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Baseball is a zero sum game. One team always wins at the expense of another. It is not possible for one team to win without another losing. In order to win, a team must be able to produce more runs (or prevent runs from scoring) than the opposition. It's success in producing wins is directly tied to its ability to produce more runs than its opponent. Any competitive advantage a team has must, in some way, translate to better on-field performance to be valuable.
A commodity which is easily available to all teams at no or low cost confers no competitive advantage, and therefore is of minimal value. Thus, baseball value comes from scarcity.
The talent distribution in baseball can be summed up as follows: there are very few "superstar" level players, a somewhat larger number of "average" producers, and a practically unlimited number of "scrubs". This is usually represented as the tail end of a bell curve or normal distribution, with the vast majority of the overall population already weeded out through other factors prior to reaching professional ball.
Average players have value. Measures that use average production as a reference point, such as TPR, incorrectly estimate the contribution of average players by failing to recognize the value of average playing time.
Replacement level is a less concrete mathematical concept, but it is an important economic one. In particular, it more correctly values durability and playing time versus rates of production.
Let's look at an example to see where an average-value analysis lets us down. Compare two players on otherwise identical teams.
AVG OBP SLG
Joe Average: 600 PA .260/.330/.420
Flash Fragile: 100 PA .300/.400/.550
Joe is a steady, but unspectacular producer, while Flash hits like an MVP when he's in the lineup, which is rarely.
Assume that 600 PA's are needed to complete a season. Where are the other 500 PA's at this position coming from? If Flash's durability problems were not known, then the team may be stuck playing a utility bench player, bringing up a AAA player, or finding some other journeyman to fill the gap. That's the best the team can do without sacrificing more resources (including future value in the form of prospects) to replace Flash's playing time.
Suppose that the team has Bill Backup playing at AAA and calls him up. Now he might turn out to be the 2nd coming of Frank Thomas and start hitting immediately, but that's unlikely. The team has some basic idea of what to expect based on his minor league track record -- probably significantly worse than a regular player. For the sake of argument, let's say that they expect a .225/.295/.385 performance.
Now, Bill is just one of many players floating around who can be expected to put up comparable numbers. There's nothing special about Bill's ability -- he just happened to be the one who got the call. In fact, Bill's team probably would have sold or traded Bill to some other team cheaply, or simply released him if they had a hot prospect to promote. That makes Bill (or players like him) reasonably part of any *other* team's backup strategy. A virtually no-cost replacement to get plugged into a lineup in a time of need.
So what does Bill do while filling in for Flash? The two teams (let's call them the Anarchists and the Zebras) get the following production:
AVG OBP SLG
Team- Anarchists
Joe Average: 600 PA .260/.330/.420
Team - Zebras
Flash Fragile: 100 PA .300/.400/.550
Bill Backup: 500 PA .225/.295/.385
Looking at comparisons to league average, Flash looks like the most valuable player -- contributing about 7 runs above average. Joe, unsurprisingly is exactly average, and contributed 0 runs. Bill, forced into playing by Flash's health problems, was nearly 15 runs worse than average. For the sake of simplicity, let's call Joe's TPR 0.0, Flash's TPR 0.7, and Bill's TPR -1.5.
So let's go back to the start of the season and give the GM's of Joe's team and Flash's team a crystal ball, so they can see exactly how each player will perform in the upcoming season. Would Flash's team trade Flash for Joe straight up?
Well, the Zebras' GM looks at the future and sees that overall, Flash and Bill will produce about 8 runs less than league average over the course of the season. Trading for Joe would eliminate the need to play Bill at all, and thus improve the team's overall run production. Thus, the Zebras would love to trade Flash for Joe, despite Flash being a better player on a per-game basis, because Joe's durability keeps them from either having to play Bill, or from expending other organization resources to obtain a more capable replacement.
