To apply the concept of replacement level to this analysis, it is helpful to know how much a run above replacement level is worth in dollars. I have calculated this based on 2003 payroll data, based on the assumption that a replacement level team would win 30 percent of its games.
The average Major League team in 2003 paid out $70,445,900 in payroll. A replacement level team would make the league minimum of $8,400,000. Thus, the league average marginal payroll, paid for performance above replacement, is $62,045,900. Supposing that a replacement level team would allow and score 344 runs more and less (respectively) in total than an average team (calculated using the Pythagorean theorem), than each run above replacement level is paid an average of $180,366 in 2003 MLB dollars.
If we know how many runs a given player contributes above replacement, then we can determine his worth in dollars.
Notes:
1. Since I do not have league averages by position, we will have to examine offensive runs above replacement and adjust our findings based on where a player is places on the defensive spectrum later.
2. I have placed replacement level defense at the league average .
3. UZR data are not available for 2003, so I use the average of a players 1999-2002 UZR
The first step is to determine as closely as we can the true performance level of a player. To do this, we take a weighted three year average, with the most recent year worth 3 times, the prior year twice and the third year counted once. Years are also weighted by AB, so a player would be averaged as follows:
(2003 * 2003 AB * 3) + (2002 * 2002 AB * 2) + (2001 * 2001 AB)
divided by appropriately weighted AB.
These OBP and SLG data then need to be converted into runs created, adjusted for year, league, and park. First, each year of data is adjusted to the 2003 league averages for that respective league. Next, the averaged three year data is adjusted to the Major League averages. Since the park factors we will use apply to runs only, we will calculate RC using the basic formula, then apply the three year halved run factor to these RC.
Replacement level runs will differ by AB, so we calculate this based on a weighted average of AB for each player. First, the 2003 MLB average OBP and SLG are used to calculate average RC in the given AB total, then this number is multiplied by .75 to arrive at replacement level runs.
Subtraction of the above results gives offensive RC above average, to which defensive runs are added.
League Averages
Year |
NL |
AL |
MLB |
2001 |
.327/.425 |
.329/.428 |
.328/.426 |
2002 |
.327/.410 |
.327/.424 |
.327/.417 |
2003 |
.327/.417 |
.329/.428 |
.328/.422 |
Miguel Tejada
Avg AB |
Avg OBP |
Avg SLG |
LGADJ OB |
LGADJ SL |
RC |
PKadjRC |
LgAvgRC |
ReplRC |
RAR |
DefR |
TotR |
636 |
.336 |
.480 |
.335 |
.473 |
100.8 |
103.2 |
86.0 |
66 |
37.2 |
4.5 |
41.7 |
Our method finds Tejada to be worth $7.5 million over replacement, or $7.8 million in total, in 2002 dollars. This figure can be adjusted up because Tejada is a shortstop, and then adjusted down to account for the current state of the market. Tejada is likely to be overpaid.
Note: In calculating Tejada's averaged statistics, his 2001 was counted twice and his 2002 once, because his 2002 was an abnormal year for Tejada, a likely career year.
Vladimir Guerrero
Avg AB |
Avg OBP |
Avg SLG |
LGADJ OB |
LGADJ SL |
RC |
PKadjRC |
LgAvgRC |
ReplRC |
RAR |
DefR |
TotR |
570 |
.413 |
.587 |
.414 |
.594 |
140.2 |
128 |
78.9 |
59.2 |
68.8 |
21 |
89.8 |
We thus find Vlad the Impaler worth $16.5 million dollars. This is the 2003 dollar worth of a healthy Guerrero. The buyer assumes the high priced risk that Guerrero will not play up to his full potential, on account of his known back condition. The above figure may be adjusted down due to the fact Guerrero plays a corner outfield position – a high offense position.
Note: Guerrero's 2003 AB are low due to injury. The proposed AB are for a healthy Guerrero.
Mike Cameron
Avg AB |
Avg OBP |
Avg SLG |
LGADJ OB |
LGADJ SL |
RC |
PKadjRC |
LgAvgRC |
ReplRC |
RAR |
DefR |
TotR |
539 |
.345 |
.444 |
.344 |
.438 |
81.2 |
86.4 |
74.6 |
55.0 |
31.4 |
12 |
43.4 |
Cameron's superb defense and above average bat make him worth $8.1 million dollars.
Luis Castillo
Avg AB |
Avg OBP |
Avg SLG |
LGADJ OB |
LGADJ SL |
RC |
PKadjRC |
LgAvgRC |
ReplRC |
RAR |
DefR |
TotR |
589 |
.370 |
.377 |
.371 |
.382 |
83.5 |
87.3 |
81.5 |
61.1 |
26.2 |
1 |
25.2 |
It appears that Castillo has not lived up to his reputation as a defender, and thus his value is a mere $4.8 million dollars. If we assume that Castillo's excellence at small ball skills creates an additional five runs, Castillo's worth increases to $5.7 million. Castillo's worth may be adjusted up because he is a second baseman, but as with every player adjusted down again to account for the state of the market.
Jose Cruz, Jr
Avg AB |
Avg OBP |
Avg SLG |
LGADJ OB |
LGADJ SL |
RC |
PKadjRC |
LgAvgRC |
ReplRC |
RAR |
DefR |
TotR |
521 |
.344 |
.443 |
.344 |
.443 |
79.4 |
79.4 |
72.1 |
54.1 |
25.3 |
** |
** |
The calulation of Cruz's offensive numbers is complicated by the fact Cruz has switched teams and leagues. The park factor used is a weighted average of the three year run factors for Pac Bell Park and the Skydome, which works out to about neutral. The calculation of his league adjusted stats was combined with the first step, therefore the first averages and LG adjusted averages columns are identical.
Evaluation of Cruz is further complicated by the fact that Cruz has played all three outfield positions, to varying degrees of success. He has played the most time in center field over the period considered, but played that position terribly, posting UZR runs of –22 as a centerfielder. As a left fielder, Cruz has been worth 16 runs above average (this figure is pro-rated to a full season; Cruz has not amassed a full season at this position from 1999 to 2002.) in left field, and 3 runs above average in right field (previous condition applies as well). Depending on his position, Cruz' total runs vary from 3.3 to 41.3, and his dollar worth from $895,200 to $7.7 million.