Trevor Hoffman, Hall of Famer?

Congratulations to Trevor Hoffman.  A few weeks ago, Trevor notched his 500th career save, which makes him a virtual lock for the Hall of Fame.  And as my father would say at this juncture, I think that’s nice.  Really.
I don’t want to come off as saying that Trevor Hoffman is a bad pitcher.  In fact, I think he’s a rather good pitcher, and if I were a Major League manager, I’d love to hear “Hells Bells” playing and knowing that he was taking the mound for my team.  It’s just that I’m not sold on closers going into the Hall of Fame based only on how many saves they’ve racked up.  (I’m also not a believer in magic numbers for HOF admission, such as 3000 hits, 500 HR, etc.  For more information, please see McGriff, Frederick Stanley.)  If you’d like to make the case that Hoffman strikes a lot of batters out, keeps runners off base, doesn’t give up homeruns in key situations, has good control, or signed a lot of autographs for kids before batting practice and you want to put in him in The Hall for that, I’m listening.  Just understand that I’m not all that impressed with large numbers of saves. 
Those who follow Sabermetrics (or are even casual fans of the game) have probably heard the arguments on why saves aren’t a reliable indicator of a relief pitcher’s skill set.  Sure, a save means that the pitcher did something right that day.  He pitched, recorded the last out of the game, didn’t blow the lead, and his team won.  And in fact, he might have performed stunning feats of pitching heroism and actually deserve a gold star next to his name.  He may have pitched a very tense ninth and guarded a one-run lead against the middle of the best-hitting lineup in the league.  But, then again, he might have gotten a cheap save, coming in to guard a 3-run lead against some league patsies.  Just about any serviceable Major League pitcher can guard a three-run ninth inning lead almost as well as the established “closers” out there.  The save rule doesn’t discriminate.
Like it or not (and I am decidedly on the side of “not”) there is a small cadre of pitchers who make $6-8 million a year because they have attained the magical tag of “closer.”  Compare this to their brothers who make about a quarter of that, based on the fact that they are “only” middle relievers.  How did they attain this coveted status?  Why they racked up a bunch of saves in a season.  How does one rack up saves?  Well, nowadays, by pitching the ninth inning (or in the event of an extra innings game, the last inning), whether that was actually the most critical juncture in the game or not.
It’s easy to see why people might believe that the ninth inning is the most important point in a game.  It seems a little strange to suggest otherwise.  After all, the ninth inning is the last inning.  It’s all over afterwards.  However, it’s not always the case that games are most decided by what happens in the ninth inning.  In a blowout, where the score is 16-1 and the utility infielder is living out his lifelong dream of pitching garbage time mop up relief (likely pitching to his fellow utility infielder!) what happens in the ninth inning does nothing to decide the game.  But what about the following situation?  Runners on first and third with one out in the bottom of the seventh, with your team up by a run.  You would scratch your head if the manager brought in your team’s “closer” here, because it’s not the ninth inning, but perhaps this would be a good time to do so.  Consider, your team’s chances of winning are hanging in the balance here.  A strike out or a double play would be fantastic right about now.  A home run puts you two down.  Even a base hit ties the game.  A lot depends on this at bat.  You want your best in the game right here, not your fourth best.  But, the fourth best is usually what you get, because it’s not yet a “save situation.”
How important is this situation compared to any other situation?  Well, we have a statistic called the leverage index that tells us exactly that.  The intricacies of leverage have been discussed elsewhere, but the only important thing to understand is that it’s a mathematical way of determining exactly how important any point in a given game is.  So, when does the most important at-bat (the highest leverage point) in a game occur most often?  In what inning does it usually happen?  Well, at least using data from 2000-2006, the answer may surprise you.  Take a guess.
If you said the 8th inning, you’re right, at least technically (more on this in a minute).
Inning    % of games in which highest leverage point occurred
1st          6.7%
2nd        9.0%
3rd        10.8%
4th        8.6%
5th        9.2%
6th        8.6%
7th        12.8%
8th        15.8%
9th       14.9%
extra    3.6%
I think it’s a good idea to combine the 9th inning with extra innings for this discussion because they are the “last” innings, so perhaps there is some merit to the idea that baseball games are won and lost most often in these innings (added together, the 9th and later innings account for 18.5% of all highest leverage points), but I’m betting that few fans think much about the 8th inning and how important it is.
Now, the preceding table represents all games, including blowouts where saves are generally not awarded.  (There is the odd game here and there where a reliever will go the last 3 innings to mop up in a 9-2 winning effort and be awarded a save for his effort.)  Since our discussion concerns saves, let’s restrict ourselves to games in which a save was awarded.  Highest leverage points by inning in those games where a save is awarded:
Inning    %
1-6        37.7%
7            16.6%
8            23.4%
9+         22.3%
Oh really?  In less than a quarter of the games where a save was awarded did the highest leverage situation occur in the 9th inning, and the critical inning the plurality of the time was the eighth inning not the ninth.  Given that closers generally only pitch the ninth inning, this means that it’s likely that they weren’t the ones on the mound when the big moment came.  I re-ran the numbers to account for all games in which the final score was within 3 runs, figuring that there might have been a save situation in the bottom of ninth, but whoever was in there blew it, thus there would be no save awarded.  The numbers did change a bit from above, turning into 32.0%, 15.7%, 23.1%, and 29.2%.  So, the ninth inning contains the most critical situation in close games about 3 out of 10 times, but the eighth inning is still checking in at 23%. 
Finally, I looked at what percentage of the time that the gentleman who was awarded the save was actually the one on the mound at the point of highest leverage in the game (where his team was in the field).  The answer: 26.7% of the time.  In only 26.7% of games where a save is awarded does the “savior” actually handle the biggest at-bat that his team faces in the game.  Padres fans, in case you were wondering, In games Trevor Hoffman saved from 2000-2006 (covering 254 of his saves), he was on the mound 25.6% of the time at the point of highest leverage.
Does anyone else want to make the case that closers are overpaid?  They generally make their millions based on how many saves they rack up, yet it seems that most of the time, they’re not the ones who actually save the game.  They were simply cunning enough to get their managers to let them into the game last and took advantage of what was probably a pretty good bullpen in front of them.  A bullpen that already did the dirty work.
A few objections come to my mind.  One is that lately, teams have been designating one pitcher as an eighth inning guy in addition to designating someone as a closer.  He’s generally not quite as good as the closer, and he might “make” some high leverage situations for himself by putting a few runners on in a close game (runners usually increase leverage).  So, it might be a mark of distinction that the closer is so good that he didn’t make a mess for himself.  Another is that I could, I suppose, take a look at things from the standpoint of win probability and check to see which relief pitcher added the most win probability to the team’s chances during his tenure on the mound.  I might do that as a follow up.
Update: I ran the win probability numbers.  Percentage of games in which a save was recorded that the gentleman recording the save was the same gentleman who added the most in terms of win probability to his team (using the assumption that everything that happens while the pitcher is on the mound is his credit/fault): 20.5%.

