Salary vs. pWORL
Baseball Player Won-Loss Records
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Salary vs. pWORL: Measuring Player Value

I am an economist in my day job. In economics, the definition of "value" is very straightforward. The "value" of a good or service is whatever somebody is willing to pay for it. Applying this to baseball players, the economic "value" of baseball players can be measured by what baseball owners are willing to pay them.

There are a number of reasons why this may not be a particularly useful "value" measure of major-league baseball players. Players' salaries are set in advance based on expected, not actual, performance. The economic value of player performance may not be constant across all teams and all situations - e.g., a team's 85th win, which could significantly improve the team's playoff prospects could be more valuable than a win that improves a team from 61-101 to 62-100. As Branch Rickey reportedly said about Ralph Kiner and the 1953 Pittsburgh Pirates, "We finished last with you, we can finish last without you." Finally, and perhaps most importantly, the labor market for major-league baseball players is not an entirely free market. Players are restricted to their original team - and American players are assigned to their original team via a draft - until they have accumulated six years of major-league experience, so that "what baseball owners are willing to pay" players may be considerably more than what baseball owners actually do pay players.

Because of this, it is probably not a good idea to attempt to estimate either the value of an individual player based on that player's salary or even, necessarily, to attempt to draw conclusions about the marginal dollar value of a win from overall player salaries.

What may be reasonable, however, is to use relative salaries as a basis for measuring the relative value placed on different positions or on different components of player value by major-league general managers.

Sean Lahman's wonderful database includes data on player salaries for many (probably most) players from 1985 - 2014. I have added these salaries to my database. The next table compares the distribution of Player won-lost records and salaries, for those players for whom I have salary data. The first part of the table compares the distribution of player value and player salary by position. Player data were divided proportionally based on a player's decisions by position. So, for example, if a player earned 50% of his player decisions at second base and 50% of his player decisions at third base, then 50% of his salary was treated as having been earned at second base and 50% at third base. Below that, the table compares the distribution of player value and player salary by the four basic factors for which player value is accumulated: Batting, Baserunning, Pitching, and Fielding. As with the data by position, a player's salary is distributed across the four factors in proportion to their relative proportion of that player's value.

The table has four columns. The first two represent the distribution of Player won-lost records. The first column is calculated based simply on the sum of pWins and pLosses. The second column is based on pWins over replacement level (pWORL). The numbers here only include players for whom I have salary data.

The last two columns then are calculated based on two measures of salary. The first is simply total salary. The second is salary above the minimum (which was $500,000 in 2014). My thinking is that this would correspond to wins over replacement level - replacement-level players are not technically "freely available", they're available for the major-league minimum.

Distribution of Player Decisions vs. Salary
1985 - 2014
Player Decisions Salary
Position Total over Repl. Lvl. Total above Minimum
Catcher5.9%
4.8%
5.2%4.9%
First Base7.3%
6.5%
8.5%8.9%
Second Base7.9%
6.9%
5.1%5.1%
Third Base7.9%
6.9%
6.4%6.5%
Shortstop8.1%
7.1%
5.4%5.4%
Left Field8.5%
6.6%
7.5%7.6%
Center Field8.5%
6.6%
5.8%5.9%
Right Field8.7%
6.7%
7.9%8.2%
Designated Hitter2.8%
3.4%
4.3%4.6%
Pinch Hitter1.4%
0.6%
1.3%1.1%
Pinch Runner0.1%
0.0%
0.1%0.0%
Pitcher Offense1.3%
1.7%
1.4%1.5%
Starting Pitcher22.7%
28.8%
25.7%26.6%
Relief Pitcher9.0%
13.5%
15.4%13.9%


Player Decisions Salary
Factor Total over Repl. Lvl. Total above Minimum
Batting46.9%
40.7%
42.0%42.6%
Baserunning4.2%
3.6%
3.4%3.4%
Pitching30.9%
41.2%
40.1%39.5%
Fielding18.0%
14.5%
14.5%14.5%


I think that the relevant comparison is between the second (pWORL) and fourth (Salary above Minimum) columns. Overall, the results are broadly similar. The numbers for catchers, third basemen, and relief pitchers, in particular, are extremely similar. Several other positions differ more significantly, however.

For non-pitchers, there appears to be a pattern to differences between pWORL and what I'll start calling SORL - Salary over Replacement Level. "Hitting" positions tend to be over-paid - first base, left field, right field, and DH - while "Fielding" positions tend to be under-paid - second base, shortstop, and center field.

In terms of the four factors, the share of salary paid seems fairly close to the share of value for all four factors, although batting appears to be somewhat over-valued and pitching somewhat under-valued, in terms of salaries.

As I mentioned earlier, Major League Baseball players' salaries are limited in their earliest seasons, and players are not eligible for free agency - and, hence, a fully free labor market - until they have played six full major-league seasons. It is fairly common for major-league players to shift from "fielding" positions to "hitting" positions as they age. For example, Carlos Beltran played all but a small handful of games in center field through 2010, his age-33 season. Beltran has played five seasons since then, but has only played CF in one of them - in a total of 9 games for the 2012 St. Louis Cardinals. Instead, Beltran has been mostly a rightfielder since 2011 and an occassional designated hitter.