Looking at a replacement-level analysis, we can see this quite clearly. Joe's value over a replacement player is about 18 runs, while Flash is just 10 runs above replacement level due to his limited playing time. Bill, of course, is exactly replacement level due to the assumptions we used above.
So if Joe is more valuable than Flash, a measure that is supposed to correctly measure value can't have Flash ranked higher. Our TPR-in-concept has Flash at 0.7 ahead of Joe at 0.0. Therefore, TPR is missing some element of value -- namely, the value of playing time or durability.
Replacement level is the *expected* level of performance the average team can obtain if it needs to replace a starting player at minimal cost.
Individual replacements can perform above or below the expected level, but that does not change what the expectation was at the time of the decision.
Specific teams may have better-than replacement level players available in their own systems. This does not change the concept of replacement level -- it shows that team context is important when evaluating particular decisions. If *all* teams had better-than replacement-level players easily available, then that would indicate that your level is set too low.
With the preceding ideas about replacement value in mind, I've designed a measure called VORP -- Value Over Replacement Player.
We define a replacement level player as one who hits as far below the league positional average as the league backups do relative to league average, who plays average defense for the position, and is a breakeven base-stealer and baserunner.
VORP is the number of runs contributed beyond what a replacement level player would contribute if given the same percentage of team plate appearances.
To estimate the run contribution of the hitter, we use Marginal Lineup Value (MLV). MLV measures the impact of run scoring that a single player has on a league average team, using the Runs Created model. MLV was invented by David Tate (with extensions by Keith Woolner) and is described in mathematical detail here.
Replacement-level delta is set at 70 points of OPS below league positional average (based on previous unpublished studies). The same delta is used for all positions (this is a possible area for future research).
For pitchers, VORP is defined as the number of runs a pitcher surrenders below what a replacement level pitcher would have given up in the same number of innings. Replacement level is set at +1.00 above the league average RA.
The latest VORP reports for the current season are available for hitters and pitchers.
Note: OBP & PA are estimated from H, AB, and BB
Each player listed only at the position he appears at most (not prorated according to % of time spent at each position). If two or more positions tie for the most appearances, then he's listed at each one.
VORP is park-adjusted using 3-year park factors through 1997 (where possible). Arizona and Tampa Bay have league-neutral park factors until more park data is collected.
VORP, by itself, does not make any measurement of the quality of a player's defense at the position he plays. In other words, VORP implicitly assumes that all defenders at a position are equally good fielders. However, you can combine VORP with your favorite run-denominated version of fielding performance (Total Baseball's Fielding Runs, or similar measures based on Zone Rating or Defensive Average, for example), to get what I call VORPD (VORP + Defense). This would be a reasonably complete measure of player value.
Now, in theory, any club should be able to field a team of 0 VORP players, and thus guarantee some minimum level of performance from each position. In practice, there are some reasons why you might find a player with negative VORP. Among these are: (a) sample size -- a player might have a slump for 10 games, and then lose his job, and his performance would appear to be negative over that sample, (b) incorrect projections -- you give a truly bad player too many opportunities under the mistaken belief that he has some ability, (c) injury, (d) prospects -- a highly touted young player might struggle for awhile, but reasonably be expected to have significant positive value in the future, (e) sub-optimal decision-making -- you gave Greg Vaughn a big contract, and you're going to play him come hell or high water, even if he's not your best alternative, or (f) defensive contribution -- Ozzie Smith early in his career may have had negative VORP, but added so many runs defensively that his VORPD (VORP + intrapositional defensive runs) was positive.
So what level of performance does a VORP=0 team represent? Well, using the 1998 season MLB statistics to date, a all-replacement-level team would hit about .235/.300/.356 and have a RA of 5.85. The Pythagorean projection over 162 games would be 44-118, for a .271 winning percentage. This is comparable to the performance of the worst teams in history (e.g. '62 Mets who went 40-120 for a .250 Win%).
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Copyright 1997-2001 by Keith Woolner. All included authors retain the copyrights to their original works.