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August 18, 2005 Lies, Damned LiesRunning down SOB
Reader Mike Mitchell writes:
Watching Jose Reyes in Fox's Mets/Cubs Flat Earth Society Game of the Week, I couldn't help but wonder if modern sabermetrics does a fair job accounting for lowOBP, highspeed players like Reyes, who score in a higher percentage of their times on base than slower players.... A lot of times you'll hear the case made that OBP undervalues a player like Jose Reyes or Carl Crawford because it doesn't account for their baserunning ability. This is a perfectly reasonable argument. Getting on base, as Mike intimates, is not the goal. Rather, getting on base is a means to an end, that end being scoring runs. But running the bases well is also a means to that end. If Bill Mueller gets on base five percent more often than Scott Podsednik, but Podsednik scores 10 percent more often than Mueller those times that he does reach base, which player is the more valuable rungenerator? Actually, this question isn't as straightforward as it might seem. Much of the value in reaching base is really in avoiding outs. Stealing second base once you've reached first, or scoring from second on a double when a slower runner might have held up: these are valuable skills. But they aren't as important as reaching base in the first place, which not only puts a runner on base for the team to work with, but also preserves one of its irreplaceable 27 outs. What would be useful, as Mike suggests, is a way to be able to quantify baserunning contributions in terms of OBP. Why OBP and not, say, slugging percentage? Because OBP is essentially a measure of setting oneself up to score runs, whereas SLG is a measure of driving runs in. Compare, say, a single and a walk. Each of these outcomes makes it just as likely that you're going to score for yourself, but the former does more to advance other runners along; it makes sense that a single improves a player's slugging percentage while a walk does not. Similarly, compare a single and a subsequent stolen base to a double. Either way, the batter winds up on a second base, but the double does more to drive other runners in. The notion that baserunning ability belongs in the same category as onbase ability is a sensible one. The way to attack this problem is to think in terms of times reaching base (TRB). Is a stolen base 80% as valuable as a TRB? Is it 40% as valuable? For purposes of this column, by the way, we're going to think of TRB as specifically referring to reaching first base with the bases empty. This allows us to sidestep a nasty little ambiguity of the OBP/SLG system: a leadoff double does more to facilitate scoring runs than a leadoff single, even if there are no other runners on base to advance. There's an argument that, if OBP is a measure of the runner's ability to set himself up to score, then a double should be given more credit than a single in terms of OBP. But at least the double is reflected in the SLG side of the OBP/SLG dyad, whereas a stolen base disappears into the ether. Similarly. with a runner on second base as opposed to the bases empty, a single becomes proportionately more valuable than a steal. But this is presumably what's reflected in the SLG side of the equationdriving other players toward a run. It might be worthwhile, at some point in the future, to try and redefine OBP and SLG entirely, but that effort is beyond the scope of this article, and we'll keep things simple by defining a TRB in the narrow way that I have above. With that caveat in mind, let's take a look at some key figures from the 2004 Expected Runs Matrix. These are the major league average run scoring figures that resulted in 2004 given various numbers of outs, and various numbers of runners on base:
[A]: Zero outs, bases empty: .538 runs/inning [B]: One out, bases empty: .287 runs/inning. [C]: Zero outs, runner on first: .926 runs/inning. [D]: Zero outs, runner on second: 1.160 runs/inning. When the leadoff hitter comes up to start the inning, his team will score an average of .926 runs if he reaches first base [C], but .287 runs if he doesn't [B], for a difference of .639 runs. If reaches first base and subsequently manages to steal second, his team's run scoring expectation increases from .926 runs [C] to 1.160 runs [D], a difference of .234 runs. We can define the value of a stolen base in terms of TRB as:
[D][C] 1.160.926 .234  =  =  = .366 [C][B] .926.287 .639 In other words, for the leadoff hitter, a stolen base is worth about 36.6% of a TRB; twenty steals are about as valuable as seven walks. Continuing to use figures from the 2004 Expected Runs Matrix, if we change the situation slightly, and assume that the leadoff hitter makes an out, a TRB for the #2 hitter is worth .436 runs, while a stolen base is worth .160 runs, or 36.7% as much. With two outs and nobody on, a TRB is worth .246 runs, and a stolen base .090 runs, or 36.6% as much. It's probably just a coincidence that these ratios come out as close to one another as they doif we looked at the 2005 Expected Runs Matrix instead, they wouldn't work out quite so evenlybut we'll define a stolen base as equal to .366 of a TRB. What about a caught stealing? Given the way that we've defined a TRB, this question is easy to answer: a caught stealing exactly nullifies the value of a TRB, and so it is worth exactly 1 TRB. This implies, by the way, a breakeven stolen base success rate of about 73%. This is materially higher than the .67 (twothirds) figure that is commonly cited. Without getting into too much of a tangent, there are a couple of reasons to think the higher figure is valid:
