Why First Basemen Get Paid So Much

First basemen and outfielders seem pretty overpaid if we look at their salaries and their WAR. At the same time, catchers and the three other infield positions seem pretty underpaid. As I showed in February, second basemen were only paid about $3 million per WAR from 2007 to 2011; first basemen were paid exactly twice that much. I think I might know why.

Claims that some positions are relative bargains using $/WAR hinge on “positional adjustments” — estimates of how much more valuable equivalent production is from different positions — using what hypothetical defensive performance would be if you moved players between positions. Last month, I looked into how much credit general managers seem to give performance at different positions, and how offensive performance varied across those positions. My logic was that, if the average first baseman produces only a few more runs per season than the average second baseman, then it may explain why general managers pay so much more for power-hitting first basemen.

In that story, I produced the following table:

Table 3—Average FanGraphs adjustment based on defense, average general managers’ adjustment 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

Offensive performance was usually pretty close to the positional adjustment, which is evidence that GMs weren’t valuing positional adjustments correctly. Of course, the average offensive performance at each position is not the perfect metric to use. The real question is not the difference in average performance, but the difference in replacement-level performance.

Let’s say you’re a general manager and the free-agent market is wrapping up, but you still need a first baseman and a second baseman. Your owner tells you that you have $10 million left to spend, and fortunately there is a first baseman on the market who you expect to have a .330 wOBA and a second baseman who you also expect to have a .330 wOBA. If you sign the first baseman, you have a few minor-league veterans who are prepared to take over at second base, and there are also a few more minor-league veterans who are prepared to play at first, if they’re needed. If you ask WAR, it will say to go with the .330 wOBA from the 2B, since he plays the harder position. But a general manaher must determine how much pop they will get from the replacement-level players.

But who are these replacement-level players we keep talking about? To know what replacement-level is, we need to know who is a replacement-level player. The standard sabermetric definition is “a freely available talent who could fill into a player’s role at little cost.” You can’t use salary to define “at little cost,” unless you limit yourself to players with service times close to or exceeding three years, since most young players get paid little but are not easily available and won’t come cheap. On other words, “cost” can’t just mean salary. Using playing time to find back-ups and looking at their performances is tricky too, since players who get lucky and play over their heads are going to get more at-bats in case they can keep it up. On the other hand, using future-performance projections to eliminate that concern only makes it harder. After all, projections for fringe players are based on “Minor League Equivalencies,” which are the performances only for minor-leaguers who were given the chance to be promoted.

So I came up with three different methods to look at replacement-level, and they all lead me to similar conclusions:

1) I separated players into “major-leaguers,” who were among the top 50 players in their position in PA that year, and “replacements” who were not.
2) I tried to use all the replacement-level players who had enough service time to be paid more, but were not.
3) I found all the players who were older than 26, who had at least 20 plate appearances in Double-A or Triple-A  and who had fewer than 400 plate appearances in the major leagues. I called them “replacement level”.

Method 1

Taking the 50 players with the most PA at each position in a season, we can estimate who would be on a major league roster if everyone were healthy. But we also probably include some people in the “replacement level” pool who we shouldn’t and perhaps we’re excluding some people we should consider replacement-level. Anybody who plays above their true talent level is going to get extra plate appearances, so this method excludes over-performers (who end up with too many PA) and includes relatively more underperformers. It’s no surprise that this method yielded the biggest gap between “major leaguers” and “replacements” among the three methods.

I calculated what I call a “run gap” for each position, which is the difference in performance for “major leaguers” and “replacements” in batting runs, baserunning runs and UZR (though UZRs were pretty close to zero, on aggregate).

Since I only had a few thousand plate appearances at each position, and since the sample is somewhat biased, I took the “run gap” for majors versus replacements, normalized it to a 20 runs per position average (normal FanGraphs replacement-level) and regressed the differences between positions halfway back to average hitting performance for each position. This gave us some new numbers for replacement-level, which I used on my free-agent data to determine $/WAR.

This gives us pretty similar conclusions to last time. Outfielders are overpaid across the board; middle infielders and third basemen are underpaid; and designated hitters are a little underpaid. But catchers and first basemen are both paid pretty fairly. This is quite different than looking at average performance at each position. As it turns out, minor-league catchers are not all that much worse than minor-league first basemen at hitting — which changes our perceptions star first basemen’s value.

