from an OBP of .284 to .302, while the Indians would go from .368 to .377. It goes up more for the Astros because Mantle replaces a guy with a lower OBP. Then I had to estimate how many additional PAs each team would get in a season due to their respective OBP increase (the Indians would go up about 61 PAs while the Astros would go up about 48).

Then I calculated each team's frequencies per PA for the following events: 1Bs, 2Bs, 3Bs, HRs, BBs, SBs, CSs. Then I calculated how much each team's frequency for each event would change if Mantle replaced an average hitter. Using the new PA total for each team (based on the change in team OBP), I found how many 1Bs, 2Bs, etc. each team would get if Mantle were added. Subtracting the actual totals for those events from the estimated totals gave me the change in how many times each event would occurr. The 1996 Indians would hit about 38 more HRs while the 1963 Astros would hit about 50 more. Both teams would have fewer singles and doubles but alot more walks.

So how would this change scoring? That is where Tangotiger's "custom linear weights" table comes in. The run values of these events are lower for the 1963 Astros than they were for the 1996 Indians because the Indians were a higher scoring team, hit more HRs, etc. A walk is more valuable on the Indians because they hit more HRs, for example.

Here are the run values for the Astros

1B = .42
2B .73
3B = 1.03
HR = 1.42
BB = .28
SB = .18
CS = -.28

For the Indians

1B = .51
2B .82
3B = 1.12
HR = 1.42
BB = .37
SB = .17
CS = -.32

So, if the Astros hit 50 more HRs, that would increase their runs by 71. If the Indians hit 38 more HRs, that is about 54 more runs. With each team hitting fewer singles, that would enter as a negative. But adding up all of the changes times their run values for each team, the Astros would score about 95 more runs while the Indians would score about 67 more runs. So the Astros do 28 runs better. That is less than the 42 run difference I found in the previous article, but the increase is still alot bigger for the Astros.

One last thing. The run values of these events will probably change for each team since each team's OBP has gone up. Tangotiger has a site with a graph that shows how the run value of various events changes with team OBP. It is at

http://www.tangotiger.net/runscreated.html

For the most part, over relevant ranges of team OBP (OBPs that actual major league teams might have), the values of each event increase and the increase seems linear (the trend line is straight). Since the Astros had twice the OBP increase, the run values of the events will increase more for them than the Indians. Using the graph to make a rough estimate of how the change in run values would impact each team, I then had the Astros going up 99 runs if Mantle were added and the Indians go up 68. So not too much difference in the story if we account for the changing run values of the various events.