So, for example, we might look at Endy Chavez, who reached base 170 times in 535 opportunities last year (plate appearances less sacrifice hits), for a paltry .318 OBP. Chavez also stole 32 bases last year, equivalent to 11.7 TRB, while being caught 7 times (7 TRB). His stolen baseadjusted OBP (SBOBP) can be defined as:
H + BB + HBP + (SB * .366)CS 139 + 30 + 1 + (32 * .366)7  =  PASH 54712 This works out to .327, not quite ten points better than Chavez' conventional OBP, and certainly not enough to make him an adequate hitter. As I've alluded to, however, there is another part of the equation to consider: baserunning ability above and beyond stealing bases. Developing an effective measure of baserunning ability is a complicated matteryou need to consider the baseout situations very precisely, while also accounting for things like the arm strength of the outfielders. Fortunately, James Click has done all of the heavy lifting in his baserunning article for Baseball Prospectus 2005, which takes all of these things into account, and boils them down into Equivalent Basestealing Runs (EqBR). (We hope to have regularly updated EqBR reports up on the site very soon). EqBR measures everything in terms of runs relative to league average. In order to come up with our SOB formula (I like Mike's suggestion for the name of this statistic), we need to translate back into times reaching base. Returning to the Expected Runs Matrix, we find that with nobody out and nobody on, a TRB is worth .639 runs, with one out and nobody on, .436 runs, and with two outs and nobody on, .246 runs. The average of these numbers is .440, or slightly less than half a run. To be more precise, a marginal basestealing run is worth 2.27 times (1/.440) as much as a TRB. That gives us our formula for SOB, or SpeedAdjusted OBP.
H + BB + HBP + (SB * .366)CS + (EqBR * 2.27) SOB =  PASH Here, for example, is Tony Womack's figure; Womack had 26 steals last year, was caught 5 times, and produced 3.04 EqBR.
170 + 36 + 3 + (26 * .366)5 + (3.04 * 2.27) SOB =  = .369 6068 Womack's SOB is .369, which compares favorably to his conventional OBP of .349. Let's take a look at a couple of leaderboards for the 2004 season. First, here are the fifteen major league regulars (minimum 500 PA) who benefitted the most from the baserunning adjustments:
Best Baserunners, 2004 Player SB CS EqBR OBP SOB +/ Carlos Beltran 42 3 +3.9 .367 .398 +.030 Rafael Furcal 29 6 +4.9 .344 .370 +.025 Scott Podsednik 70 13 +2.2 .313 .338 +.025 Vernon Wells 9 2 +4.5 .337 .357 +.019 Tony Womack 26 5 +3.0 .349 .369 +.019 Ryan Freel 37 10 +3.4 .375 .394 +.019 Aaron Rowand 17 5 +3.9 .361 .380 +.019 Bobby Abreu 40 5 +1.5 .428 .446 +.018 Carl Crawford 59 15 +2.5 .331 .349 +.018 Endy Chavez 32 7 +2.1 .318 .335 +.018 Eric Byrnes 17 1 +2.3 .347 .363 +.017 Omar Vizquel 19 6 +3.7 .353 .368 +.015 Scott Rolen 4 3 +4.5 .409 .424 +.015 Mike Cameron 22 6 +2.7 .319 .334 +.015 Royce Clayton 10 5 +4.4 .338 .351 +.014 For the most part, these are exactly the names that you'd expect to see, though there are a couple of players like Scott Rolen who aren't prodigious base stealers, but are very efficient baserunners. A pretty good baserunner might be worth 15 or 20 points of OBP more than his conventional stats would indicate; a truly elite baserunner like Podsednik or Carlos Beltran could be worth some 25 or 30 points of OBP more. The very best season I could find using this method was Rickey Henderson's 1985; Henderson stole 80 bases that year, was caught 10 times, and produced 8.10 EqBR. That gives him an SOB of .476, fully 57 points better than his already impressive .419 OBP. That underscores just how great a player Henderson was, but his season also appears to be something of an outlier; there were few other seasons that crept above the 30 point threshold, and nobody was in the neighborhood of Rickey's 57point gain. Conversely, here are the players whose baserunning hurt them the most in 2004:
Worst Baserunners, 2004 Player SB CS EqBR OBP SOB +/ A.J. Pierzynski 0 1 4.4 .319 .297 .022 Jorge Posada 1 3 3.7 .400 .380 .020 Mike Piazza 0 0 4.7 .362 .342 .020 Jim Thome 0 2 3.6 .396 .380 .017 Sammy Sosa 0 0 3.4 .332 .318 .014 Jacque Jones 13 10 1.5 .315 .301 .014 Carlos Delgado 0 1 3.0 .372 .358 .014 Rafael Palmeiro 2 1 3.8 .359 .346 .014 Mike Lieberthal 1 1 2.6 .335 .323 .012 Lance Berkman 9 7 2.0 .450 .438 .012 Manny Ramirez 2 4 2.0 .397 .385 .012 Jose Guillen 5 4 2.1 .352 .340 .011 Jose Cruz Jr. 11 6 2.3 .333 .322 .011 Phil Nevin 0 0 3.0 .368 .357 .011 Derrek Lee 12 5 2.7 .356 .346 .010 The bad baserunners don't appear to hurt quite as much as the good baserunners help. In any event, this list is chock full of aging catchers and first basemen, as we'd anticipate. Brian Sabean's unceremonious dumping of A.J. Pierzynski looks a little bit better now. As for Derrek Leewho is a big first baseman but has a reputation as a good baserunnerwell, these figures do not compensate for the Wendell Kim factor.
