Relievers and the Hall of Fame

Tomorrow evening, the 2017 inductees to the Baseball Hall of Fame will be announced. Last year, Trevor Hoffman was named on just over 67% of the ballots, and stands a decent chance of attaining the 75% threshold for election. With just over half of vote public, he's just shy at 72.4%, but he outperformed last year by 7% with the voters who don't reveal their ballot or only do so after the election. A similar bump this year would put him over, and moreover his rate of being added is pacing slightly ahead of what he needs.

But even if he falls short this year, next year should be a slam dunk. And when he does give his speech, there is one person to whom he owes a major thank you: one Jerome Holtzman. Holtzman was the sportswriter who came up with the concept of the save in 1959, and helped usher in the idea of the modern one inning specialist closer. Trevor Hoffman has 601 saves, was at one point the all-time leader,  and it is that (and only that) that will get him into Cooperstown.

That's not to say Hoffman wasn't a fine pitcher. In fact, of post-WWII pitchers with at least 750 career innings, his adjusted ERA ranks 12th. That's really great, but he didn't even reach 1,100 career innings, which a healthy starting pitcher would do in five years. But consider a couple similar relievers:

Both Quisenberry and Franco pitched a similar number of innings, and neither even stayed on the ballot beyond one year. But the former was a fireman, and the latter straddled the era of the fireman and modern closer, so combined they barely surpassed Hoffman's save total.

Saves, of course, are right up there with RBI in terms of largely useless statistics for measuring player value and impact. In fact, Hoffman isn't the even the best reliever on the ballot. Billy Wagner threw about 200 less innings, but his 54 ERA- is virtually unprecedented other than Mariano Rivera, who will sail into the Hall of Fame two years from now.

In fact, setting aside adjustments for role, Baseball-Reference estimates Wagner prevented 195 runs relative to league over his career, whereas Hoffman only prevented 180. If I had to pick one, I'd definitely favour Wagner, but even then I'm not sure he did enough. After all, Brandon Webb prevented 202 runs better than average, and no one talks about him for the Hall of Fame since injuries ended his career after six seasons.

The question is then what to do with relievers when it comes to Hall of Fame standards, both in terms of intraposition equity (not just rewarding big save totals) and interpositional equity (very good to great starting pitchers are being kept out behind these guys). I don't think anyone wants Cooperstown to become a Hall of Relievers. So this is what I want to explore: what should be the standard for relievers?

Historical precedents don't help a lot here. There are currently five relievers in the Hall of Fame, and Hoffman will be six. Hoyt Wilhelm and Dennis Eckersley don't tell much, since they both exceeded 2,000 innings (on par with starters in the Hall of Fame). Rollie Fingers and Goose Gossage pioneered the fireman role in the 1970s. Neither was quite as effective at preventing runs on a rate basis, but they also had a had a higher degree of difficult with longer outings, frequently exceeding 100 innings a year. They pitched around 50% more career innings than durable modern closers will.

Finally, there's Bruce Sutter and Trevor Hoffman, both of whom got into thanks to the save. I view both as marginal at best selections, since setting aside saves there are similar pitchers who had very similar careers, and didn't receive any serious consideration.

Let's then turn to the conceptual side. At the most basic level, the job of a pitcher is to prevent runs, and the value of a pitcher is in the runs he prevents compared to his peers. A run prevented in the first inning counts the same as a run prevented in the ninth inning. It is true that modern closers on average pitch more important innings, and therefore should receive at least some credit for that higher leverage (there is a lot of dispute about how much). However, it is also the case that saving a team's best pitcher for late in close games has not materially changed the rates of leads converted into wins.

Moreover, one inning specialists also have several significant advantages. They don't have to turn a lineup over multiple times and have batters make adjustments to them. They don't need the same depth of repertoire (which is why relievers are failed starters); some only needing one excellent pitch. Almost invariably today, they start innings clean. They can air it out for one inning rather than having to pace themselves. Which is why the average reliever allows about 10% less runs than the average starter).

There's no precise formula to balance all this off in terms of an adjustment for the value of roles, but at best I'd be inclined to call it a wash. That is, a run saved by a reliever counts the same as a run saved as a starter, with no adjustment. So what exactly has the standard traditionally been for induction in terms of preventing runs?

Despite the various magic numbers (300 wins), this is actually surprisingly clean. Below is a chart showing all post-WWII starting pitchers who are in, or who were not selected (that is, excluding active players and those on or yet to appear on the ballot) according simply to adjusted ERA and innings pitched:

Basically, there's a very strong trade-off between the rate at which a pitcher suppresses runs, and career length. There are some Hall of Fame compilers, some shorter careers with brilliant peaks, and then the immortals who combine both. Save a couple of outliers, a straight line can basically be drawn separating the two, as I have done. And then we could just extend the same line for relievers, and have a very consistent standard.

This is a good practical answer, but conceptually it doesn't really work. In terms of total runs prevented, the relationship breaks down at extremes. 3,000 innings of 80 ERA- are much more valuable than 1,500 at 70 ERA-.

To adjust for this, I created a "points system" that combined innings and ERA- [(100-ERA-)*innings/100], which is basically just wins above average scaled differently. It turned out there were two important thresholds. Above 550 points, players are almost guaranteed, with 21/22 inducted (Kevin Brown really got the shaft). Below 400, there's almost no chance, with just 5/226 chosen. Between those two numbers is the borderline, with 6/18 inducted.

Below is the same chart, with two red lines representing the threshold to get 550 points (higher), and 400 points (lower). The idea is, players above 550 should be pretty easy slam dunks, below 400 are probably too marginal.

Now let's apply that these lines to relievers. Below is the same chart as above, but for players who were not mostly starters (mostly straight relievers, but some who did a little of both). Note the difference in scale, so the slope of the lines looks different, but is the same.

There's a lot here, but the big takeaway is that the standard chosen makes a big difference for pitchers under about 1,250 innings. To frame the debate, I've added some data points. First, Rivera. Despite the fairly low innings count, he was so good that he prevented runs over his career on par with slam dunk starters. And that doesn't include playoffs. I put Sandy Koufax's best years there as a comparative points, since it's his entire case and on par with modern relievers.

In my view, the black line should be a minimum for Hall of Fame induction. All the modern reliever inductees fall below, but they simply don't prevent that many runs. Johan Santana likely has no shot at the Hall of Fame because he only pitched 2,000 innings. But they were brilliant innings, on par with all but Wagner and Rivera among closers despite a much higher degree of difficulty. If he doesn't in, why should closers with half the innings?

The big question mark is Wagner. He barely clears the 400 point threshold for borderline status. Personally, I'd be inclined to go with a higher threshold (if not the 550 slam dunk level), but especially for "bigger Hall" people, he's a decent candidate.