Position	PA majors	PA rep. level	Majors Runs per 600 PA	Replacements Runs per 600 PA	Run Gap Majors vs. Replacements	Half regressed normalized Run Adjustment	Method 1 $/WAR
C	82,598	14,355	-6.6	-24.58	17.98	7.73	$5.30
1B	92,805	6,412	13.63	-10.36	23.99	-9.76	$5.45
2B	92,004	7,995	4.28	-25.35	29.63	3.3	$2.99
3B	88,667	8,486	5.42	-29.5	34.91	7.97	$4.11
SS	94,067	6,380	-1.93	-30.99	29.06	5.21	$3.46
LF	80,740	13,690	9.81	-9.91	19.72	-7.23	$7.16
CF	94,147	7,120	6.25	-16.12	22.37	-2.98	$6.05
RF	87,717	8,697	13.03	-9.22	22.25	-9.59	$6.71
DH	33,536	3,551	8.12	-15.67	23.8	-3.81	$4.22
All hitters (non-P non-PH)	746,281	76,686	5.64	-18.99	24.63	–	$5.05

Method 2

The next thing that I tried was to look for players whose salary and service time suggested that they were replacement level. These were guys who made under about $1.4 million, even though the CBA allows them to be bid up if they are worth it. First, I found all players eligible for free agency who had low salaries. Next, I found all players who were eligible for arbitration, but were non-tendered and then received low salaries. Unfortunately, this does not give me many players at all. It also seemed to include many players on “make good” contracts, who had non-guaranteed deals. Some weaker players got Spring Training invites, looked bad, and were released, so they were not included in the sample, while other players made the team but had low salaries. As a result, these players were only about six runs below an average major league player at batting, baserunning, and fielding combined, so they looked a little too good to be “replacement level.”

Nevertheless, when I normalized the positional differences to the FanGraphs standard 20 runs per season, and then used these to determine replacement level, I found that free agents’ salaries (in my original free agent data for 2007-11) followed the same pattern. Middle infielders and 3B are underpaid, and outfielders are overpaid. But now catchers do look a little underpaid and 1B do look a little overpaid. Designated hitters still seem pretty fairly paid.

There seemed to be a problem with sample size for SS, CF, and RF, which might suggest this isn’t a great method. With half as many PA at these three positions, it looks like players like these were placed at easier positions more often and regular backups were shifted over to harder defensive positions.

Position	PA replacement level	Replacements Runs per 600 PA	Normalized Run Adjustment	Method 2 $/WAR
C	8,326	-20.88	-14.75	$3.72
1B	6,313	5.63	11.77	$5.98
2B	5,846	-7.09	-0.95	$3.24
3B	6,846	-14.11	-7.97	$3.94
SS	3,688	-20.58	-14.44	$2.84
LF	8,250	-1.6	4.54	$6.24
CF	3,727	7.24	13.38	$7.58
RF	3,692	6.24	12.38	$7.91
DH	3,077	3.21	9.35	$5.12
All hitters (non-P non-PH)	49765	-6.14	–	$5.05

Method 3

This is my favorite method, though it took the most work. I figured that replacement-level players were probably expendable enough that they were shuffled up and down between the major and minor leagues. Sometimes, prospects get moved up and down, but players older than 26 are rarely considered prospects. Players were replacement-level if they were older than 26 years old, had fewer than 400 plate appearances in the majors, and had more than 20 plate appearances in Double-A or Triple-A. The result was a larger player sample that appeared to represent most replacement-level players.

The overall replacement level for these players came in at about 13 runs below average, which is smaller than the typical 20 runs used at FanGraphs. Note that this doesn’t account for “chaining,” where backups are put in the field and weaken the available pinch-hitting pool. I suspect that this might account for the difference between 13 runs calculated and 20 runs used. (When I tried experimenting with lower replacement levels in the past, I found that superstars appeared to be underpaid using $/WAR. Because of that, I agree with the 20 runs below average replacement level). After normalizing the “run gaps” to average 20 at each position, I got the table below.

The results are pretty similar to what we found in the other two methods: Outfielders still appear to be very overpaid, especially corner outfielders; and middle infielders and third basemen are underpaid. This is partly because replacement-level players had poor UZRs in the infield and good UZRs in the outfield. But the table still looked very similar when I re-set everyone’s UZR to zero, so that doesn’t drive the results.

