The Yankees with no Mo

The following article first appeared in the 2011 Hardball Times Annual.

Mariano Rivera had pitched in 917 games through 2009. In his first two years, he was still establishing himself and his eventual role. Once John Wetteland left, Rivera was the undisputed ace of the Yankees bullpen. Let’s break down his 837 games as ace reliever, and see how the rest of the Yankees bullpen has fared in comparison during that time.

Ninth inning, ahead or behind

As we have shown in the past in The Book, a three-run lead heading into the ninth inning is a very safe lead. While an ace reliever will protect that lead 98 percent of the time, an average reliever will protect that lead 96 percent of the time. Basically, it’s tough to add value when everyone else is finding success in the same situation. So let’s see what happened with Rivera and his backups.

Rivera was brought into a game to protect a three-run lead 124 times (116 times with no outs, four times with one out, and another four times with two outs). The Yankees won 122 of those games. The rest of the Yankees bullpen, when given a three-run lead, was even better. They protected that lead every single time. When a saberist says that just about anyone can save a three-run lead, well, this is what we are talking about.

Let’s start keeping a running total:
Subtotal (three-run lead): Rivera, minus two wins.

In the ninth inning with a two-run lead, Rivera entered the game 141 times, and the Yankees won 139 of those games. Seems pretty impressive. The rest of the Yankees bullpen, however, never lost a game with a two-run lead! Subtotal (two-run lead): Rivera, minus two wins.

How about a one-run lead? The Yankees won 122 of the 138 times Rivera entered such a game. If we focus on those in which there were no men on base and no outs when Rivera entered, he went 120 for 135. The rest of the Yankees bullpen faced only 19 one-run situations in the past 13 seasons, and the Yanks came away with the win 15 times. Prorating up to 135, that comes out to 108 wins. Big edge to Mariano. Subtotal (one-run lead): Rivera, plus 12 wins.

With a four, or more, run lead in the ninth inning, Rivera was 130 for 131, a match for the rest of the bullpen. Subtotal (four-plus runs lead): Rivera, no wins.

Rivera also came into a game with the Yankees trailing in the ninth 34 times, and the team eventually won five of those games, which is a bit better than the four that the rest of the bullpen delivered. Subtotal (behind): Rivera, plus one win.

Ninth inning, tied game

Now let’s look at tied ballgames. The Yankees won 43 of the 76 tied games that Rivera entered. Of those, 61 games were in the top of the nnth at home, with the Yankees still having a chance to bat. They won 37 of those games. The rest of the Yankees bullpen won 16 of 30 similar games, which prorates to 32 wins, making Rivera plus five wins in this category.

Rivera came in to start the bottom of the ninth in tied games only eight times and the team won five of those. The rest of the Yankees bullpen won 35 percent of its games, which prorates to three wins, making Rivera plus two wins.

Rivera came in another seven times in tied games in the ninth inning under various other base/out configurations. The team won only one game. Pro-rating the rest of the Yankees bullpen onto Rivera’s opportunities, and they won four times, making Rivera minus three wins. Subtotal (tied): Rivera, plus four wins.

Overall, in the ninth inning, Rivera was 13 wins better than the rest of the Yankees bullpen.

Other innings

What about the other innings? Repeating the exercise, and controlling for the various base/out/score configurations, here’s how Rivera compares to his bullpen in total:
{exp:list_maker}Extra Innings: Rivera minus one win
Ninth Inning: Rivera plus 13 wins
Eighth Inning: Rivera plus seven wins
Seventh Inning: Rivera minus one win
Total: Rivera plus 18 wins.{/exp:list_maker}Here’s a summary graph of all situations and Rivera’s performance vs. the other Yankee relievers.

Inning Score Games Wins Win % Wins vs other Yanks relievers
7th Trailing 2
7th Tied 1 -1
7th Up By 1
7th Up By 2
7th Up By 3
7th Up By 4+ 2 2 1
8th Trailing 5
8th Tied 4 4 1 2
8th Up By 1 56 50 0.893 6
8th Up By 2 39 35 0.897
8th Up By 3 29 28 0.966
8th Up By 4+ 18 18 1 1
9th Trailing 34 5 0.147 1
9th Tied 76 43 0.566 4
9th Up By 1 138 122 0.884 12
9th Up By 2 141 139 0.986 -2
9th Up By 3 124 122 0.984 -2
9th Up By 4+ 131 130 0.992
10th+ Trailing
10th+ Tied 23 11 0.478 -1
10th+ Up By 1 9 8 0.889
10th+ Up By 2 1 1 1
10th+ Up By 3 4 4 1
10th+ Up By 4+

Summary

Mariano Rivera has been 18 wins better than the rest of his bullpen over his career. That’s fewer than two wins per year. I know it’s a shockingly low figure, but that’s what the method shows.