A comparison of the 2004 OBP and SOB leaderboards: OBP SOB Barry Bonds .609 Barry Bonds .614 Todd Helton .469 Todd Helton .477 Lance Berkman .450 J.D. Drew .448 J.D. Drew .436 Bobby Abreu .446 Bobby Abreu .428 Lance Berkman .438 Melvin Mora .419 Scott Rolen .424 Jim Edmonds .418 Ichiro Suzuki .418 Albert Pujols .415 Albert Pujols .417 Ichiro Suzuki .414 Melvin Mora .416 Travis Hafner .410 Travis Hafner .416 Scott Rolen .409 Jim Edmonds .413 Jorge Posada .400 Eric Chavez .407 Jason Kendall .399 Vladimir Guerrero .401 Eric Chavez .397 Jason Kendall .398 Manny Ramirez .397 Carlos Beltran .397 Jim Thome .396 Hideki Matsui .397 Erubiel Durazo .396 Adam Dunn .396 Gary Sheffield .393 Ryan Freel .394 Mark Loretta .391 Gary Sheffield .393 Vladimir Guerrero .391 Johnny Damon .390 Baserunning should have its place in sabermetric analysis, and it's nice to see someone like Ryan Freel, who also ranks very well in the preliminary 2005 SOB figures that I've prepared (see below), get his due. In a few marginal cases, like that of Podsednik, baserunning might even be enough to warrant placing a player in the lineup when he otherwise should not be. For the most part, however, baserunning and base stealing ability just doesn't make a large enough magnitude's worth of difference to change our conclusion about who the good offensive players are, and who are the bad ones. Finally, presented without further comment, the best and worst baserunners of the 2005 season to date (minimum 300 PA):
Best Baserunners, 2005 Player SB CS EqBR OBP SOB +/ Carl Crawford 34 5 +2.7 .317 .343 +.026 Nook Logan 20 5 +2.6 .299 .325 +.026 Mike Cameron 13 1 +2.2 .341 .367 +.026 Ryan Freel 29 7 +1.7 .381 .405 +.024 J.J. Hardy 0 0 +2.7 .303 .323 +.020 Coco Crisp 12 5 +4.3 .341 .361 +.020 Bobby Kielty 3 2 +3.5 .356 .375 +.019 Bill Hall 13 1 +1.4 .311 .329 +.018 Edgar Renteria 8 3 +3.9 .342 .360 +.018 Marcus Giles 13 3 +2.8 .383 .400 +.017 Julio Lugo 30 5 +1.2 .354 .371 +.017 Ruben Gotay 2 2 +2.9 .284 .301 +.017 Jose Reyes 41 10 +1.6 .296 .312 +.016 Alfonso Soriano 18 2 +1.4 .327 .343 +.016 Mark Teahen 5 1 +1.8 .302 .317 +.015 Worst Baserunners, 2005 Player SB CS EqBR OBP SOB +/ Matt Lawton 16 9 4.3 .380 .351 .029 Phil Nevin 1 0 4.0 .301 .273 .028 Chris Snyder 0 1 2.9 .297 .272 .025 Mike Cuddyer 3 3 2.7 .341 .317 .024 Sammy Sosa 1 1 3.8 .303 .280 .023 Brad Ausmus 3 2 2.7 .328 .305 .023 Freddy Sanchez 0 1 2.6 .330 .307 .023 Cesar Izturis 7 8 1.6 .306 .286 .020 Frank Catalanotto 0 2 1.8 .353 .335 .018 Jason Phillips 0 1 2.4 .291 .273 .018 Melvin Mora 7 3 3.4 .343 .325 .018 Hank Blalock 1 0 4.2 .338 .321 .017 Daryle Ward 0 2 2.1 .328 .311 .017 Omar Vizquel 19 9 2.6 .334 .317 .017 Kevin Millar 0 1 2.5 .357 .341 .016
Nate Silver is an author of Baseball Prospectus. 0 comments have been left for this article.