16 Responses to Trevor Hoffman, Hall of Famer?

  1. I’ve always thought personally that the 8th inning is far more important for building back momentum (for a team that is currently losing) or for putting the game away (for a team that is currently winning). Of course, you occasionally get the 9th-inning rally but it just seems that more things happen in the 8th.

  2. tangotiger says:

    20.5%: can you limit that to relievers?

  3. Pizza Cutter says:

    Tango, already did. That 20.5% figure is only among those who appeared in relief for the game. I double checked it and it’s accurate.

  4. Fred Zierau says:

    I really don’t understand what the numbers mean. Just because “momentum” is up 1% in the 8th inning than the 9th inning, doesn’t mean that every game played will have the same scenario.
    The thing is we have modern day closers, and the saves are more of a modern statistics as opposed to the closers of old (ie Gossage). In another 10-20 years, the “modern” closers’ “HOF-Save-plataeu” will be revealed a little more clearly (as in 3,000 hits, 500 HRs). 500 Saves is impressive in the sense that closers seem to come and go nowadays. Many teams are having problems finding consistant closers.
    While yes, I understand your point of view on the subject, I feel this is just one of those things in baseball that people are going to wind up having to adjust to.
    I think the idea that “HOLDS” are now an official stat are kind of silly. Especially since when a HOLD is blown, a pitcher receives a BS, not a Blown Hold on their record. If a setup man becomes a closer, his career statistics are going to be flawed.

  5. UCLA John says:

    I agree, and I’m a huge Padre and Trevor fan. But you really can’t argue with it anymore. The selection committee knew the controversy would start when they finally decided to induct Bruce Sutter, which opened the door for Rollie Fingers, and gave hope to Goose Gossage, Lee Smith, Dave Righetti, and Mariano Rivera, among others. Don Sutton, a good starting pitcher, is in based on wins, which itself was based in large part on his longevity. The selection committee is of course anxious about setting precedents and thus opening the excusive door too wide too quickly. But even though the Bruce Sutter induction pretty much ensures that Trevor Hoffman and the others mentioned above will get in, I still think it’s a stretch.

  6. Guy says:

    PC: That 20.5% figure is very surprising. But does it include relievers on both teams in that game? It’s hard to imagine that in 80% of save games, another reliever on the same team had more WPA than the closer. Among the current top 50 WPA pitchers, 16 are closers, and many others recorded some of their WPA in games they saved. Where is all this other WPA going? There is more WPA going to non-closers than I might have guessed, but still I find the 20.5% figure very surprising.

