Valuing Relievers: Correction or Bubble?

Yesterday, the Cubs acquired the final couple of months of Aroldis Chapman’s contract, adding the flamethrowing lefty to their bullpen for the stretch drive, but paying a high cost to win the bidding; shortstop Gleyber Torres is considered a top #25-#50 prospect in baseball, the kind of asset that is worth something like $40 million right now, and they had to throw in some sweeteners on top of that, including a big league pitcher was was worth +2 WAR just last year. Overall, the package of talent the Yankees received was probably worth around $50 million; that’s a staggering price for a rental.

In fact, I think it’s probably correct to say that the Cubs paid more for two months of Chapman than the Red Sox did for 2.5 years of Drew Pomeranz. And while this deal might prove to be an outlier in terms of deadline prices — the Cubs are somewhat uniquely positioned to overpay for relief help, given the strength of the rest of their roster, and how difficult it would have been for them to upgrade at another position — it also looks like a continuation of rising prices for relief pitchers.

Last winter, the Red Sox gave up a significant prospect package to acquire Craig Kimbrel from the Padres, and the Astros put together a five player combination for Ken Giles that the Phillies simply couldn’t turn down. Even the mid-tier relievers benefited, with seemingly every bullpen pitcher with a pulse landing a multi-year contract, and three year deals becoming standard for arms coming off strong seasons. With the game trending more towards shorter outings from starting pitchers and the Royals showing you can win a World Series with lousy starting pitching, teams have begun to alter their calculations on what relievers were worth.

But is this increasing emphasis on specialists an acknowledgment of the growing importance of bullpens, or simply an overreaction to the Royals winning the 2015 World Series on the backs of Wade Davis, Kelvin Herrera, and Ryan Madson?

On the one hand, the case against paying a price for a guy like Chapman is pretty easy. For example, you can do it with this one handy chart.

Even without Chapman, the Cubs were expected to win the NL Central 94 times out of 100; a seven game lead with 64 games to go is a pretty significant advantage, and the Cubs are likely an even better team than their current .602 winning percentage suggests; their BaseRuns expected winning percentage is .652, easily the best in baseball. They were a juggernaut even without Chapman, and acquiring him doesn’t really move the needle on their playoff odds that much. So, realistically, the Cubs gave up something like $50 million in assets for the right to deploy Chapman as a monster relief ace in the postseason.

And this really seems to be where the big disconnect in valuation between teams and the public lies. When we talk about the relative insignificance of a single reliever in comparison to a starting pitcher or a position player, we’re mostly talking about the quantity of innings they can throw in the regular season. But that all changes in the postseason.

I wrote about this a couple of years ago, but the percentage of innings a reliever can throw in October is dramatically different than the percentage of innings they can throw in the regular season. In that post, I noted that a typical reliever will throw about five percent of a team’s innings during the year, but that the most aggressive use of relievers pushed them towards 10% during the postseason. If we look back at last year’s Royals run, a similar pattern holds.

During the regular season, Kansas City pitchers threw 1,452 innings. Of that total, 70 innings (4.8%) were thrown by Kelvin Herrera, 67 innings (4.6%) were thrown by Wade Davis, 63 innings (4.3%) were thrown by Ryan Madson, and 51 innings (3.5%) were thrown by Luke Hochevar. Those four relievers combined to throw 17.2% of the Royals innings from April through September.

In the postseason, those percentages spiked up to 9.2% for Herrera, 7.2% for both Davis and Hochevar, and 5.6% for Madson; those four combined to throw 29.2% of the team’s postseason innings. Extrapolated to a regular season innings total, that’s the equivalent of getting about 425 innings from that quartet during the regular season. And because you can deploy your best relievers in situations where preventing runs has the largest impact on the outcome of the game, you’re looking at roughly a 1.5x leverage multiplier on the value of those innings; with leverage included, those four combined to throw the regular-season equivalent of about 640 innings during the Royals run to the World Series.

Put simply, when the calendar flips to October, the idea that relievers don’t pitch enough to be highly valuable just isn’t true. They still don’t throw as many innings as starting pitchers, but because of leverage, a team’s best few relievers are arguably just as important in October as all the non-ace starters.

So our valuation models — the ones based on regular season workloads, anyway — fall short in capturing a reliever’s impact in the postseason. And that helps explain why teams have been paying significantly more for relief pitcher WAR than they have been for any other position for a long time now. While the uptick in prices paid is more recent, MLB teams have long disagreed with the public view of reliever valuation.

And as Jeff Sullivan showed last year, having an elite reliever probably helps more in the regular season than we’ve been crediting them for, as well. It’s not like relief aces are only valuable in October; they also help you get there. That probably wasn’t a huge factor for the Cubs in the Chapman trade, but it was definitely a factor for the Red Sox and Astros in their offseason trades for Kimbrel and Giles, respectively. And it will likely be a factor for other buyers at this deadline, ones looking to upgrade their bullpens to help get to October.