A measure such as Win Probability Added (WPA) gives Rivera an impact of plus 44 wins above the average pitcher from 1997-2009. However, WPA compares a player against the league average, and you can be sure that the Yankees bullpen would have been better than a typical major league bullpen, even without Rivera.

Also, the Yankees certainly would use a better pitcher in a close game than your typical major league reliever. This raises the bar against which Rivera is compared, turning the +44 wins that WPA gives him to +18 wins in the more detailed method offered here.

By the way, we are ignoring the fact that Rivera has been possibly the best pitcher ever in postseason history. That certainly counts for a great deal.

If the Yankees can keep finding arms, they should be able to weather Rivera’s loss at an impact of under two wins a season. Two wins is plenty, something that teams pay an extra $10 million for. And, that’s pretty much what’s going to happen as the Yankees might go from a $15 million dollar ace to the typical $5 million next-best reliever.

Just as it was not the end of the world when the Twins lost Joe Nathan—a team that that is currently (as I write this in late August, 2010) sixth in the majors in WPA for relievers, about 1.2 wins less than the Yankees bullpen—so too might the Yankees be able to absorb most of the loss of Mariano Rivera.

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Comments

  1. Don said...

    You fail to tell us how many times the rest of the pen faced all of those situations. That would be nice to know.

  2. Metaox said...

    Is there any screen for the quality of opposition Rivera faced, relative to the rest of the bullpen? I.e. was he left on the bench against worse hitting?

  3. Jim said...

    To many variables left out. The other members of the pen don’t get the difficult opportunities.

  4. Rich said...

    This has nothing to do with the overall point of your article, but you stated, “Once John Wetteland left, Rivera was the undisputed ace of the Yankees bullpen”.  I would argue that in 1996, Rivera was the ace of the bullpen, as he came in 3rd in the Cy Young voting as a setup man – a rare, if not unique, occurence.

  5. Tangotiger said...

    Rich:

    I didn’t ask who was the ace, but rather, who was the *undisputed* ace. 

    You can argue that Mo was the ace in 1996, but it’s still Wetteland that got the prime spot, and Wetteland was the W.S. MVP.  Neither Mo nor Wetteland was the undisputed ace in 1996.

    Jim:

    I controlled for the inning, score, base, out, which is the largest determinant of the difficulty of the opportunities.

    Metaox:

    While a legitimate question, you are really stretching if you think you will find anything remotely like that over a period of 800+ games.

    Don:

    I occasionally noted the number of opps for Rivera’s teammates, at the points I felt relevant.

  6. Dave Studeman said...

    Tango, CJ Nitkowski just started slamming this article on Twitter, but he did raise one legitimate question.  What might be the impact of losing Rivera on the rest of the bullpen?  The fact that Robertson moves up means that lesser pitchers have to take the place of all the other relievers, right?

    I know this is probably outside the scope of what you studied, but what do you think of this impact in general?

  7. Tangotiger said...

    I can’t respond to Twitter from the office (I can’t even see Twitter), so ask CJ that if he’s interested in having a discussion, he can email me:
    tom~tangotiger~net
    (Replace ~ as appropriate.)

    ***

    As for the impact of losing Rivera, and the chaining effect, that’s pretty easy to figure.

    Rivera gives up runs at half the league average, which is insanely good.  Best ever in the history of the game, something that I think only Pedro and RJ would be able to do if they were relievers.

    Anyway, he’s worth say +2.2 runs better than a run of the mill reliever, per 9IP, or +17.6 runs over 72 innings.

    The average pitcher converts 9 runs into a win, and a fully-leverage pitcher will convert 4.5 runs into a win.  Because those leverage opps are going to be there, and someone is going to take over that role, Rivera’s leverage is to convert almost 7 runs into a win (6.75 let’s say). 

    So, 17.6/6.75 = 2.6 wins.

    That’s how much Mariano is worth.  If you pay 5MM$ per win, that’s 13MM$ of value.

    And that’s pretty much how much the Yankees are paying him.

  8. Dave Studeman said...

    Thanks, but it’s unclear to me if your 6.75 runs/win figure includes the impact of the person who takes the place of the person who takes Rivera’s place.  That chained replacement will also result in lost runs and wins, right?

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