Looking for a good bullpen investment strategy? There isn’t one

San Diego’s Craig Stammen was one of eight relievers who, after signing as free agents last year, were worth at least 1.0 WAR out of the bullpen. David Zalubowski/AP file/Associated Press

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As the Red Sox filter into spring training, the questions about their bullpen will hover prominently. Who will close? Did they do enough to reinforce their relief ranks?

In the face of those questions, it’s worth asking another: Who was the best reliever signed in the winter of 2017-18?

There were a lot of notable names and deals inked last offseason, when teams continued to invest heavily in their bullpens. Based on data from MLBTradeRumors.com’s 2017-18 free-agent tracker, a total of 42 players who were employed as relievers in 2018 signed major league contracts as free agents, with the group receiving more than $366 million in combined salary commitments.

Wade Davis’s three-year, $52 million deal with the Rockies served as the headline reliever contract. He was one of 15 relievers who received at least a $5 million average salary last year.

So who was the best of those 42 players?

It wasn’t Davis. Despite posting a National League-leading 43 saves, Davis recorded the worst ERA (4.13) of his bullpen career and a good-not-great 0.9 WAR (in Fangraphs’ calculations) while seeing his strikeout and walk rates decline and his homer rate go up.

It wasn’t Davis’s former Royals teammate, Greg Holland, who got released midway through the year by the Cardinals after signing a one-year, $14 million deal.

Of the 15 free-agent relievers who signed deals of at least $5 million per year, none was worth a single Win Above Replacement. Davis, Holland, Brandon Morrow, Jake McGee, Bryan Shaw, Tommy Hunter, Juan Nicasio, Addison Reed, Pat Neshek, Joe Smith, Anthony Swarzak, Steve Cishek, Luke Gregerson, Yusmeiro Petit, and Brandon Kintzler averaged 0.3 Wins Above Replacement.

Free agent reliever performance by contract type *Includes pitchers who signed on minor league free agent deals and who pitched at least 20 innings in the big leagues. Many pitchers who signed minor league deals did not perform in the big leagues. They are not included in this data set.

AVERAGE ANNUAL VALUE (AAV)	NUMBER	AVERAGE WAR	WIN PROBABILITY ADDED
$5M plus	15	0.3	-0.10
< $5M	27	0.4	0.31
Minor league deal*	17	0.1	-0.03

SOURCE: MLBTradeRumors.com, Fangraphs

There were eight relievers who, after signing as free agents, were worth at least 1.0 WAR out of the bullpen, but none received one of the biggest contracts.

The group was topped by Craig Stammen of the Padres (2.3 WAR, two-year, $4.5 million deal), Tony Watson of the Giants (1.8 WAR, three-year, $8.5 million deal), Hector Rondon of the Astros (1.3 WAR, two-year, $8.5 million deal), Jared Hughes of the Reds (1.2 WAR, two-year, $4.5 million deal), Seunghwan Oh (1.2 WAR, one-year, $2 million contract), Jesse Chavez (1.2 WAR, one-year, $1 million deal), and David Hernandez (1.0 WAR, two-year, $5 million deal).

For good measure, one reliever signed to a minor league deal — lefthander Oliver Perez — was also worth more WAR (1.1) than all 15 relievers who received guarantees of at least $5 million per year.

Here’s a sobering thought for teams as they invest in relievers: The correlation coefficient between the average annual values of last year’s free agent relief class and those pitchers’ WARs was 0.002 — which is to say, there was no relationship at all between the money spent on big reliever deals and the performance of those relievers.

Teams have long accepted the volatility of the bullpen species, the notion that performances don’t track well from year to year. That volatility is what makes the best of the best — recent Hall of Fame electee Mariano Rivera, as well as Craig Kimbrel, and recent megadeal signees Kenley Jansen and Aroldis Chapman — so remarkable.

Far more often, relievers endure performance collapses — or seismographic year-to-year jumps of the needle — at some point along the way, particularly once they’ve been around long enough to qualify for free agency. The disappointing returns on the high end of last year’s reliever free-agent class point to a good chance of underperformance by this year’s class. Surprises could again emerge as the best performers, delivering an impact that vastly exceeds their modest contracts.

The Red Sox are making a fascinating bet on that proposition. With spring training soon to commence, they have added just one reliever from outside the organization — righthander Colten Brewer, acquired from the Padres in a trade — to the 40-man roster. Otherwise, they have added players who showed either impressive stuff, impressive performance, or both on minor league deals, while also waiting to get a look at some of the options matriculating through the farm system.

It’s a strategy that could blow up in the Red Sox’ face — though the bullpen is an area where teams frequently rearrange pieces, and add new ones, during the season. Consider the recent history of closers in World Series clinchers (season-opening closer in parentheses):

2018: Chris Sale (Craig Kimbrel)

2017: Charlie Morton (Ken Giles)

2016: Aroldis Chapman (Hector Rondon)

2015: Wade Davis (Greg Holland)

2014: Madison Bumgarner (Sergio Romo)

2013: Koji Uehara (Joel Hanrahan)

2012: Sergio Romo (Brian Wilson)

2011: Jason Motte (Ryan Franklin)

Not since 2010, when Wilson held down the final three outs for the entire season, has a team entrusted closing duties in the World Series clincher to the same pitcher it expected to serve in that role entering the year. And only Kimbrel came anywhere near going wire-to-wire.

All of that serves as backdrop to a winter in which the Red Sox prioritized the returns of a role player (Steve Pearce) and a mid-rotation weapon (Nathan Eovaldi) while taking a passive approach to the reliever market. Their work might not be done, but if they do add anyone, it’s probably not going to be Kimbrel — or anyone else making more than a couple million dollars.

There is risk in such an approach, but recent free agent history also suggests there’s plenty of risk associated with a big-dollar signing.

Every reliever decision represents something of a roll of the dice. So there is something to be said for stockpiling (through minor league deals, and while building prospect inventory) quantity in hopes of finding the right mix of qualities. The remaining opportunities to do so with pitchers available for $1 million per season may be just as great as they are with pitchers who will receive millions, and perhaps tens of millions, more.