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Monday, September 15, 2008

Putting Linear Weights in Context

As most of the readers here are probably aware, my favorite method for evaluating offensive performance is using batting runs as calculated by linear weights.  Linear weights are flexible, thorough, and can be easily manipulated to compare players to average players, replacement-level players, and players who play the same position.

The key to linear weights is understanding that every positive or negative outcome has a commensurate run value.  Since runs are the key to winning baseball games, linear weights gives us what I think is the bulk of the information we need to look at why teams score or don’t score, which then tells us why they win or lose.

However, this year, the Yankees have exposed some of the flaws in using a context-neutral statistic like linear weights when looking back at past performance.  The normal linear weights formula assume that every single is worth a certain amount, every double is worth a certain amount, every out is worth a certain amount, etc., However, we all know this isn’t really true in real life. A single with runners on second and third is worth more than a single with the bases empty, but in the normal linear weights formula, they’re treated equally.

That’s fine if you are trying to assess the skill level of players, but it’s not quite as useful when looking back at results retroactively.  I messed around with the Hardball Times’s version of clutch as defined by Bill James but reader feedback and some more thinking led me to realize that it’s fairly limited.  So then I looked at some situational splits using wOBA which I liked better, but that’s more of a rate stat and less useful when trying to look at what it means as far as runs.

I am still morally opposed to WPA because I think it’s far too timing and teammate dependent.

Thankfully, there’s a way to make linear weights more useful in retroactive analysis by contextualizing them.  To do this, I’m going to use the information from this study by Tango Tiger called linear weights by men on base.  The subject here is coincidentally enough how linear weights value differ based on the different baserunner states.  You could take this out to a more precise extreme by factoring in the out states but I think that’s a lot of extra work for very little additional payoff.

So what I did is use the matrix from the article linked above and split out every hitter’s performances in the eight different baserunner states.

-No one on
-Runner on first
-Runner on second
-Runner on third
-Runners on first and second
-Runners on first and third
-Runners on second and third
-Bases loaded

If you look at the chart in the linked article, you can see for example that a single with no one on base is worth .29 runs, and a single with the bases loaded is worth 1.38 runs.  So I ran the splits for each of the eight situations above for 2008, and calculated the batting runs per out for each of the eight splits for each player as well as for the average player. Then players are compared to the average player in each splits and their batting runs above average for each of the eight splits are added to get their contextual linear weights value.  This is compared to their context-neutral linear weights to get a difference.  The bigger the difference, the more productive a player in situations with runners on base.  I’m going to use comparisons to average here instead of comparisons to replacement level, and I’m not position-adjusting for now. 

One other thing I like about this is it accounts for the fact that strikeouts are more damaging in certain situations.  With none on, a strikeout is no worse than any other out (-0.2 runs).  Put a runner on third though, and a strikeout is worth -0.48 runs compared to -0.29 for other types of outs.

One issue I have with this data is the data source I’m using (David Pinto’s Day by Day Splits Database) does not differentiate performance for players who’ve played on multiple teams, so I am going to exclude people like Xavier Nady and Richie Sexson in this initial run through, although I can modify my start and end dates to include just their Yankee tenure later on.

So, without further ado, here’s what this measure says for the players who have only seen MLB time with the Yankees this year.

None on: Batting runs above average with no one one base.
1—: Batting runs above average with a runner on first.
-2-: Batting runs above average with a runner on second.
—3: Batting runs above average with a runner on third.
12-: Batting runs above average with runners on first and second.
1-3: Batting runs above average with runners on first and third.
-23: Batting runs above average with runners on second third.
123: Batting runs above average with the bases loaded.
cTotal: contextual linear weights total (all 8 of the above added together)
cnTotal: context-neutral linear weights batting runs above average.
Diff: cTotal - cnTotal

A positive difference between cTotal and cnTotal indicates a player was more productive with runners on base.  Alex Rodriguez has been less productive with runners on base this year, and that’s indisputable. However, he’s still been the most valuable offensive player on the Yankees.  His critics will ignore that and cherry-pick the numbers that “prove” their point, but they’re wrong. 

Bobby Abreu has been more productive this season than his raw numbers show. His defense still stinks though.

Jason Giambi’s hit poorly with runners in scoring position, but he’s done well with runners on first and overall he’s not been as bad with runners on as his RISP numbers make him look.

Johnny Damon, Hideki Matsui, and Derek Jeter haven’t been much different with runners on vs. not.

Jose Molina, Melky Cabrera, and Robinson Cano have been equal opportunity suckers for the most part, although Cano’s actually been about five runs worse than his context-neutral numbers show.

Just looking at this set of Yanks, we can see that they’ve fallen around 19 runs worse than they should have so far this season given their actual YTD performance and how it’s translated to runs in linear weights.  Their context-neutral linear weights runs above average are 44.5, but when you contextualize it they drop to 25 runs above average.

In actuality the Yankees have been only 8 runs better than average, so we still have to account for 17 runs.  If we add in Pudge Rodriguez (-6), Alberto Gonzalez (-7), and Xavier Nady (+5), that’s another -8.  So we still have nine or so missing runs, which could just be double plays and/or baserunning issues, or a limitation in this model.

Bear in mind, this is above and beyond their actual underperformance compared to their pre-season projections, particularly for Cano and Cabrera.

The other thing this may be useful for is MVP balloting, if I had a vote.  Which I don’t.  Here’s a look at the MLB leaders in contextual linear weights.

Remember that this is strictly offense and not position-adjusted.  Albert Pujols is just a monster.  What’s interesting is the gap between him and Lance Berkman narrows if we contextualize it, although Pujols is still having the better season and this ignores Pujols’s significant defensive edge.

Manny and Teixeira’s numbers are spread across leagues, so they’re not realistic MVP candidates.

The name that pops out to me here is Justin Morneau.  His raw stats make him look like a bad MVP candidate, but a lot of intelligent Twins fans insist he’s the Twins’ MVP, and if you look at the shape of his production it makes sense.  He’s a barely average performer with no one base, but get runners on and he’s above average in just about every split.  He’s neck and neck with Kevin Youkilis, who had a slight edge defensively last I checked.

As with other methods I’ve mentioned or read about, I don’t necessarily think this is an ideal way to look at the issue of clutch either, but it may add something to the discussion.