Monday, February 9, 2009

One Last Word on Shawn Hill: He's STILL Underpaid

I've been startled at the reaction on blogs and chatrooms about Shawn Hill's arbitration victory. People seem actually disappointed that Hill won. Or if not disappointed, then at least somewhat bemused.

I always think it's weird when fans root for the owners in contract disputes, and I don't see why any Nationals fan would be cheering for Ted Lerner to get a tiny bit richer at Shawn Hill's expense. It's not like the $100k or $200k difference between Hill winning and losing is going to allow us to sign John Lackey next year.

But the big disconnect is that, even after winning a one-year deal of $775k for 2009,
by my estimate, Hill is underpaid.

Some quick background for those who aren't yet totally familiar with how things work: MLB players for their first three seasons have essentially no say in the terms of their employment. They have to play for the team that drafts them, and they have to take whatever salary they are offered. They can quit Major League Baseball and play for the Fort Worth Cats, but otherwise they have no rights whatsoever and almost always make something close to the league minimum ($390k in 2008).

In years 4-6 players can begin to negotiate, but they still can't negotiate with any other teams, and ultimately a panel arbitrators decides what they deserve to earn. It's a system that gives the players something closer to their real market value, but not really, because the owners win about two-thirds of the time in arbitration. Players aren't paid their true market value until they reach their seventh major league season when they qualify for free agency and can peddle their services to whatever employer they choose (a right most Americans take for granted every day).

Back to Hill and why I think he's underpaid. It's actually pretty hard to say what would be fair market value for a player without actually allowing the market to set that price, but Dave Cameron made a solid attempt at calculating "deserved" player value under the "Value" stats category on the player pages at Fangraphs.

Dave did a lengthy series of posts explaining the methodology, but the quick summary for pitchers is that he used Fielding Independent Pitching (or FIP, which is a stat that projects ERA based on a pitcher's rates for HRs allowed, Ks, and BBs, and HBPs--four stats a pitcher has a great deal of control over) to quantify pitchers' run prevention value above replacement level, neutralized those stats for park factor and other variables, then converted those runs prevented into wins above replacement at a rate of about 10 runs per win, and then multiplied that by the average amount of money per win that teams were willing to spend in free agency. That was a wicked run-on sentence, so if you didn't follow all that, just think of this as a system for figuring out what a guy would get if he was a free agent.

Dave's analysis tells us that Shawn Hill in 2008 pitched 63.1 innings with a 4.06 FIP, which is worth a skosh less than one win over replacement. Teams the previous off-season spent on average $4.6 million per additional marginal win in 2008. Therefore, Hill's fair market valuein 2008 by this metric was $4.4 million. In 2007, when teams spent $4.1 per marginal win, and Hill pitched 97 innings with a 4.03 FIP, he was worth 1.5 wins over replacement and about $6 million.

Hill's actual salary for those two seasons was $800k. So that means going into 2009, he's at least $5.2 million short of what old school hip-hop geniuses Eric B. and Rakim would call "paid in full."

Now some of you I'm sure are thinking, "wait, I'm looking at his baseball card right now and it says his ERA in 2008 was 5.83. How can that be worth anything over replacement?" The answer is that ERA is a wildly flawed stat that lumps in the whole team's overall run prevention ability and lays it all at the feet of the starter. Factors like fielding range, the bullpen's effectiveness stranding inherited runners, and pure sample-size flukiness all skew the pitcher's ERA, and it's not at all unusual to see a pitcher with an ERA a run or more above or below what he really "deserves." There are two stats out there that do the best job of isolating pitcher skill and rendering that as an ERA-like stat--FIP and tRA*. Both give you pretty similar results, so no need to get into that raging debate here.

In Hill's case, he was a bit lucky in 2007 and a quite a lot unlucky in 2008. His FIPs were pretty much the same--4.03 and 4.06, while his ERA swung from 3.42 to 5.83. How does that happen? His BABIP against rose from .269 to .373 (something around .305 is probably the mean for a groundballer like Hill), and his strand rate sunk from 71.6% to 61.9% (70% is typical). So those of you looking at his one win and ERA and thinking he stunk up the joint are looking at the wrong stats and drawing wrong conclusions.

Now back to the value per win calculation. I actually have a little issue with Cameron's method, which is that it implicitly assumes that if every player was a free agent that teams would keep spending the same amount per marginal win. Obviously, if every player was a free agent, the market would be flooded and simple supply and demand laws tell you that the marginal value per win will fall, and by quite a bit.

I prefer the method used by FiveThirtyEight's Nate Silver in his contribution to Baseball Between the Numbers, an essay titled "Is Alex Rodriguez Overpaid?" In it, Nate looks at the effect of each additional marginal win on team revenue, and figures what I think is a better measure of player value--not what owners will pay to acquire players, but what fans will pay to see them. Looking at all a team's revenue sources, from gate receipts to merchandise sales to revenue-sharing, he was able to
use a bunch of fancy math regression analyses to conclude that in 2004 an average team generated about $1.1 million in additional revenue for each win. MLB total revenues increased 50% from 2004-2007, however, so we should raise that number to at least $1.65. (I haven't seen total revenue numbers for 2008; if anyone has them lemme know.)

