Are these large reliever contracts worth it? It's complicated

Mark Melancon and Aroldis Chapman are among the late-inning relievers to strike gold this offseason Getty Images

In the past two playoffs, the Kansas City Royals, New York Mets, Cleveland Indians and Chicago Cubs relied on elite late-inning relievers to help take them to the World Series. As a byproduct of that and several other factors, MLB teams are breaking the bank to acquire similar players.

History suggests, however, that doing so might lead to bad things for those teams. Sometimes these mega deals work out, but sometimes they backfire significantly. Below are a few examples of long deals given to free-agent closers and how they worked out. We'll look at these deals mostly through a traditional lens of valuation while also considering win probability added (WPA).

B.J. Ryan - 5 years/$47 million with Blue Jays in 2005

Value during deal: 4.4 WPA, 3.7 WAR

Ryan’s contract might be the gold standard in examples of why teams should avoid spending big over many years for a top reliever. He didn’t even finish his five-year contract with Toronto.

In his two years before free agency, Ryan had a 2.35 ERA over 157 1/3 innings. And in his first season with the Blue Jays, he had a 1.37 ERA over 72 1/3 innings while posting 3.5 WAR (his single-season high). Over the rest of the contract, however, he had a 4.34 ERA in 83 total innings.

Billy Wagner - 4 years/$43 million with Mets in 2005

Value during deal: 5.6 WPA, 5.3 WAR

Wagner performed well for the Mets for two years and four months, helping them to a National League East title in his first season with 40 saves in 45 chances with the team and 34 saves in 39 chances in the Mets’ near-miss in 2007.

He was solid in 2008, but he tore his ulnar collateral ligament in August, necessitating Tommy John surgery that sidelined him the rest of the season (they finished one game out of the wild card, losing on the season’s final day) and almost all of 2009. The Mets then made a deal with the Red Sox, netting back 2 minor leaguers. Wagner pitched 17 games with the Mets and Red Sox but did not have a save in the final year of his contract.

Jonathan Papelbon - 4 years/$50 million (plus 2016 option) with Phillies in 2011

Value during deal: 7.4 WPA, 7.4 WAR

When considering Papelbon’s performance strictly on the field, it’s hard to deny he was a successful signing for the Phillies, even though he never pitched a postseason inning with the club. The question is how successful he was when you consider that he signed the largest free-agent contract for a reliever at the time of his deal.

Among relievers to pitch at least 150 innings from 2012-2016, the time Papelbon was pitching on his free agent contract, he ranked 18th in ERA+ (150) and strikeout-to-walk ratio (4.3).

David Robertson - 4 years/$46 million with White Sox in 2014

Value during deal: 1.6 WPA, 1.7 WAR

Robertson left the Yankees after a 39-save season in 2014 (the Yankees’ first post-Mariano Rivera season). In two seasons with the White Sox, he has 71 saves (34 and 37), but he’s also blown 14 (one shy of the MLB high of 15 by Santiago Casilla). Robertson’s numbers declined in 2016, particularly with regard to strikeouts and walks. He’s reportedly on the trade block as the White Sox are in the midst of a full-scale rebuild.

Francisco Cordero - 4 years/$46 million with Reds in 2007

Value during deal: 4.9 WPA, 5.1 WAR

Cordero had only one truly elite season with the Reds: 2009, when he had a 195 ERA+ and was selected to his third All-Star team. Still, he was among the more reliable relievers in the major leagues over the life of his contract, ranking 12th in ERA+ (141) among relievers to pitch at least 250 innings in that span.

Is there a chance these deals make sense?

Using WAR and other context-independent metrics for closers might not be an ideal approach to determining their value. The nature of a closer is that they will be used most frequently in high-leverage situations where the context around their appearance places increased importance on their role. Even though the highest-leverage situations aren’t always the ninth inning, that inning often has context that leads to larger changes in win probability with each result.

It might make sense to look at win probability added (WPA) before concluding that the best high-leverage relievers are being overpaid. Included is a table of notable high-leverage relievers in the market this offseason and how their WPA compares to their WAR.

In every case, WPA suggests the relievers provided more value than WAR did. The primary reason for the difference is that WPA is measuring how much an individual’s contributions (both positive and negative) affected a team’s chance to win, whereas WAR is measuring the situation-independent value of those contributions.

More simply put, WPA suggests closers and their contributions are more valuable than perceived without context because they are consistently asked to pitch in high-leverage situations. Since it is expected that these individuals will continue in those roles, it makes sense that their efforts could be more valuable than their WAR suggests.

But teams should be wary. More high-leverage situations also mean more opportunities for those relievers to hurt their team’s chances of winning. WPA also does not address the volatility of relievers like B.J. Ryan or their potential for significant injury as seen in the previously mentioned case of Billy Wagner.

For a while, these relievers might be worth the assets used to acquire them, but history says things might turn sour quickly.