The Futility Infielder

The big news in New York today is that the Yankees have signed Mariano Rivera to a two-year, $21-million contract extension, with a vesting option for the third year based on games finished. It's sick money to be sure, especially for a reliever who has averaged only 68 regular-season innings a year over the past seven seasons. But don't forget that those have been some pretty incredible innings -- Rivera's ERA is 86 percent better than the park-adjusted league average for his career, 2.49 vs. 4.63, and if you throw out his rookie season, when he started 10 games, it's an eye-popping 2.15, 116% better than the park-adjusted league average (in other words, an ERA+ of 216).

None of that is even counting the postseason, where Rivera has been even better: a 0.75 ERA in 96 innings to go with his 7-1 record and 30 saves. Yes, you can point to the gopher ball he yielded to Sandy Alomar in 1997 or the broken-bat bloop Luis Gonzalez eked out in 2001 as evidence that he's fallible, but there isn't a single Yankee or Yankee fan from here to Sedna who would hold those two mishaps against him or who wouldn't tell you that he's worth every single penny of that contract. The confidence that the Yanks have when Rivera is on the mound is worth its weight in golden World Series rings, and collectively, they've got a pile of them to show for the brilliant work that he's done.

Is Rivera a Hall of Famer? The New York Times article linked above, along with most talking heads, would seem to think sot. But we know that the Hall is especially stingy when it comes to relievers, with the newly-elected Dennis Eckersley just the third to go in behind Hoyt Wilhelm (a great choice) and Rollie Fingers (a mediocre one). With stalwart firemen such as Goose Gossage, Bruce Sutter, and Lee Smith stymied, it's certainly a fair question to ask whether Rivera is more deserving than these men.

Back in January, I attempted to answer the question of whether the aforementioned trio, all of whom are still on the Hall of Fame ballot, are deserving of enshrinement. As with the hitters, I used Baseball Prospectus's Wins Above Replacement Player (WARP3) to create a system which attempted to define the Hall's standards for pitchers by looking at a weighting of their career WARP3 totals, and their five-consecutive-season peak. Here are the aforementioned pitchers and Rivera, along with the stats for the average Hall starting pitcher:

           PRAA   PRAR   WARP3   PEAK   WPWT

Eckersley   277   1128   115.3   36.3   75.8

Wilhelm     269    888    91.2   30.7   61.0

Gossage     238    757    80.8   34.1   57.5

Fingers     165    692    74.2   31.1   52.7

Smith       229    664    71.9   29.8   50.9

Rivera      224    469    54.4   35.2   44.8

Sutter      148    471    50.6   28.0   39.3

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AVG HOF SP  239   1002    97.0   44.9   70.9

PRAA and PRAR are pitching runs Above Average and Above Replacement. WARP3 is the career total, PEAK is the five-season total, and WPWT is my god-awful acronym for WARP3 Weighted Total (JAffe WARP Score -- JAWS? In my weaker moments, I've thought about it). From the looks of the chart, the relievers totals for PRAA are in line with their starting brethren, but their totals for PRAR are well short. The problem, as you should be able to guess, is that even the best relievers don't have nearly the innings to measure up to the starters.

But does that mean we should ignore them entirely when it comes to the Hall? I'm uncomfortable with that conclusion. There's a body of research done by a man named Tangotiger which has shown, using play-by-play data and something called a Win Expectancy Matrix, that good relievers have a quantifiably greater effect on the outcome of a ballgame. Tangotiger's research suggests that the results of the plate appearances against relievers are magnified by some factor, which he called the Leverage Index. A starting pitcher will have a Leverage Index very near 1.0, but an ace reliever might have one approaching 2.0, meaning that the batters he faced were twice as important to the outcome of a ballgame.