Even with this more conservative definition of player value, fair compensation for Hill's 2.5 wins above replacement for 2007-2008 would amount to $4.1 million total for the two years, $3.3 million over what he was actually paid.

Of course, this method actually understates what players would get in a competitive bidding environment. The concept of the "winner's curse" in economics says that in a competitive bidding environment (like an auction or the MLB free agent market) the winning bid almost always overestimates the true value of the product. It's probably most fair to say that Hill's true fair market value for 2007-2008 is somewhere between $4.1 million and $6 million, or something on the order of $2.5 million a year, which coincidentally is what Daniel Cabrera got for 2009. And I'd rather have Hill than Cabrera, so that all sounds about right.

So y'all can root for the owners in arb if you want, but as far as I'm concerned, I'm with Jay-Z when he says, "Pay us like you owe us for all the years that you hold us / We can talk, but money talks so talk mo' bucks."
  • Update: Scott Olsen and the Nationals settled on a one-year, $2.8 million contract. Applying the same process to Olsen that we did for Hill, we find that Olsen's 2007 176.2 IP and 5.33 FIP was worth 0.3 wins above replacement, while his 2008 201.2 innings and 5.02 FIP was worth 0.6. (If it seems odd to you that the durable Olsen hasn't been as valuable as the fragile Hill, but the fact is that 170 innings of pretty good pitching is more valuable than 370 innings of lousy pitching.) Total, the 0.9 win Olsen gave would be worth as much as $2 million per year using the free agent market to establish value and as little as $750k per year. I'll again split the difference and call him a $1.4 million pitcher--in other words we're paying him roughly twice as much as he's been worth the last two seasons. I don't begrudge Olsen--you gotta overcharge the game for what they did to the Cold Crush. But let's not act like Olsen's millions are fair and Hill's thousands aren't, ok?


Anonymous said...

after seeing you on FOXNews, I never wouldve thought in a million years that youd be a Jay-Z fans..something about you screams Josh Groban.

Steven said...

You gotta present yourself for your audience. The average middle american viewer of cable news wouldn't really get it if I went on and said to Cavuto, "bitch, please. your shit is weak. I ain't even messin' wit' you."

James Bjork said...


I won't take issue with your elegant statistics-- that Hill is being paid less than typical market value per win share. However, I frame it all differently. It's not that Hill is underpaid. I think the whole system is bananas when teams are actually paying almost $5 milliong for but a single projected win about replacement pitcher!

I'm really hoping this "collusion" this season in free-agent salaries is actually a "recallibration." that better enjoins salaries to actual win shares as determined by adequate consideration of both offensive and defensive impact!

Regarding your whole repeating meme about how players are ostensibly screwed in service years 1-7, including in arbitration, I believe that the best players who are the most "screwed" early in their careers are the same ones who get OVERpaid for what they will actually produce once they hit free agency around age 30. For every underpaid Zim, there are albatrosses like Andruw Jones.

While you are certainly under no obligation to cater to addressing arguments or proving anything to peanut gallery types like me, I would love to see a comprehensive analysis of this! Calculate dollars per win share of older skilled veterans like Griffey or Thome or whoever. Calculate how "underpaid" for winshares (or VORP) early in their careers relative to other players' pay that year each year, then compare how much they were "overpaid" per win share once they hit free agency (relative to player salaries and performances that year across the league).

This would take work but would be do-able. While one could argue that by axiom, the overpaid will exactly equal the underpaid, since the "underpaid" status is relative to "overpaid" free agents driving up the typical cost per win share, it may be that young players truly do get a raw deal in that overpayments to certain free agents drive up the salary average, where multiple young players get screwed since many will peter out performance-wise and never get the sweet FA deal.

If you can demonstrate that overall the existing system screws players ON AVERAGE, considering the entire player career (including free agency), this is something you could permanently post and link to.

Hendo said...

Two notes of many I could make but haven't time right now.

1. Jay-Z's economic insights notwithstanding, assuming that the player should be awarded 100 percent of his marginal value kind of de-incents investment in baseball franchises.

2. Silver's point in the article, IIRC, is that Rodriguez was overpaid.

Steven said...

@Hendo--1. I don't disagree; I'm just trying to establish some objective sense of what's fair. 2. you do indeed RC. I don't think that takes anything away from my point here, b/c I'm not defending ARod contract. But yes you are correct the metholdology that I used to conclude that HIll is underpaid found that ARod is overpaid.

@James--I don't disagree with your basic point that if a player manages to stay healthy and have a typical career arc that he'll make up much of what he lost in his early years. I haven't done the math on it, but intuitively my sense is that this is probably right in many cases.

