### Clutch, WPA/LI, and the Home Run Bias

The stat Clutch, as published on FanGraphs and Baseball-Reference, is designed to quantify how much better or worse a hitter has produced in situations based on how critical those situations are in the immediate context of a game.  Players who perform better in more critical situations (for example, late in a close game) than they normally do will have a positive Clutch rating, and players who perform worse in such situations will have a negative Clutch.  It does this by comparing two values for a hitter:  his WPA and his WPA.LI.  I will assume you are familiar enough these two stats (not necessarily their inner workings, but at least what they are) as a prerequisite for this piece; if not, you can catch up on B-R's or FanGraphs' explanation pages.

WPA.LI follows two key constraints.  The first is that, for a given game state (i.e. the inning, the score, the number of outs, and the placement of any runners on base), the relative value of a play is determined by how much that play affects the team's chances of winning.  If the bases are empty, a walk is credited the same as a single.  If the bases are loaded with the winning run on third, a walk is credited the same as a home run.  This constraint works exactly like WPA (as one might expect from a WPA-based metric).

The second constraint differentiates WPA.LI from WPA.  One of the properties of WPA is that some situations are inherently weighted more strongly than others.  A key at bat late in a close game can swing a team's chances of winning by several times as much as the same result in a blowout, and it is credited accordingly.  WPA.LI, on the other hand, ensures that the average play in every situation gets the same weight.

So, on the one hand, you have WPA, which weights PAs according to their immediate impact on the game.  One clutch PA might be worth as much as 4 or 5 normal PAs, and one mop-up PA might be worth practically nothing.  On the other hand, you have WPA.LI, which weights every PA equally, just like most other stats do.  Basically, it is linear weights, but with the ability to tailor the value of each event to the specific situation rather than sticking to a blanket value for each event across all situations.  While WPA tells the story of clutch hitting (who got the big hit when the team most needed production), WPA.LI tells the story of situational hitting (who got on base when the team needed baserunners, put the ball in play when the strikeout was most costly, or hit for power when advancing runners quickly was more important than getting another guy on first).

There is a third important constraint which WPA.LI does not adhere to, however.  Ideally, the average value of each event would match its linear weights value.  If a home run is worth 1.4 runs above average across all situations, then you would like the average WPA.LI value of a HR to be 1.4 runs (or rather, the equivalent value on the wins scale).  That is not the case, however.

The following linear weights values represent the average change in run and win expectancy for that event across all situations, along with the average WPA.LI value of each event.  All three versions have been placed on the runs scale by setting the value of the out at -.27 in order to make them easier to compare directly:

 RE WPA WPA.LI 1B 0.47 0.47 0.44 2B 0.77 0.75 0.75 3B 1.05 1.06 1.04 HR 1.41 1.42 1.58 BB 0.31 0.30 0.31 K -0.29 -0.30 -0.29 out -0.27 -0.27 -0.27

As you can see, WPA.LI does fine at assigning the correct value to most events, but the value of the HR is way off.  This may seem counterintuitive; if WPA.LI just creates custom linear weights for each situation based on the WPA values, why would the average WPA.LI value be different from the average WPA value?  We can look at the mathematical relationship between WPA and WPA.LI to see why this is.
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### The Pujols Decision: One Fan's Reflections

Stan Musial is the man in St. Louis.  Nearly 50 years after Musial last played for the Cardinals, he remains the undisputed king of Cardinal baseball.  His statue alone stands tall outside the main entrance to Busch Stadium, a few hundred feet south of the plaza where all the lesser (albeit much more attractive) statues of other Cardinal greats sit.  For decades, no one in St. Louis thought they would ever see a player rival Musial.

And then Albert came along.  Just one year and one Bobby Bonilla injury removed from his professional debut as a 13th round draft pick, Pujols was in the starting lineup and lighting up the National League.  He hit for average.  He hit for power.  He got on base.  He eventually learned to play a very good first base.  For the first time, St. Louis fans saw a player and thought, "this could be the guy who tops Musial."

The accolades came.  The MVPs (three of them, same as Musial), the All Star appearances, the Silver Sluggers and Gold Gloves, the home runs and hits and RBIs; all of them flocked to Pujols' Baseball-Reference page like moths to Matt Holliday's ear.

The wins followed.  Led by Pujols' success, the team made the playoffs 7 out of 11 seasons, winning 3 pennants and 2 World Series along the way.  From 2001-2011, only the high-spending Yankees and Red Sox won more games than did Pujols' Cardinals.  Pujols was the best player in the game, a superstar of whose order the franchise had not seen in decades.  Fans watched in awe and wondered how high his career would stack by the time it ended.

Pujols was, over his 11 years with St. Louis, remarkably similar to Musial when Musial was at his best.  Compare Pujols’ career in St. Louis to Musial’s best 11 year stretch (1943-54):

 PA H RBI HR BB R Musial (1943-54) 7564 2251 1174 281 990 1301 Pujols (2001-11) 7433 2073 1329 445 975 1291

 AVG OBP SLG wRC+ brWAR fWAR Musial (1943-54) .346 .434 .591 171 88 98 Pujols (2001-11) .328 .420 .617 167 84 88

In both traditional counting totals and more sabermetric evaluations, the two come up as near equals.  Musial got on base a bit better (in an environment where hitters got on base more than they do today) while Pujols hit for more power (in an environment where hitters hit for more power than they did in Musial’s day).  The two were comparable fielders, good for their position, but at the weak end of the fielding spectrum.

Musial rates slightly better in both Baseball-Reference’s and FanGraphs’ implementations of WAR, but they are close enough that which one you would pick will largely depend on how you approach the different eras (i.e. how you want to adjust for things like integration, expansion, population growth, international development, improved scouting, the war years, etc).  They’re close enough that it would reasonable to take the position that no Cardinal fan has ever seen one of their own play at a higher level than Pujols has over his 11 years with the team, not even Musial.  It’s not a slam-dunk position; maybe you still take Musial.  But, for the first time since Musial retired, you’d probably at least have to think about it.

Watching Pujols play ignited Cardinal fans like watching Musial did, and we loved every minute of it.  Naturally, we wanted that to continue.  We wanted another all-time great to stay a career Cardinal.  Then, out of nowhere, the report swept in from the winter meetings that Pujols had signed with the Angels.  No build up, nothing.  No one had even talked about the Angels in the weeks of negotiating that led off the offseason.  Just like that, he was gone.

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