Interestingly, first base, catcher and designated hitter all seem to be slightly underpaid using this method. The varying results for catcher and designated hitter show the difficulty figuring  replacement level at these positions. Catchers are a unique breed, since other players cannot play catcher well and catchers cannot play other positions well. Designated hitters are the opposite. Anyone can be a designated hitter, though there are varying skills to staying fresh while sitting on the bench.

Position	PA majors	PA rep. level	Majors Runs per 600 PA	Replacements Runs per 600 PA	Run Gap Majors vs. Replacements	Half regressed normalized Run Adjustment	Method 3 $/WAR
C	86,346	10,847	-7.32	-24.57	17.26	12.31	$4.15
1B	98,452	5,883	12.94	-10.91	23.85	-5.23	$4.54
2B	97,634	7,755	2.61	-12.89	15.5	0.72	$3.27
3B	95,431	7,449	3.69	-23.51	27.2	6.33	$4.04
SS	96,769	6,649	-2.85	-18.07	15.22	5.87	$3.72
LF	93,288	11,370	7.69	0.75	6.94	-9	$7.93
CF	95,909	10,460	5.71	-9.07	14.78	-2.43	$5.98
RF	96,741	7,757	10.51	6.66	3.85	-13.86	$8.75
DH	42,616	5,639	5.99	-5.94	11.93	-3.85	$4.22
All hitters (non-P non-PH)	853,812	80,315	0.87	-12.08	12.95	–	$5.05

Note that I also regressed the “run gap” halfway to the average positional difference using this method as well. The results would be more extreme, but qualitatively similar had I not done so.

Averaging all three methods, I get the following table with $/WAR for each position, which reinforces the arguments above.

Position	Methods 1-3 average $/WAR
C	$4.39
1B	$5.32
2B	$3.17
3B	$4.03
SS	$3.34
LF	$7.11
CF	$6.54
RF	$7.79
DH	$4.52

Other People’s Players?

So how do teams get their hands on these undervalued infielders? Can they? Or do teams lock them up quickly? Take a look at the upcoming free agents this offseason and you see that solid infielders are poised to reach the open market. There are Kelly Johnson and Marco Scutaro, but no superstars. Dustin Pedroia and Troy Tulowitzki both would have reached free agency this winter, but the Red Sox and Rockies signed them to long-term deals.

One point that I have hammered hard for several years is that teams get a pretty bad deal when they sign free agents from other teams. Teams get far better bargains on re-signing their own free agents. This is far truer for pitchers than hitters, but it’s still true for hitters. So what if we look at re-signed players (RSP) $/WAR and other team’s players (OTP) $/WAR separately? Do we still see this difference between outfielders and infielders? Yes.

Position	Re-signed Players (RSP)	Other Team’s Players (OTP)	OTP Premium
C	$5.39	$2.84	-47%
1B	$5.76	$7.53	31%
2B	$3.55	$2.24	-37%
3B	$4.76	$3.52	-26%
SS	$3.31	$3.77	14%
LF	$6.31	$8.01	27%
CF	$8.16	$4.80	-41%
RF	$5.23	$6.53	25%
DH	$7.95	$7.20	-9%

The argument holds up: Infielders are better bargains than outfielders, even if you restrict it to players who reach free agency. The best-priced infielders on the market in recent years have been Adrian Beltre (on three different deals), Alex Rodriguez’s 2001-2007 deal, Edgar Renteria’s 2005-2008 deal, Luis Castillo’s 2004-2007 deal, Mark DeRosa’s 2007-2009 deal, Miguel Tejada’s 2004-2009 deal, Orlando Cabrera’s 2005-2008 deal and Troy Glaus’ 2004-2008 deal. There are other players, as well, but the point is that these bargains are out there for savvy general managers to find.

What Should Teams Do?

Once again, it seems that the best bargains are in the infield and the worst prices are in the outfield. When Josh Hamilton becomes available this winter, teams should be wary about just how much they want to spend. It’s pretty obvious that  teams will have an opportunity to put decent role players in outfield positions who can get the job done.

On the other hand, the mantra that teams should stop spending so much on first base might be wrong. Although you won’t get the same WAR for the money, the replacement-level first baseman who teams use often is below the technical replacement level. Teams are often forced to pay a lot to get “one of the good ones.” Even still, the best bargains remain at other infield positions, and smart general managers would be wise to make sure that they have money available when star infielders become available.