THE BOOK--Playing The Percentages In Baseball

Tuesday, September 16, 2008

Linear Weights, By Men on Base

By Tangotiger, 03:14 PM

There are different ways to do Linear Weights. You can do it by men on base, as SG is doing here, or by the base/out states, or by game state (inning, score, base, out, and shown at Fangraphs as WPA/LI). They all tell a story. The nice thing about the men on base one is that it’s only 8 lines per player, which is a heckavu lot easier to swallow than 24 or the thousands by game state.

I’m wondering, under the “less is more” scenario, construct the 24 base/out set into something more manageable. For example, we can have these states:
1- man on 1B, 3B (runner on 2B optional), less than 2 outs
2- man on 3B (excluding above), and less than 2 outs
3- man on 1B, 2B (excluding all the above), less than 2 outs
4- man on 1B (excluding all the above), less than 2 outs
5- man on 2B or 3B (excluding all the above)
6- man on base (excluding all the above… when I think just leaves me with man on 1B, 2 outs)
7- bases empty less than 2 outs
8- bases empty 2 outs

Do these make sense in terms of trying to segregate based on how the batter/pitcher might change his approach to the base/out state? This is my reasoning for those 8 categories:

1. SF and DP situation
2. SF situation
3. DP, and run-driving situation
4. DP situation
5. run-driving situation
6. runner on base
7. no one on, still can start a rally
8. no one on, tough to get a rally going without extrabase hits

So, all PA would be split into one of these 8 categories, and all 8 categories are mutually exclusive. What do you guys think? Is this a good segregation? Can we merge some of the categories? I really don’t want to go past 8, but I will if we think it makes more sense.

• Sabermetrics • Linear_Weights

#1 Tangotiger (see all posts) 2008/09/16 (Tue) @ 15:41

Here’s how it looks like, with the numbers in the chart corresponding to the 8 states above:

XXX | 0 1 2
=== | = = =
--- | 7 7 8
1-- | 4 4 6
-2- | 5 5 5
12- | 3 3 5
--3 | 2 2 5
1-3 | 1 1 5
-23 | 2 2 5
123 | 1 1 5
=== | = = =

#2 SG (see all posts) 2008/09/16 (Tue) @ 16:12

Yeah, I’m using the 8 basic men on situations because it’s easier to pull the data using David Pinto’s splits comparison database.

I think you’ve got a good start here, although I would think 7 and 8 will end up being redundant. I’m also not sure how easy it is to get the data for the splits you’re looking for without PbP data, which is fine retroactively, but somewhat limiting in-season.

I’d probably add bases loaded as its own state and not lump it in with scenario 1 (force at every base, nowhere to put the batter etc.,) and then combine 7 and 8.

So my list would look like this:
1- man on 1B and 3B
2- man on 3B, < 2 outs
3- man on 1B and 2B, < 2 outs
4- man on 1B, < 2outs
5- man on 2B or 3B
6- man on 1B, 2 outs
7- bases empty
8- bases loaded

Incidentally Tango, if you want the spreadsheet I’m using to pull the data let me know and I can e-mail it to you. You should be able to modify it to use whatever splits you want if you know anything at all about MS VBA for Excel and web querying.

#3 Tangotiger (see all posts) 2008/09/16 (Tue) @ 16:32

Thanks SG, feel free to email it to me.

Your Bases Loaded reasoning probably makes more sense than my reasoning for splitting up the bases empty one. Maybe. I might have to go to 9 states.

Just for reasons of hierarchy, SG’s Bases Loaded state would really be #0, since it would take precedence over the state #1 I have. That’s just to clear up any kind of confusion.

#4 Tangotiger (see all posts) 2008/09/16 (Tue) @ 16:58

What I did was take Table 50 from The Book, and divided each of those values by the run value of the out.

Then, I took the overall run value for each event, and divided that by the run value of the out.

I took the result of paragraph 1 and divided it by the result of paragraph 2 to get an index for each event by base out state.

If the base/out state has no special meaning for the event, the index value for that event at that base/out state will be 1.00. The double, for example, is a base/out state neutral event. It is always worth the same, more or less, relative to the run value of the out, across all states.

Here is the full chart, which I hope will format nice:

1B    2B    3B    Outs  Sngl      Dbl      Trpl      HR      NIBB      RBOE      K      Out 
--    --    --    0     1.0      0.9      1.0      0.8      1.4      1.0      1.0      1.0 
--    --    --    1     1.0      0.9      1.1      1.2      1.5      1.0      1.0      1.0 
--    --    --    2     0.7      0.7      0.6      1.8      1.1      0.7      1.0      1.0 
1B    --    --    0     0.9      0.9      0.9      0.7      1.2      0.9      0.8      1.0 
1B    --    --    1     0.8      1.0      1.0      1.0      1.0      0.8      0.9      1.0 
1B    --    --    2     0.6      1.1      1.2      1.5      0.8      0.7      1.0      1.0 
--    2B    --    0     1.2      1.0      1.0      0.8      1.0      1.0      1.3      1.0 
--    2B    --    1     1.1      1.0      0.9      0.9      0.7      0.9      1.0      1.0 
--    2B    --    2     1.3      1.1      0.8      1.1      0.3      0.8      1.0      1.0 
--    --    3B    0     0.8      0.7      0.8      0.6      1.1      0.8      1.4      1.0 
--    --    3B    1     1.5      1.1      1.1      1.1      1.1      1.4      2.2      1.0 
--    --    3B    2     1.4      0.9      0.7      0.9      0.4      1.3      1.0      1.0 
1B    2B    --    0     1.0      0.9      0.8      0.6      1.3      1.0      1.0      1.0 
1B    2B    --    1     1.0      1.0      0.9      0.8      1.1      0.9      0.9      1.0 
1B    2B    --    2     1.2      1.2      1.1      1.2      0.7      0.8      1.0      1.0 
1B    --    3B    0     0.8      0.8      0.8      0.6      1.0      0.9      1.2      1.0 
1B    --    3B    1     1.0      1.0      1.0      0.9      0.8      1.0      1.5      1.0 
1B    --    3B    2     1.1      1.0      0.9      1.0      0.5      1.0      1.0      1.0 
--    2B    3B    0     1.5      1.2      1.1      0.9      1.3      1.3      1.5      1.0 
--    2B    3B    1     1.2      1.1      0.9      0.9      0.5      1.1      1.9      1.0 
--    2B    3B    2     1.4      1.0      0.7      0.8      0.3      1.0      1.0      1.0 
1B    2B    3B    0     0.9      0.8      0.7      0.6      1.3      0.8      1.2      1.0 
1B    2B    3B    1     1.0      1.0      0.9      0.8      1.3      1.0      1.2      1.0 
1B    2B    3B    2     1.1      1.0      0.8      0.8      1.1      0.9      1.0      1.0

Ok, that looks nice.

So, where do we have the biggest change in terms of impact by base/out state?

The easy one is the K. Runner on 3B and less than 2 outs, but NOT the bases loaded situation. Interesting.

The double is neutral, and the triple is virtually neutral (sole exception: bases empty, 2 outs).

The HR is very powerful with 2 outs and either bases empty or runner on 1B. That’s easy to understand. The HR has less impact with 0 outs across all states. That’s because with 0 outs, so much can still happen, that the difference between a HR and a triple is not that big a deal.

The single is a bit tougher: man on 3B only, with 1 or 2 outs, man on 2b+3b with 0 outs. Those are the situations where a single is more valuable than expected. With runner on 1B and 2 outs, the value of the single is not that much.

Finally, for the walk: runners on base, 1B open, and 2 (and sometimes 1) out. The value of the walk plummets. Bases empty and 0,1 out: value of walk jumps.

For the walk/K relationship, that dynamic completely changes with one state in particular: man on 2b and 3b with 1 out. In this case, a walk costs very little and a K is extremely valuable. So, a Nuke Laloosh would be fantastic here.

Ok, after doing all that, I’m not sure I can buy my argument for the 8 states I constructed. Well, it all really depends on how the batter/pitcher respond to the situations. They SHOULD respond to it according to my chart above. How they ACTUALLY respond to it is another matter.

#5 Peter Jensen (see all posts) 2008/09/16 (Tue) @ 17:03

The value added method described by Tom Ruane contextualizes linear weights by taking the value added for each at bat directly from the RE tables. This gives the same run value that you would get by figuring linear weights for each base out situation and then giving the batter that value, but it just skips a step. It is also very easy to set up the Retrosheet database so that a single query will give the value added totals for each player. I think it was Baseball Cube that used to keep track of the player’s value added numbers during the season. I don’t know if they still do or not. The only problem with Ruane’s methodology was that he used RE tables based on a single season. But it is easy to use any RE table that you feel comfortable with.

#6 Colin Wyers (see all posts) 2008/09/16 (Tue) @ 17:27

Fangraphs does what Peter is talking about and calls it BRAA. I don’t know what RE table they use, however.

#7 terpsfan101 (see all posts) 2008/09/16 (Tue) @ 20:06

I think Tangotiger derived the RE tables that Fangraphs uses. I think they use his Win Expectancy tables as well.

#8 tangotiger (see all posts) 2008/09/17 (Wed) @ 07:01

Right, I should have pointed that out to SG. Fangraphs does calculate LWTS by the 24 baseout states, and it is called BRAA on Fangraphs. I forgot that.

But, it is always nice to see someone explain the process, as the uninitiated won’t accept things on blind faith necessarily.
http://www.fangraphs.com/winss.aspx?team=Yankees&season=2008

#9 SG (see all posts) 2008/09/17 (Wed) @ 09:41

That’s good to know, and saves me a ton of work. Thanks guys.

#10 Tangotiger (see all posts) 2008/09/17 (Wed) @ 10:30

SG, here is the explanation at Fangraphs:

http://www.fangraphs.com/blogs/index.php/get-to-know-braa/

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THE BOOK--Playing The Percentages In Baseball

Tuesday, September 16, 2008

Linear Weights, By Men on Base

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