Was Tulo Robbed?

This was a piece that I published on the Rocky Moutain SABR website.

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I know most Rockies fans were hopeful that Troy Tulowitzki would lay claim to the National League Rookie of the Year Award. Well, the award was given out last Monday and in what was the closest race in the NL since the current system was put in place in 1980, Milwaukee's Ryan Braun edged Tulo 128 to 126 in the voting. Braun received 17 first place votes to Tulowitzki's 15.

While it's hard to fault voters for choosing Braun given the monstrous offensive season he had - breaking the rookie record for slugging percentage held by Mark McGwire and hitting 34 homeruns in two-thirds of a season - one gets the impression that the voters may have underappreciated the difference between the two players on the defensive side of the ball. Be that as it may we shouldn't be too hard on them, however, since historically defense has defied meaningful analysis and looking at things like error totals (Braun made 26 while Tulowitzki made 11) don't really give a good feel for the more important aspects of defense such as range.

But we're here to correct that.

Below you'll find a table that compares the two players in terms of their raw numbers using two of the advanced performance measures we track at Baseball Prospectus.

          Actual 
          Offense             Defense 
Name         Outs    BRAR     POS    AdjG    FRAR   Total 
Tulowitzki    445      30     SS    152.3      46      76 
Braun         315      50     3B    106.1     -15      35 
                                       Difference      41

BRAR stands for Batting Runs Above Replacement and is the number of runs the player contributed above and beyond what a replacement level offensive player (think of a pretty weak bench player and you'll have the idea) would contribute if allowed to make the same number of outs. We use outs instead of plate appearances or at bats since ultimately baseball is predicated on the idea of avoiding outs if you're on offense and finding a way to get outs on defense. BRAR includes basic baserunning and is adjusted for things like the league and home park context. The latter is of course key in the case of Tulowitzki since he plays at Coors Field which, even in the humidor era, is a ballpark with a marked hitter's advantage. FRAR stands for Fielding Runs Above Replacement and is the number of runs the player saved on defense over a replacement level player (a relatively poor fielder) at his position. Outs is obviously the number of outs each player consumed offensivley and AdjG is the number of 9-inning game equivalents the player played at his position.

So from the table we can divine that while Braun contributed twenty more runs offensively while consuming 130 fewer outs, Tulowitzki amazingly was responsible for saving 61 more runs on defense. Put together Tulowitkzi contributed 76 runs to Braun's 35, a differene of 41 runs and equivalent to about 4 wins (10 additional runs for a team in the big scheme of things is roughly equivalent to a win). Can that be right? Such a large number makes one immediately suspicous and so let's take a look at an alternate metric.

John Dewan of Baseball Info Solutions has created a Plus/Minus system that tracks each ball hit to any fielder and determines in the aggregate how many balls plus or minus the fielder was able to handle as compared to an average fielder at his position. In Dewan's system Braun came up with a total of -41 and Tulo was at +35. In other words, Braun didn't handle 41 balls that an average third baseman would have while Tulowitzki made 35 more plays than would have been expected. Not incidentally, Braun's rating was the lowest of any position player and Tulowitkzi's was the highest among shortstops as he was crowned the best fielding shortstop in baseball by Dewan in the 2008 Bill James Handbook.

We can convert Dewan's plus/minus values to runs by assuming that each ball not fielded became a single (an assumption that is kind to Braun since he plays third base where some of the balls he failed to field undoubtedly became doubles and not singles) and knowing how much a single and an out are worth in terms of runs. Luckily, there are a series of run estimatation formulas known collectively as "Linear Weights". In that system each single is given a "weight" equivalent to 0.47 runs and each batting out -0.25 runs. So given these values it turns out that a would-be out that turns into a hit costs a team roughly 0.70 runs. If we then take the difference between Braun and Tulowitzki, 76 plays, and multiply by 0.70 we get 53.2 runs. Both systems are saying essentially the same thing - Tulowitzki was worth somewhere between 50 and 60 runs more defensively in 2007.

But of course Braun didn't play an entire season and so could it be the case that if we gave him a full season his offensive dominance would wipe out the difference?

To answer that question below is a table that pro-rates both player's offensive and defensive statistics to the same number of outs consumed on offense and adjusted games on defense.

          Pro-Rated 
          Offense             Defense 
Name         Outs    BRAR     POS    AdjG    FRAR   Total 
Tulowitzki    450      30     SS      162      49      79 
Braun         450      71     3B      162     -23      49 
                                       Difference      30

If both players had consumed 450 outs Braun would have produced 71 more runs than a replacement player while Tulowitzki would still have been at 30. Those 41 additional runs are not inconsequential. However, had Braun played 162 games on defense he would have given up 23 more runs than a replacement level fielder while Tulo would have saved 49 runs. When you add it all up the gap between the two players shrinks to 30 runs or the equivalent of three wins. As my colleague Joe Sheehan noted, Tulowitzki was robbed, perhaps not by much - but in the end he was the more deserving.

But Rockies fans shouldn't feel too bad. Look what happens when you add the name Hunter Pence to the list and use the same rationale as discussed above.

          Actual 
          Offense             Defense 
Name         Outs    BRAR     POS    AdjG    FRAR   Total 
Tulowitzki    445      30     SS    152.3      46      76 
Braun         315      50     3B    106.1     -15      35 
Pence         315      36     CF     93.5      20      56 

          Pro-Rated 
          Offense             Defense 
Name         Outs    BRAR     POS    AdjG    FRAR   Total 
Tulowitzki    450      30     SS      162      49      79 
Braun         450      71     3B      162     -23      49 
Pence         450      51     CF      162      35      86

The Astros' Pence comes out on top just barely by virtue of a solid season both offensively and defensively. Still, there is value in playing time and that, in my estimation anyway, should push Tulowitzki back over the top.