It could well be the case, then, that the players at hitting positions are older, on average, than the players at fielding positions, and are, perhaps, more likely to be free agents. This could, then, explain why hitting positions appear to be overpaid, if these players are simply more likely to be paid their full market value.

To test this theory, the next table only includes players whose major-league debut was at least 7 years before the season in question (my thinking is that most players don't play a full season in their first year, so most players will have appeared in 7 seasons before qualifying for free agency).

Distribution of Player Decisions vs. Salary
1985 - 2014, Veterans only
Player Decisions Salary
Position Total over Repl. Lvl. Total above Minimum
Catcher6.2%
4.7%
5.0%4.8%
First Base8.5%
7.3%
9.1%9.3%
Second Base7.9%
6.8%
4.9%4.8%
Third Base7.9%
7.0%
6.7%6.8%
Shortstop7.2%
6.7%
5.2%5.2%
Left Field9.3%
7.3%
7.9%8.0%
Center Field7.1%
5.9%
5.5%5.5%
Right Field9.3%
7.0%
8.2%8.4%
Designated Hitter4.7%
5.8%
5.3%5.4%
Pinch Hitter1.6%
0.6%
1.3%1.2%
Pinch Runner0.0%
0.0%
0.0%0.0%
Pitcher Offense1.2%
1.6%
1.4%1.4%
Starting Pitcher21.3%
26.9%
25.3%25.8%
Relief Pitcher7.8%
12.2%
14.1%13.4%


Player Decisions Salary
Position Total over Repl. Lvl. Total above Minimum
Batting49.9%
43.7%
43.7%43.8%
Baserunning4.2%
3.7%
3.4%3.4%
Pitching28.4%
38.1%
38.4%38.2%
Fielding17.5%
14.4%
14.5%14.5%


My hypothesis is at least partially confirmed. Note that the share of pWORL amassed at hitting positions by veteran players is greater than for all players - 7.3% vs. 6.5% for first basemen, for example; 5.8% vs. 3.4% for designated hitters.

One interesting result, however, is that the tradeoff is not so much at fielding positions - especially infielders - but is, instead, pitchers. Overall, pitchers generated 43.9% of total pWORL, but only 40.8% of total pWORL amassed by veteran players.

This explains the earlier result that batting was being overvalued and pitching somewhat undervalued. Focusing only on veteran players here, the salary mix between batting, baserunning, pitching, and fielding is nearly perfect as compared to the mix of value as measured by Player won-lost records.

Looking at the data by player position, focusing only on veterans definitely brings the shares of pWORL and SWORL closer together. The numbers for catchers, for example, are an exact match. The numbers are also extremely close for third basemen and designated hitters. Even focusing only on veterans, however, it still appears that first basemen and corner outfielders earn a higher share of total payroll than they do of pWORL (at the expense of up-the-middle defenders - second basemen, shortstops, and center fielders).

For pitchers, starting pitchers appear to be somewhat underpaid, but relief pitchers tend to be somewhat overpaid, so that, overall, the share of total pWORL earned by pitchers, 40.8%, is very close to pitchers' share of salary (over the minimum), 40.6%.

The numbers in the previous two tables cover thirty years, 1985 through 2014. With recent advances in player analytics and with those advances working themselves more and more into major-league front offices, has the distribution of veteran player salaries fallen more in line with the distribution of player "value" as measured by Player won-lost records - i.e., pWORL?

The final table of this article takes a look at that question by focusing on only the last decade.

Distribution of Player Decisions vs. Salary
2005 - 2014, Veterans only
Player Decisions Salary
Position Total over Repl. Lvl. Total above Minimum
Catcher6.0%
4.1%
4.7%4.4%
First Base8.6%
7.4%
9.0%9.2%
Second Base7.9%
6.5%
5.0%5.0%
Third Base8.7%
8.1%
7.6%7.7%
Shortstop7.7%
7.0%
5.1%5.1%
Left Field9.0%
6.9%
7.7%7.7%
Center Field6.7%
5.7%
5.1%5.2%
Right Field9.5%
7.2%
7.6%7.7%
Designated Hitter4.7%
6.1%
5.4%5.5%
Pinch Hitter1.4%
0.5%
1.2%1.1%
Pinch Runner0.0%
0.0%
0.0%0.0%
Pitcher Offense1.2%
1.5%
1.5%1.5%
Starting Pitcher20.6%
25.2%
26.0%26.6%
Relief Pitcher7.9%
13.7%
14.1%13.3%


Player Decisions Salary
Position Total over Repl. Lvl. Total above Minimum
Batting50.6%
44.2%
43.3%43.5%
Baserunning4.0%
3.4%
3.3%3.3%
Pitching27.8%
37.9%
39.0%38.8%
Fielding17.6%
14.4%
14.4%14.4%


The discontinuities observed in the 30-year table - first basemen vs. middle infielders and corner outfielders vs. centerfielders - remain, but, I think, less dramatically so. Overall, the distribution of pWORL and the distribution of SORL are quite similar. As an economist, this comforts me that Player won-lost records seem to be accurately assessing player value.



All articles are written so that they pull data directly from the most recent version of the Player won-lost database. Hence, any numbers cited within these articles should automatically incorporate the most recent update to Player won-lost records. In some cases, however, the accompanying text may have been written based on previous versions of Player won-lost records. I apologize if this results in non-sensical text in any cases.

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