But a lot of guys don't have 7-9 years of productivity. A lot of players have a 2-3 window of above replacement level value, either because they get hurt or just because that's all their talent allows. They never "make it up." So the system screws young players but more than that it screws solid but unspectacular players with a brief peak.

If you want to measure the overall fairness of the system, probably the best metric is to look at the share of MLB revenue that goes to the players. Right now it's about 50-55%. In the old days before Curt Flood it mostly fluctuated between 20-25%, occasionally reaching 30 or dipping to 17%.

It's more of a philosophical question--how much is the appropriate share of MLB's revenue to go to players v. owners, and I haven't committed myself to a number that I think is 'right.' But 50% seems if anything a little low to me.

Bottom line though, if the system is bananas, I really think you're just commenting that American culture is bananas. MLB makes a lot of money becasue people find baseball entertaining and are willing to spend a large share of their disposable income on this entertainment. If you are turned off by our cultural values, you're not alone, and I'd agree with you. A lot of people think we're messed up. In this way I'm actually kind of more aligned with cultural conservatives who say our culture is degenerating (my hip-hop taste notwithstanding). But don't blame Shawn Hill for America's cultural values. He's just trying to make sure he gets his fair cut, and if he gets less than what's fair, then that just means Teddy gets more. It's not like ticket prices or beer prices go down when players earn less. (This I think is the mistaken assumption most fans make when they root for players to lose in arb. But prices are set by supply and demand in our economy, not by the cost of production.)

El Rey said...

The fact that the Lerners would go to arbitration over $250K proves yet again they are cheapskates. I suspect Z Man is counting the days when he can be a free agent so he leave this tinker toy operation. At least the fans can enjoy Stan's new centerfield "fire pit" and mystery object that will soon be atop the Red Loft. Hey, won’t the "fire pit" jeopardize the stadium's green status? Stan has such a tin ear, we will probably soon see an Exxon oil can perched atop the Red Loft.

Steven said...

El Rey--I agree I think this is probably the most important take home point from this whole episode.

Wil Nieves said...

I'm not sure about whether Hill is over/underpaid, but I am not sure you are accurately assessing injury risk as a part of the salary. Even if 170 innings of quality pitching are better than 370 innings of not-as-quality pitching, if someone is an extreme injury risk, you need to pay an equally competent backup with the assumption that the player will likely be hurt for at least part of the season. You have to get the other 200 innings of pitching from somewhere...

For the Nats, accounting for how young the players in the farm system are, it seems as if they particularly need to take into consideration the value of a pitcher's durability so that they do not need to rush the young guys up to the majors too soon (leading to too many innings, more injuries, cycle repeats itself).

Steven said...

Wil--I'm not measuring the value of Hill's potential. I'm measuring the value of what he's already done. If you were to try to quantify the value of his potential future contributions, that would only go on TOP of what I'm measuring.

It's not fair to say that he shouldn't get paid fair value for his work in 2007 and 2008 because he might get hurt in 2009.

Section 222 said...

My general POV is that I really don't care if the players are "overpaid" by whatever standard you want to use. I'm happy to see some of the Lerners' ill gotten gains (from the inflated price of a Ben's halfsmoke at the Park, for example) go to someone, even a bench player, who has athletic skills I can't even dream of. But leaving that aside, I'm not sure I understand why you think that salaries should or do reflect what a player has done in the past rather than their potential for the period during which they will receive the paychecks. The only reason that past performance is relevant is that it's the best predictor of future performance. If we knew to a certainty, for example, that Hill (or Olsen) would be injured for most of the coming season, would there be any justification for paying them based on a complicated statistical analysis of last season?

Steven said...

@222--Mostly I'm just trying to establish that Hill hasn't been paid what he's been worth, and that those you are bellyaching about how overpaid he is aren't looking at the facts.

But let me take a crack at your broader point. If you had a system where players from the time they entered the league they could peddle their services to any organization at any price just as most Americans can in their careers of choice, then you would have the perfect marketplace where players' value would be established based on past performance, future potential, 'intangibles,' etc.--the collective judgment of the GMs (aka the invisible hand of the marketplace) would function and money would flow in perfect Milton Friedman-esque elegance to the most talented and deserving.

The problem, is that if you had this kind of total FA situation, it would cause problems for the game. Competitive balance would probably go out the window without a draft or 6-year reserve system, and players would move around so much that MLB would start to look like roto baseball, and it would be hard for fans to form any allegiances.

So instead my proposal, which I posted about a few weeks ago, would be to keep everythiung the same as far as the draft, the 6 years of team control, etc., and then have a system where players would be paid based on a league/union negotiated statistical metric so that like golfers and tennis plaeyrs salaries would be directly tied to performance.

I don't think this system would be perfect--every statistical analysis you could do would be limited, but it would be a damn sight more "fair" than what we have now, when in 2008 Elijah Dukes got paid one-tenth what Paul Lo Duca got.