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Monday, March 17, 2014

Was Homer Bailey's Contract An Overpay?

The Reds locked up Homer Bailey this offseason,
but was the cost too great?
Photo credit: David Slaughter
The Reds' biggest offseason player move was unquestionably handing Homer Bailey a $105 million/6 year contract extension this offseason.  While this was exciting for most fans (myself included), reaction around the internets tended to lean toward this being a pretty substantial overpay.

I'm sure that people have done nice analyses of Homer's contract.  I didn't really look around at the time, though.  So, I decided to finally take a look myself.  Well, a few looks.  

Approach #1

The first approach I used is close to what I've been doing for years to understand contracts, and is inspired by people like tangotiger.  It works as follows.
  1. Make a projection for a player during the contract.  I used 2014 Steamer and ZIPS projections for that (courtesy of FanGraphs), and then did a "standard" 0.5 WAR/year decline.  That might be generous aging for a pitcher given pitchers' inherent tendencies to break, but we'll run with it.
  2. Come up with a cost per win translator for each year of the contract.  This is trickier than it used to be, because some of Dave Cameron's recent work has made it clear that the cost per win is not constant anymore; above-average players are getting more dollars per win than below-average players.  Fortunately, in that article he presented a regression line for this relationship, and it showed a really simple relationship: 2 WAR players (i.e. league-average) are getting $6M/win, 3 WAR players are getting $7M/win, 4 WAR players get $8M/win, etc.  I'm assuming that this "bonus" is set in the first year, such that players do not see their $/win decline as their performance declines.
  3. Estimate salary inflation.  I'm guessing wildly here, but based on past increases, as well as the amazing amount of money coming into the game right now with all of the TV contracts, I'm estimating a fairly aggressive 10% inflation on the $/win of an average player.  I'm just going to assume that the extra million bonus a 3-WAR player gets per WAR is fixed and not subject to inflation.
  4. Multiply the estimated WAR each year by the player-specific $/win numbers.  This gives salary value each year.  Then, you just sum up all of the years to get total contract value.
Here's what I got when I did this for Homer:

On the far left are years, my estimated average $/win with inflation, and Homer's actual salary.  I'm assuming the Reds will not exercise their part of his mutual 2020 option, so they pay the $5 million buyout.  Then you have the Steamer projected WAR, his $/win, and estimated salary.  Similarly, I report ZIPS estimated salaries.  Finally, on the right, I'm presenting a projection that would be required for the contract to make sense using my salary model.  In other words, this is apparently how the Reds are valuing Bailey.  Also, please note that I'm ignoring the fact that 2014 is Bailey's last arbitration year; we should really subtract $3 million from his total 2014 salary in each case to account for the fact that players make about 80% of their free agent value in their 3rd arbitration year.

It doesn't look like a particularly good contract, does it?  Steamer and ZIPS have his contract valued at between $50 and $67 million over six years.  Furthermore, Steamer's projection for 2014 is low enough that it doesn't even make sense to give him a 6th year.  The difference between the Steamer and ZIPS projections is entirely playing time: Steamer projects a 3.62 FIP in 173 innings, while ZIPS projects at 3.62 FIP in 192 innings.  Homer has thrown 200+ innings for two consecutive years, and has been very healthy in those seasons.  But just one trip to the DL would drop him into the 170-territory, and the floor in any given season is 0 innings.

To get the contract to make sense, you have to set his 2014 projection to 3.3 WAR.  That's not outrageous; Bailey was worth 3.7 fWAR last season (and 3.2 bWAR), after all.  But that was easily his best season thus far.  It's pretty hard to project that he'll do that again this season, at least based on standard player behavior.

On the other hand, what we're really dealing with here is a projected difference of 0.6 to 0.9 wins.  Given how large the error bars are on projections, this really isn't that bad.  If the Reds have special scouting information that indicates that Bailey really did take a significant step forward last year, and one that he's very likely to continue in future seasons, you could at least make an argument that this is a reasonable projection...

Approach #2

Dave Cameron recently posted a pair of new models that look at free agent salaries.

The first is a model that just takes total projected WAR in a contract and uses that to estimate a player's salary.  It's a simple regression equation, but it explains 95% of the variation in free agent salaries from the offseason.  Not too shabby!  Let's run it for Homer and our various projections:

This is a bit more encouraging.  Based on the regression equation, and our projection systems, Homer Bailey's contract estimate comes in at between $70 million and $85 million over 5 years (or six years, for that matter; he's projected to be replacement level in 2019).

I adjusted the Apparent Reds projection a bit here, because this regression model tends to result in higher estimated salaries than my first approach. Here, a projection of 3.1 WAR gets him where he should be for the contract to be an even value.  That's an 0.4 to 0.7 WAR difference from projections.

Approach #3

In that same article, Cameron also put together a salary estimation "toy."  It's very simple, not horrifically rigorous, but it works pretty well.  You can go to the article to read about it.  I applied it to Homer:

Cameron's toy suggests that, based on the Steamer and Zips projections, the market length of a salary like Homer's would be about 4 years.  But if we extend it to 6 total years, we get total estimates between $72 million and $81 million.  That's pretty close to the regression equation above.

The closest I could get his contract to the actual value was 3.2 WAR.  Push it to 3.3 WAR, and Cameron's toy extends him another year to 7 WAR, and the total contract value shoots to $115 WAR.  But again, the estimates are indicating that the +Cincinnati Reds are valuing Homer by about a half-win higher than the projection systems.


By the numbers, I think it's pretty easy to see why so many see this as an overpay.  Steamer, which has been the champion of pitcher projections the last few years, estimates his monetary value between 50% and 70% of the actual contract value, depending on which approach one takes.  That's a tough pill to swallow, especially when you consider that the salary models I'm using aren't making any allowances for the fact that pitchers are inherently more risky than hitters, aside from the projections.

That said, the other thing that this exercise impressed upon me was that the systems that I, at least, am using are highly volatile when examining long-term salaries.  For the most part, we're dealing with differences of just a half a win.  That's easily within our margin of error.  Any small difference in projection gets compounded with each year of an extension.  This is further enhanced by the fact that the cost per win changes with player quality.  As a result, a difference of less than a win in a projection can result in a $50 million difference in a contract valuation.  In Homer's case, that's half of his salary!

What do you think?  Is it reasonable to project Homer to have a 3+ WAR season in 2014?  Are these salary approaches so sensitive to small changes in player projection that they are almost useless?  Or was this a big overpay by the Reds?