How valuable was Mariano Rivera?

Yesterday, Mariano Rivera became the first player ever to be elected to the Hall of  Fame unanimously, and on his first try to boot--something that players like Babe Ruth, Ted Williams, Willie Mays, Henry Aaron, Mike Schmidt, and many others, failed to achieve.  He was elected because he was (as we shall see) a very effective pitcher, who played what many people believe to be a key role for the New York Yankees for many years, during most of which they enjoyed extraordinary success.  He certainly proved, over a long period of time, that he had Hall of Fame ability.  Yet for reasons having nothing to do with his ability, he actually contributed extraordinarily few extra wins to his team over the course of his long career.

The principle of reductio ad absurdum has solved a number of problems in mathematics, both theoretical and applied.  Essentially, it suggests that if the logical extension of a premise leads to an absurd conclusion, the premise itself is false.  For several decades now fans and writers have believed, and baseball organizations have acted as if, a pitcher who can reliably protect a lead of 1-3 runs for one inning (the ninth) plays a critical role in his team's success.  In 2016, in a typically thorough and insightful presentation at the SABR Convention in Miami, Dave Smith of retrosheet.org proved that that assumption is false.  An analysis of the career of Rivera--generally regarded as the greatest closer of all time--will confirm that conclusion in spades.

After a year as the Yankees' set-up man in 1996--a year to which we shall return--Rivera was the Yankees' closer for 16 of the next 17 years.  He was an extraordinarily effective pitcher for most of those seasons.  In Baseball Greatness, I use the measurement of Wins Above Average to measure the value of all players, and by that measure, Rivera appears to be the best relief pitcher of all time. Only once did he ever come close to the 4 Wins Above Average figure that represents a superstar season, but no other reliever has ever pitched enough to reach that figure either.  He exceeded 2 WAA in four out of five seasons from 2003 through 2008--seasons in which he pitched between 70 and 80 innings.  No other reliever--including those from earlier eras who pitched well over 100 innings a year--has been over 2 WAA that many times.  That means that if he could have pitched 220 innings, let's say, at the same rate of effectiveness, he would  have earned about 6.5 or 7 extra wins for his team, which represents an outstanding season for any of the greatest pitchers in history, such as Lefty Grove or Bob Feller or Roger Clemens.  I have no doubt that, given the chance, and if he could have stayed healthy for long enough, Mariano Rivera might have pitched his way into the Hall of Fame as a starter.  But we will never know.

Yet the New York Yankees, as it turns out, got remarkably little value, in terms of games won, out of this great pitcher.  The reason is that, as a closer, Rivera only came into the game when the Yankees already had an overwhelming chance of winning it.

I have not been able to find a thorough year-to-year record of Rivera's saves and blown saves, but an article by Jim Caple of ESPN written on the eve of his retirement has good aggregate data.  Rivera, he reports based on data from Elias, had 652 saves and 80 blown saves. That is a percentage of 89.1.   Unfortunately, I don't know how many of the blown saves resulted in  Yankee defeats.  They obviously lost all the games on the road in which Rivera actually surrendered enough runs to lose the game, and the vast majority--around 90%--of the games in which he fell behind in the top of the ninth at Yankee Stadium.  They should have won about half the games in which he allowed the other team to tie the game.  I'm going to be generous, for reasons that will become apparent, and guess that the Yankees might have won 20 games in which Rivera had blown the save.  That would mean that the Yankees won 92% of the games in which Rivera came into the game in a save situation.

How would an average pitcher have done?

Dave Smith's presentation provides some answers.  Team winning percentages in games in which the team enjoyed a 1-, 2- or 3-run lead going into the ninth inning are extraordinarily consistent from 1912 to 2015.  A 3-run lead gives a winning percentage of 97%, a two-run lead 93%, and a one-run lead,  84%.

Now the Caple article does break down Rivera's saves into 1-run, 2-run, 3-run and 4-run situations, but it doesn't do the same, alas, for his blown saves.  (Caple states, in effect, that even an entrance with a 4-run lead can result in a save, while Smith did not.  I don't know where this discrepancy came from, but I'll count 3- and 4-run leads together for the next calculation.)  I'm going to assume, generously I think, that Rivera blew 2/3 of his blown saves with a lead of just 1 run, and 1/3 with a two-run lead.  Adding that estimate into Elias's figures for successful saves, we would find Rivera entering with a one-run lead 263 times, with a two-run lead 241 times, and with a 3- or 4- run lead, 226 times.  Applying Smith's figures for success in those situations, we find that the Yankees with average 9th-inning pitching could have expected to win 664 of the of the 732 games that Rivera entered in a save situation, or 91% of them.  With  Rivera, we have estimated that they actually won 672 of them, or 92%.  That's 8 extra games in 16 full-time seasons as closer--exactly one-half a game a year.

Now as I have said, Rivera actually exceed 2 WAA a year four times as a closer--the most of any reliever--and he also exceeded 1 WAA on ten other occasions, implying that he was worth more than half a win a year to the New York Yankees.   But he wasn't, because the Yankees used him as a closer.  They used him in games in which the rest of the team--the hitter/fielders, starting pitchers, and other relievers--had already established a win probability of 91%.  There was no way that he could improve on that probability very much, given the way that he was used.  The same is true, obviously, for very other talented pitcher who is wasted as a closer.  Rivera's most valuable year for the Yankees, ironically, w 1996, when he pitched 107 2/3 innings as a set-up man and earned 3.4 WAA, more than he ever did as a closer.

There is, alas, another question that we really need to ask about Rivera and other closers.  Rivera's best seasons as a closer, when he earned more than 2 WAA in four years out of five, occurred at ages 33-38.  It certainly seems reasonable to assume that he managed to sustain that level of effectiveness at that age in part because he pitched only 70 innings a year.  What we have shown, though, is that that reduced his value to his team to a very marginal level.  Rivera was a very fine pitcher, in the very few innings that he pitched, for a very long time.  But based on the actual number of wins that he and other closers contribute to their teams, none of them should even be considered for the Hall of Fame.