Tangotiger examined the implications of multiplying the components of a reliever's stat line by his Leverage Index and then comparing him to a starting pitcher in an attempt to determine Hallworthiness. In my BP article, I suggested doing something similar but not quite as drastic, applying a Leverage Index of 1.43 to the reliever's WARP3 line (for what it's worth, the top relievers on the ballot had LI's between 1.7 and 1.9, but we don't have PBP data prior to the Retrosheet Era). That's the equivalent of drawing a baseline at 70% of a Hall of Fame starter's value -- a reasonable assumption. Keeping things in the realm of my WARP3 system, here's what the reliever's standard would look like:

           WARP3   PEAK   WPWT

AVG HOF SP  97.0   44.9   70.9

70% STD RP  67.9   31.4   49.7

Looking back at the chart above with this in mind, Rivera has the highest peak of any pitcher except Eckersley, who compiled those numbers as a starter early in his career. He's well short on career value both among those pitchers and using that 70% standard. Of course, he's not done pitching yet. In a best-case scenario, Rivera can add about 7 Wins Above Replacement per year to his total -- his high is 7.8 and his average from 1996 on is 6.6. Add 20 WARP3 to that career total over the life of his contract (assuming vesting) and he's a hair ahead of Fingers on career total and about 4 wins on peak, coming in at about 5.0 WPWT over the 70% standard.

All of this is without considering the man's postseason accomplishments, of course. Just eyeballing it, we could say that those 96 innings constitute about 1.4 seasons given Rivera's post-'95 68-inning average. If his ERA were the same, we could perhaps justify adding 6.6 (WARP3/year) * 1.4 (years) = 9.2 WARP3 to his total. But his ERA in that span is roughly 1/3 of his already-microscopic 2.15 ERA since '96. Though BP's system is something of a black box, it's not so much of one for me to know that we shouldn't just triple his WARP3 total for that span -- there's the impact of fielding to consider, among other things. So instead I'm going to feel around in the dark for an answer that seems reasonable.

Turning our attention to Eric Gagne for a moment, the Dodgers' similarly unhittable closer posted a 1.20 ERA last year in 82 innings, for a WARP3 of 8.2, a neat ratio of 0.1 WARP3 per inning pitched at that extreme level of performance. Giving Rivera the same credit would yield 9.6 WARP3 if his ERA were the same. Upping the ante by multiplying that figure by 1.6 (Gagne's 1.20 ERA divided by Rivera's 0.75 ERA) we get 15.4 WARP3 -- the equivalent of two typically brilliant Rivera seasons right there, a number that feels pretty solid given my initial estimate above. That would give Rivera a line of 69.8/35.2/52.5 -- just about even with Fingers on the weighted score, and over the 70% standard shown above.

Note that if we go back and use Rivera's post-'95 numbers to do a similar calculation we get 0.09 WARP3 per inning pitched, and a multiplication factor (ERA ratio) of 2.87 -- a calculation that would yield 24.8 WARP3, the equivalent of three Gagne '03 seasons. If we simply use all of Rivera's career in WARP3 and innings we get 0.084 WARP3/IP and an ERA ratio of 3.3, which gives us 26.8 WARP3, a number even more inflated. In terms of a reasonable answer, the truck is rolling backwards down the hill, away from the two previous estimates. I can't justify that much postseason credit, so I'm going to stick with the second estimate above, the Gagne one, as his level of performance more closely resemble's Mo's.

Of course we'd have to go back and dish out postseason points for ALL of the pitchers in the Hall based on this, a project I don't think is merited based on how quick and dirty my method is. Fingers himself has a 2.35 ERA in 57.1 postseason innings including three World Championships, Eckersley a 3.00 ERA in 36 innings, Gossage 2.87 in 31.1, Sutter a 3.00 in 12 innings, Smith an 8.44 in 5.1 innings, and Wilhelm 2.1 scoreless frames. Choosing Rivera's closest competitor, if I apply Fingers' career rate of WARP3/IP and then multiply it by his ERA ratio, I get about 3.1 WARP3, a number which is probably way too low since I'm not tossing out his inferior innings split between starting and relieving the way I did for Rivera in my initial calculations.

Suffice it to say, however, that the run impact of Mo's postseason work is probably already enough to put him in the Hall of Fame picture, and with a couple more seasons of good pitching he's going to look even better -- even without considering the "intangible" value of the jewelry which has helped borderline candidates into the Hall. For all of that, Rivera is 34 and has been vulnerable to injuries the past couple years, making four trips to the DL in that time. Three more seasons at this level of excellence is anything but a given. But if the Yanks continue to baby him during the regular season in order both to protect their considerable investment and to make sure he's ready for the fall, Rivera may well reach the numbers I've set out above and find his place in Cooperstown. It would be only fitting if Gossage -- the best non-Hall of Fame reliever there is -- were there as well, but that's a story for another day.