Andrew Miller, David Robertson, and How Relief Pitching Is No Longer Overpaid

By: Brian Mangan

In saber circles, it has long been common knowledge that relievers, especially closers, are overpaid.  Closers pitch around 70 to 80 innings a year, but can recieve starter-level money on the market.  How can a pitcher that throws around 1/3 the innings of a starter — and so many of them in low-leverage, three-run lead situations — possibly be as valuable as a pitcher that takes the ball every fifth day and ends the year with 210 or more innings?

The truth is, a closer would generally have to be much, much more valuable on a per-inning basis to justify getting paid a lot, and for many years, the known market inefficiency was that closers were overpaid.

But here’s the thing with markets: they are cyclical.  Things that are overvalued get identified, and their value tends to drop.  Things that are undervalued get identified — like the market inefficiency of on-base percentage, explained in Moneyball — and their value rises.  Indeed, studies have shown that on-base percentage went from undervalued to properly valued, if not overvalued relative to other skills.

I say this because I’m looking at the contracts handed out to Andrew Miller and David Robertson over the last couple of days and I don’t think that they have been overpaid.

I’m not a fan of the $/WAR analysis, but I’ll do a quick one here for the sake of simplicity.  The value of a win on the free agent market, according to Fangraphs, is right around $7 million per win at the moment. I actually think it’s a little more than that at the moment.  Andrew Miller got a four year contract worth $36 million, while Dave Robertson is reported to be receiving four years and $40 million.

Andrew Miller has been nothing short of phenomenal over the last two years, posting a 2.23 ERA, 2.02 FIP, 0.989 WHIP and 14.6 K/9 over his last 93 innings pitched. He has been worth 2.7 WAR over that time period, or just less than 3 WAR per 100 innings. (Miller stats).

Fangraphs projects Miller to regress a little bit next year, to 2.40 ERA over 65 innings, worth 1.2 WAR.  I believe this to be pessimistic.  But even if it were not, valued at $7 million per win, Miller only needs to be worth 5 WAR over the life of the contract in order to justify it.  Here is just one example, starting Miller at 1.5 WAR (not even 2/3 of the WAR he totaled last year) and aging him by 0.2 WAR per season through the end of the contract:


If Miller puts up even a single season in the next four which resembles his last two years, he’s returning value even if he is close to replacement the other three years.

Robertson was not quite as dominant as Miller last year, but he has a longer track record of sustained excellent performance, posting 2.6, 1.7, 1.6, and 1.7 WAR over the last four seasons.  D-Rob has a 2.20 ERA and 1.09 WHIP along with a 12.3 K/9 over that period of time, spanning 258 innings.  He’s about as close to a sure bet as there is, without drilling down further into his performance. (Robertson stats).

Robertson was only awarded $40 million, which to me, sounds like a bargain.  He totaled 7.6 WAR over the last four seasons and is only 29 years old – he seems like a good bet to post 5 more in the next four.  And he wouldn’t be alone if he did — in fact, since 2000, 31 relievers have posted 5+ WAR in their ages 30-34 seasons.  It’s not that difficult a feat.  On that list are guys like Mariano Rivera and Billy Wagner, of course, but they are joined by Jose Valverde, Robb Nen, Matt Belisle, Akinori Otsuka, and many others.  If you lower the threshold to 4+ WAR, you get a whopping 49 pitchers since 2000 alone, including Kiko Calero, Jeremy Affeldt, Joe Beimel, and Jim Mecir.

The only other established closer close to this level of performance to get this type of money recently was Jonathan Papelbon, who so far has performed admirably for the Phillies. Papelbon got $50 million over four years back in November 2011, and has returned 4.0 WAR over that period of time. Like Robertson and Miller, Papelbon was 30 when he reached free agency and, not for nothing, although he was excellent he was actually less dominant than Robertson and Miller were in the last two years heading into his free agency (3.43 ERA, 11.2 K/9, 1.10 WHIP).

Every free agent contract is a gamble, and this is no different. There are no guarantees that Miller or Robertson will stay healthy or keep up their established levels of performance.

However, I think it is noteworthy that both men received less, three years later, despite increasing $/WAR figures, than Papelbon received three years ago.  I think the market has adjusted, and I think that elite relief pitching is now closer to where is should be. The same goes for other contracts signed over the last decade, every single one of which was a worse bet than Miller and Robertson:  Francisco Rodriguez, B.J. Ryan, Joe Nathan, and Francisco Cordero, among others, all received contracts north of $40 million, and did so more than five years ago, when $/WAR was much less.

One final note. WAR is not the be-all-end-all of player and contract analysis.  Among the advanced stats, there are WPA, RE24, and WPA/LI, figures that we use to try and better explain the game that we enjoy.  Yes, closers were overpaid in the past – but that doesn’t mean that having a shutdown reliever isn’t something that’s invaluable to a team. Any fan that has watched their team blow late leads knows that it’s deflating beyond what we see in the box scores.

Miller was 11th in baseball in RE24, and 13th in WPA/LI. Robertson was 6th in baseball in WPA. There is at least some value to having that relief ace out there … and if you don’t believe that, and think $/WAR is a fair measure for relievers, I there’s a good chance they’ll outperform that too.

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Brian Mangan is an attorney living in New York City.  He is a Mets fan and wishes that, at those prices, his team had been in on either of those guys.