May 31, 2007
Lies, Damned Lies
There are two ways to build a winning baseball team. One way is to have a few players who are extraordinarily good. Alternatively, you can have few players who are extraordinarily bad. Conversely, there are two reasons that baseball clubs fail. They can have an absence of good players-or an abundance of bad ones.
This distinction might seem at once too basic and too esoteric. Nevertheless, it is something that can get lost in our obsession with replacement level, which begins to assign value at a relatively low threshold, and seems to divide players into good, "gooder", and "goodest." If you take two teams whose offenses are both 180 runs better than replacement, for example, that doesn't tell you very much about how those teams are composed. You might have one team who has two stars with VORPs around 90, and a bunch of zero-value scrubs (in VORP) rounding out the roster, and another team that has no star talent at all, but gets a 20 VORP contribution out of each of its nine regulars.
Suppose instead that we divide our accounting into above-average and below-average talent. For example, looking at this year's Yankees:
Hitter PA VAA VBA Derek Jeter 230 +18.6 --- Bobby Abreu 227 --- -13.6 Alex Rodriguez 223 +22.6 --- Robinson Cano 201 --- -8.1 Jorge Posada 181 +22.6 --- Johnny Damon 180 --- -1.4 Jason Giambi 174 +3.3 --- Hideki Matsui 157 +4.1 --- Melky Cabrera 147 --- -10.6 D. Mientkiewicz 135 --- -7.6 Josh Phelps 59 --- -0.2 Wil Nieves 31 --- -5.9 Other Hitters 35 +1.6 -3.4 Hitters +72.8 -50.9 Pitcher IP VAA VBA Andy Pettitte 71.2 +12.7 --- Chien-ming Wang 48 +3.2 --- Mike Mussina 35.1 --- -4.4 Kei Igawa 30.2 --- -11.3 Luis Vizcaino 26 --- -8.4 Scott Proctor 25.1 +2.3 --- Darrell Rasner 24.2 --- -1.3 Brian Bruney 23 +9.2 --- Mike Myers 23 +4.1 --- Matt DeSalvo 21.2 --- -1.6 Kyle Farnsworth 20.1 --- -1.4 Sean Henn 17.1 --- -2.0 Mariano Rivera 16.2 --- -2.3 Carl Pavano 11.1 --- -1.1 Philip Hughes 10.2 +1.7 --- Tyler Clippard 10 +1.2 --- Other Pitchers 25.1 +1.3 -9.7 Pitchers +19.9 -27.7 Total +92.7 -78.6
The terms "VAA" and "VBA" will not be familiar to you, but you will probably have no trouble figuring out what they mean. "VAA" means Value Above Average, which is literally just a player's VORP using league average rather than replacement level as the baseline. If a player is below average, his VAA isn't negative; it is simply zero. "VBA" stands for Value Below Average, which is exactly the opposite.
If you look at the Yankees, you'll find that both their VAA and VBA are fairly high; they've had a lot of really outstanding performances (Alex Rodriguez, Jorge Posada), and a lot of really terrible performances (Kei Igawa, Bobby Abreu). If you sum VAA and VBA, you should get a number which is fairly close to a team's run differential. In this case, the Yankees' total is 14.1, which is a good match for their actual plus-19 run differential.
For contrast, let's take a look at the Brewers:
Hitter PA VAA VBA Prince Fielder 228 +13.1 --- J.J. Hardy 226 +16.2 --- Rickie Weeks 199 +0.7 --- Bill Hall 197 --- -0.9 Johnny Estrada 169 +3.4 --- Geoff Jenkins 150 +8.0 --- Kevin Mench 120 --- -4.7 Tony Graffanino 120 --- -11.2 Craig Counsell 117 --- -3.3 Corey Hart 108 --- -0.1 Tony Gwynn 76 +2.7 --- Gabe Gross 67 +2.1 --- Damian Miller 54 --- -3.0 Other Hitters 138 +2.3 -4.0 Hitters +48.4 -27.2 Pitcher IP VAA VBA Jeff Suppan 73 +4.3 --- F. Cordero 21 +9.5 --- Ben Sheets 68.1 +3.3 --- C. Villanueva 33.1 +4.6 --- Claudio Vargas 49.1 +0.6 --- Chris Capuano 59.1 --- -1.2 Matt Wise 20.2 +3.3 --- Derrick Turnbow 22.1 +2.2 --- Chris Spurling 16.2 +2.3 --- Brian Shouse 12.1 +1.2 --- Greg Aquino 7.2 --- -2.2 Dave Bush 61.2 --- -12.3 Elmer Dessens 15 --- -8.4 Pitchers +31.5 -24.0 Total +79.9 -51.2
The Brewers have had a handful of All-Star caliber performances this year, notably from Prince Fielder, J.J. Hardy, and Francisco Cordero. They are more noteworthy, however, for their absence of poor performances. Whereas the Yankees have seven players who have cost them five or more runs below average this year, the Brewers have only three. Thus, the Brewers rate as the better team, even though they have somewhat less star talent:
VAA VBA Net Yankees +108.7 -94.2 +14.5 Brewers +79.9 -51.2 +28.7
We can run this calculation, of course, for every team in the league, which is exactly what we're going to do right now:
That chart is quite an eyesore-I'm definitely not channeling Edward Tufte-but let me try and explain what's going on. We have VAA on the horizontal axis and VBA on the vertical axis. The very best teams, who have both a high VAA and a low VBA, will be in the top right-hand side of the plot, and the very worst teams in the bottom left. As for that tic-tac-toe board in the middle and all those extra letters and numbers-actually, this works better if we rotate the chart at a 45 degree angle:
The meanings of the axes have now changed. The horizontal axis now represents run differential, with the better teams toward the right, while the vertical access now represents what I'm calling "sharpness". A team is "sharp" if, like the Yankees, it has a large degree of variance in its talent base-some very good players, but also some very poor players. A team is "flat" if, like the Brewers, its value is distributed fairly evenly across its roster. Sharper teams appear toward the bottom of the graph, and flatter teams toward the top, which is slightly counterintuitive, but jibes better with our first version of the chart. Teams that are neither sharp nor flat are what we might call "natural" (I'm borrowing from music terminology), which means that have a normal assortment of stronger and weaker players.
This will probably give you a hint and what that tic-tac-toe board means. We've divided the chart into nine regions, with each region labeled according to its sharpness and the run differential of the team in question. In particular, the nine regions are as follows:
So, you're probably asking, is it better to be sharp or be flat? And is it better to be natural than either of the above? There are intuitive arguments either way. On the one hand, it's generally much cheaper to exchange replacement-level talent with average talent than it is to replace average talent with superstar talent, particularly if you have extra financial or scouting resources at your disposal. There's little chance that the Yankees will still be employing Doug Mientkiewicz, for example, if they've limped back into the race by the trade deadline, and their marginal gains are going to be very high once they replace him. On the other hand, sharp teams do not do a very good job of diversifying themselves, and may be more vulnerable to injuries or other kinds of attrition problems. The Cardinals, who were an extremely "sharp" team heading into this season, are a good example of this; then Chris Carpenter gets hurt, Jim Edmonds and Scott Rolen start showing their age, and what you're left with is a team that... well, falls flat.
It's almost like you have two of Bill James' seminal concepts at loggerheads. The Talent Pyramid would tend to suggest that sharp teams have an easier job of improving themselves, while the Plexiglass Principle might favor flat ones. My hunch is that that the argument for sharpness prevails; in fact, I'm almost certain that being sharp is better than being flat, though I don't know if it's better than being natural. But I haven't run the numbers yet, and that's going to need to wait until next week.