Why Do First Basemen Get Paid So Much? by Matt Swartz June 21, 2012 This April, Joey Votto signed a contract to man first base for the Reds for the next 12 years. For context, a dozen years ago, Jeff Bagwell was the first baseman who had just led the league in WAR. Votto is unlikely to be very productive in 2023, but the Reds already know this. This is just a $22 million-per-year payment plan to avoid having to pay Votto the $40 million they think he’s worth now. In the past couple years, we’ve seen massive contracts given out to first basemen. Seven of 30 starting sluggers on the cold corner are currently playing with contracts in excess of $100 million, including Mark Teixeira, Miguel Cabrera, Ryan Howard, Adrian Gonzalez, Albert Pujols, Prince Fielder and Votto. In contrast, there are seven other position players — combined — who are playing with $100 million contracts. When I showed off Table 1 (below) a couple months ago in this article, I pointed out that first basemen were paid pretty generously when compared to other positions, in terms of dollars-per-WAR. The question that I posed, and that readers echoed, was whether this meant that general managers needed to learn from sabermetricians — or whether sabermetricians should take a hint about WAR. Table 1- $/WAR by position for 2007-11 Position Millions of Dollars per WAR C $4.1 1B $6.2 2B $3.1 3B $4.3 SS $3.5 LF $7.3 CF $5.5 RF $6.0 DH $7.5 Sabermetricians add or subtract runs from a players value based on position to adjust for relative offensive production at different defensive positions. Our adjustments are based on the approximate difference in defensive performance that might be expected if players were to switch positions. There are several methods out there — including looking at offensive differences — but first I wanted to take another approach to look at this issue. Presuppose for a moment that the market is already efficient: all positions are paid the exact same $/WAR, because if they weren’t, teams would bid up players at underpriced positions until they suddenly were all paid the same $/WAR. Suppose that we have correctly modeled batting, base running, fielding and replacement level in aggregate — and it’s just that we have incorrectly applied the numbers of runs needed to adjust each position. What numbers would need to be applied to each position’s WAR to clear the market at $5.05/WAR average for each position in the past five years? I solved for these, and put them next to the adjustments that we use here at FanGraphs. I call this the “General Managers Adjustment,” since it’s effectively the positional adjustment that general managers are using to value free agents at each position. Table 2—Adjustment for defensive position used in WAR, and General Managers Adjustment to free agents Position FanGraphs Adjustment General Managers Adjustment C 12.5 8.5 1B -12.5 -7.9 2B 2.5 -8.8 3B 2.5 -6.9 SS 7.5 -1.5 LF -7.5 0.4 CF 2.5 7.2 RF -7.5 -3.6 DH -17.5 -9.0 The market doesn’t treat positions equally, but the extremes are much softer than traditional positional adjustments. The market treats first basemen who produce 7.9 runs more than an average hitter as an average first baseman (if their defense and base running is average). It also forgives catchers for having lighter bats as well and considers them average if they produce 8.5 runs fewer than an average hitter. But based on the defensive performance of players at these positions, we expect more of first basemen and less of catchers than general managers apparently expect. That’s why players like Prince Fielder get $200 million contracts with far fewer expected WAR on his horizon than Joe Mauer would have been expected when he was offered less than $200 million. General managers effectively are adding about 0.5 WAR to first basemen’s totals when valuing their performance but they are also subtracting 0.4 WAR from catchers. So who is right? Are the general managers right to put more money into first base and center field for less WAR? Or should they follow sabermetricians’ advice and concentrate their resources on middle infielders and catchers? To shine light on this, one option is to look at the hitting performances at these positions. Sabermetricians are indifferent between an average defender at third base and an average defender at first base who produces 15 more runs on offense. This is because they expect the third baseman to be 15 runs above average defensively if he moves across the diamond. That’s one approach. But if we view defensive positions as more rigid, this question should be asked: Does the average first baseman produce 15 more runs than the average third baseman? If so, then we’re right to treat the third baseman as a scarce resource and suggest that more money should be spent at the hot corner. But if the offensive performances aren’t markedly different, perhaps teams are doing the right thing. With the help of David Appelman, I put together offensive averages at each position. Thanks to David’s help, we have a table of positional adjustments that uses offensive and base-running averages. (Of course this would also assume that the gap between replacement level and average is the same at every position — which is almost certainly not true — and it’s something I will look at soon enough.) Table 3—Average adjustment by FanGraphs based on defense, average adjustment applied by general managers with free agents and average differences in offensive performance at each position Position FanGraphs Adjustment General Managers Adjustment Offensive Adjustment C 12.5 8.5 11.3 1B -12.5 -7.9 -9.6 2B 2.5 -8.8 0.6 3B 2.5 -6.9 0.3 SS 7.5 -1.5 5.8 LF -7.5 0.4 -4.9 CF 2.5 7.2 -2.2 RF -7.5 -3.6 -8.2 DH -17.5 -9.0 -2.2 For most positions, the offensive performance difference is closer to the FanGraphs Adjustment (based on defense) than the General Managers Adjustment. In other words, general managers could do themselves a favor by listening to sabermetricians. The offensive difference, though, is usually somewhere between the FanGraphs Adjustment and the General Managers Adjustment, meaning that there may be some information that we could learn from general managers, as well. There are two positions where the General Managers Adjustment is closer to the offensive difference than the FanGraphs Adjustment: first base and designated hitter. The FanGraphs Adjustment comes from the fact that players who are moved to first base from other positions tend to play it well, but not all players would thrive as much at first. If this adjustment were perfect, it would mean that the market was inefficient and that some teams would be better off putting one of their other defenders at first — and accepting the slightly lower offensive production — but benefiting from the extra defensive production. According to our adjustments, the average right fielder or left fielder would be five runs above average at first base (i.e., 12.5 – 7.5). This method only approximates value, since it assumes consistent changes in defensive value when going from one position to another. For example, two positions where the market may be under-pricing talent are shortstop and catcher, where we assume the average players are 7.5 runs and 12.5 runs better than the average defender on the diamond. One position where the market may be overpriced is first base, where we assume the average player is 12.5 runs worse than the average defender on the diamond. The model shows its limitations when we realize that the average catcher with his old-man knees probably would struggle with too many ground balls to be 25 runs above average at first base. Not only that, but the average shortstop is short enough that he might struggle to stretch for an errant throw while holding the bag, and fail to be 20 runs above average at first base. While it may be true that the average shortstop is five runs above average at third base, the average third baseman is 10 runs above average in left field and the average left fielder is five runs above average at first base, the average shortstop probably isn’t 20 runs above average at first base. So the 12.5 run adjustment for first baseman is an approximation. On the other hand, the average first baseman is 9.6 runs above average for a position player offensively, and the market is treating his hitting skills more scarcely than that — at 7.9 runs above average. The ideal approach is somewhere in the rough neighborhood of a 9.6 to 12.5 run adjustment, but it does appear that first baseman are a little overpaid, if not as overpaid as their $6.2 million per WAR suggests. One position where the market price may be accurate is designated hitter. The reason that sabermetricians expect designated hitters to hit so well is that a comparable hitter who plays average defense at first base should be more valuable than a DH. On the other hand, studies have shown that it is hard to hit out of the DH spot. These studies may imply that keeping active in the field helps at the plate, rather than sitting on the bench waiting to bat four times a night. As a result, hitters such as David Ortiz are coveted, and the market treats a hitter who produces 9 runs above average at designated hitter to be an average hitter. The tests above show that, on average, designated hitters are only about 2.2 runs above average for position players. So is the market undervaluing designated hitters, to? I don’t think so. Teams have the ability to put any player at designated hitter who isn’t already playing a position in the field. But the fact that the average player managers keep off the field is only an average hitter does not mean replacement level designated hitters hit as badly as average back-ups. So neither offensive adjustments of 2.2 runs nor FanGraphs’ defensive adjustments of 17.5 runs is perfect. The General Managers Adjustment of 9 runs may be just right. Catcher is a unique position, so it would appear to be one in which the FanGraphs approach to positional adjustments fits worse. After all, the average catcher would actually be bad at most other defensive positions — and most other defenders would also be bad at catcher. So the concept of valuing catchers more because of what would happen if you switched everyone’s positions would not be ideal. But the offensive difference between catchers and other position players actually suggests the FanGraphs approach is just fine. The average catcher is about 11.3 runs below average offensively, and presumably, the average replacement-level catcher hits about 11.3 runs below other replacement-level hitters. Because of that, general managers might do themselves a favor to bid on catchers a little more aggressively. The market underprices infielders other than first baseman. They are all below-average offensively, are often above average defenders if shifted to another position and the market treats them as though finding elite offense at these positions is easy. While sabermetricians generally would think that a shortstop who produces 1.5 runs more than an average hitter each year is all-star worthy, the market does not. Teams didn’t outbid the Phillies went they offered Jimmy Rollins a three-year deal for $11 million per season. Apparently, league-average batting ability is what they expect shortstops to produce for $11 million, despite the fact that the average shortstop produces 5.8 runs below average on offense. This evidence suggests that shifting money from first base to shortstop would probably help teams get more bang for their buck. Interestingly, outfielders are treated as scarce commodities, despite being above-average offensively. Even center fielders produce 2.2 runs above average offensively, but the market treats such center fielders like all-stars. The market actually treats center fielders who produce 7.2 runs below average offensively as equally valuable as shortstops who produces 1.5 runs above average offensively. Teams have ponied up significant cash to obtain the services of center fielders such as Vernon Wells, Torii Hunter and even Aaron Rowand, only to see them rapidly decline. This could be irrational behavior from general managers in a small sample size, but we may have a better picture of whether this market tendency will persist after Michael Bourn and Shane Victorino reach the open market. Every team faces slightly different choices, and we have not even begun to discuss replacement-level yet. But these findings seem to reinforce my findings from earlier this year that players at elite defensive positions — such as catchers and middle infielders — are undervalued, and that outfielders and first baseman are overvalued. Reallocating expenditure toward tougher defensive positions and suffering the consequences of weaker production from first basemen and outfielders would generate more wins than many general managers’ current strategy. At the moment, general mangers pay for elite hitters with less defensive skill and suffer weak hitting from whoever is still available to play infield on the cheap. While the limitations of assuming that any player can switch positions are obvious, the above information suggests that teams would at least be better off letting internal options or fringe players roam the outfield and first base. This would save cash for elite players at catcher, second base, third base and shortstop. Otherwise, teams will continue to be stuck with internal options at infield and catcher, all because too much money has been spent elsewhere.