So there’s plenty of evidence that suggests that relievers have been undervalued, so a price correction was probably in order. But this kind of price correction? Just because the public has been undervaluing relievers doesn’t justify any and all price increases, after all; there is a point at which a market can overcorrect. Do the Kimbrel, Giles, and this Chapman trade suggest that teams are perhaps pushing the needle too far in the other direction?

It isn’t an easy question to answer. For one, we might not have a lot of credibility on the subject, given that we’ve likely been undervaluing relievers for a long time.

By our current valuation methods, the game’s elite relievers are worth about +2 WAR in the regular season, but as Sullivan showed, teams with those kinds of elite relief performances generally win about 1.7 games more than we’d expect, so you could argue that perhaps these guys are worth closer to +4 WAR, if the team’s clutch performance was solely due to having a great reliever. Except there’s a difference between acquiring a guy who has been great in the past and guaranteeing elite performance.

As August noted this morning, relievers acquired at a premium haven’t always continued to pitch like elite relievers. Craig Kimbrel, for instance, has a -0.1 WPA for the Red Sox this year, as he’s had a few uncharacteristic meltdowns that have cost Boston some close games. Ken Giles is at -0.3 WPA, as he’s struggled with the long ball, and as such, is now the Astros seventh inning guy. David Robertson, who cost the White Sox $46 million and a first round pick to sign as a free agent before last season, has a +1.2 WPA over 1.5 seasons worth of work as the White Sox closer.

These guys were pretty safe bets as far as relievers go, but the acquiring teams haven’t gotten the kinds of performances they were expecting, at least in terms of securing leads. Because reliever performance is concentrated in such a small number of innings, predicting their performance can be really difficult, and so the valuation question has to also include the uncertainty of the future performance.

There’s uncertainty with the future performance of every player, of course, but relievers are more fickle than most. When the Red Sox traded for Drew Pomeranz, all the talk was about how risky an acquisition he was, but he’s probably no more volatile than any relief pitcher, and again, he cost less than Chapman despite coming with a couple of extra years of arbitration-controllable seasons. But then again, Pomeranz is probably less valuable to Boston in the postseason than Chapman could be to the Cubs.

Right now, Pomeranz slots in as the Red Sox third or fourth starter. If they end up in the Wild Card game, he probably doesn’t pitch. If they get to the five game ALDS, he probably makes one start, throwing somewhere between four to six innings. If they get to the seven game ALCS or World Series, he’ll either make one or two starts, depending on if they slot him or Rick Porcello in as the third or fourth starter. If he ends up as the #4, he very well might only throw 10 or 15 innings during a Red Sox World Series run, or not that many more than Chapman could be expected to throw for the Cubs if they reached the Fall Classic. And Chapman’s innings will be more important.

So, yeah, for 2016, it’s probably rational for Chapman to be valued higher than Pomeranz. But then there’s the issue of future value, and Pomeranz crushes Chapman there. Even if the Red Sox don’t plan on keeping him themselves, he could be spun off for value this winter, recouping some of the acquisition cost. Even if you think Pomeranz will lose value once teams have better options to acquire starting pitchers, it’s hard to imagine he loses enough value — barring injury, of course — to not bring back a prospect worth $20 million or so; with two cheap-ish arbitration years remaining, that would be the equivalent of the acquiring team giving him a value similar to the contract J.A. Happ signed for over the winter, for reference.

If the Red Sox spun him off for a $20 million prospect in a few months, then their acquisition cost for Pomeranz’s stretch run value would be in that $20 million range, or less than half of what the Cubs paid to have Chapman for the final few months of the season. And it’s not like the consensus was that the Red Sox got a bargain in Pomeranz. But relative to the Chapman acquisition cost, he looks like a steal.

Where does this leave us on the question of reliever valuation? Is the Chapman deal just the latest sign that the market is now correctly valuing high-end bullpen arms, or did the Cubs simply overpay because they could and felt like they had to?

Right now, I’m leaning towards the latter. The Cubs had a very specific need for an elite left-handed reliever, and the Yankees happened to control the two players who really would solve that issue for them in a season where they had a chance to win their first World Series title in 108 years. Standing pat wasn’t really an option, and so they decided they’d rather borrow from their future at a high interest rate than regret not pushing in harder on what might be their best chance to bring a championship to Chicago.

I don’t think most other teams have similar issues, though. The Giants, Indians, and Nationals have other ways of upgrading their rosters besides adding a reliever, and they don’t necessarily have to add a left-handed reliever. They can cast a wider net than the Cubs could, and weigh the pros and cons of multiple paths to upgrade their roster before the deadline.

So I think the Chapman price is going to prove to be an outlier, an overpay from a team with enough incentives to convince them to justify it this time. But I don’t think the Cubs liked paying that price for Chapman, and I doubt they’re happy about having to give up Torres and three other players for a rental.

I think relievers are worth more than we’ve given them credit for over the years, but if teams start looking at that price as the new market value of relievers, I think it would be a mistake. Relievers are valuable, especially in the postseason. But ~$50 million for a half season of a reliever? I can’t get there. The Cubs overpaid because they could and they lacked options, but teams with alternatives would be wise to spend their prospect capital other places if sellers with relievers on the market try to establish the Chapman trade as the new fair market value for bullpen upgrades.