  7. Pizza Cutter says:

    Guy, it surprised the heck out of me too. To answer your question, I only looked at one team at a time. So, each team in a game had a reliever (assuming that they used one) who got a “most WPA added” award (or at least a least WPA subtracted!) So, the “savior” is only competing against players on his own team.
    Also, looking through the top 50 in WPA (I assume we’re looking at the same fangraphs chart), shows a bunch of guys who have 0 or 1 game started, but who are also not their team’s primary closer. (Some are guys who have been setup guys but became closers, e.g. Alan Embree). In the top 15 or so, I see R. Soriano, Betancourt, and Okajima.
    A few thoughts occur to me on why this might be happening: Closers are generally more consistent than their middle relieving brethren (hence, I believe why they got the ninth inning gig). “Saviors” added an average of .077 wins during their time on the mound with a SD of .068. All other relivers added an average of -.008 wins (so they basically broke even), but with an SD of .151 wins. Since starters now usually go 6 innings, the closer generally gets a chance at a save when the guys in front of him (pitching in some high leverage 7th and 8th inning situations) do their job (i.e. preserve the lead, hopefully involving some positive WPA). So, it’s not surprising that the guys who had those assignments rack up some good WPA points in front of the closer.
    Closers generally do positive things consistently, so they build up the WPA, while the middle relievers are less reliable, so while one game, they build up the WPA, the next game, they give it all back. It’s a theory.

  8. Guy says:

    I don’t see how this adds up. In a typical save game, you’re saying the closer gets .077. Reliever #2 beats him (80% of the time), so let’s call that .09. Yet all non-closers average -.008. So that means all other relievers in the game — if there are any — have to be terrible on average (about -.1), and this is in games their team won. I guess it’s possible, but seems unlikely.

  9. Pizza Cutter says:

    Ah, a small mistake in my methodology from my previous comment. -.008 is the average for all relievers for both teams, except the guy who recorded the save. That would be why they all break even. I restricted it just to relievers from the winning team (i.e., the team that got the save). The closer numbers are the same, but the average reliever on the winning team in a game where a save was recorded, but he did not record that save added .047 wins on average, but with a standard deviation of .132. So, we’d need to know how many scores in that distrbution fall above .077. In that distribution, .077 has a z-score of +.22. That means of all the relievers WPA scores, 42% of scores will fall above .077 on a pitcher-by-pitcher basis. If a team uses two relievers to get to the closer, odds are roughly 66% that one of them will outscore the closer. If they use more than two, those odds go up.

  10. Guy says:

    Just for fun, I checked Hoffman’s 19 save games this season. He had the highest WPA in 9 of them, or 47%. Lower than I would have guessed, but also 3 SDs above .20 even w/ such a small sample. And Izzy is around 38%.

  11. Guy says:

    Actually, you need to compare the two distributions — all closers are not .077 in every game. Also, the more relievers in a given game the fewer IP for each, and so lower WPA on average. I’m not sure how this all nets out, but .40 looks a lot more realistic than .20.
    Still a surprising result, I think. The main contributors, in addition to your observation that 8th inning LI is often quite high, look to be:
    1) 3-run saves are really very low LI;
    2) 1- and 2-out saves don’t generate much WPA, even if LI reasonably high;
    3) another reliever often goes 2 IP, a big edge even if his LI is a bit lower.

  12. Pizza Cutter says:

    Another interesting piece of information that might help to explain a few things. I looked at the skew of the distributions for saviors and non-saviors on the winning teams. Those distributions are skewed in opposite directions. The non-saviors have a distribution that is negatively skewed (skew stat = -854… not bad, but still negative), meaning that the mean is probably brought down by a few extremely negative cases (poor outings with a large negative WPA). The closers’ distribution is positively skewed (1.907), meaning that their mean is influenced in an upward direction by a few very impressive (that is, high WPA) saves. In reality, there are more saves on the “cheaper” side of the graph than there are on the good side of the graph.
    It means that there are a lot of cheaper saves, which would be easy to overtake by a middle reliever, esp one that pitches 2 innings or in a much more crucial 8th inning situation as Guy suggests.

  13. dan says:

    didnt feel like reading all the comments, so someone might have said this already….
    the win expectancy numbers have to be skewed so that there are fewer “swings of fate” in the 9th inning, because the best pitcher pitches that inning, preserving the win. if the best pitcher pitched the 8th inning for the last 30 years, then the win expectancy numbers would be different for everyone. someone who is smarter than I am can extrapolate on that thought, im not in the mood to think right now

  14. Pizza Cutter says:

    Dan, what you’re describing is something that I alluded in the last paragraph of the original post, before the update. The guy who pitches the eighth inning might make a higher leverage situation for himself by not being as good as the closer and allowing for some runners. He might also give up the lead a few more times, which as you point out would, over repeated instances, affect both the calculations of win expectancy and leverage.
    A fascinating idea! Our very conceptualization of win expectancy (and everything following from it) as derived empirically is itself the product of the very usage pattern which I am studying. It would be interesting to see whether more leads are surrendered in the eighth or ninth inning (an empirical question). The closer is probably a better pitcher, but he is also more likely to face a pinch hitter or two, so there might be something that balances it out. There are also guys who pitch the eighth inning on some teams that would close on others, and vice versa. But, either way, there’s quite a bit of merit to what you say. I have a six hour drive ahead of me tomorrow. Perhaps I will spend some of it thinking. (Perhaps I should spend some of it talking to my wife… nah…)

  15. Pizza Cutter says:

    I did do some thinking on the subject. Tango has advocated the use of context neutral wins (WPA/LI) added as a way to calculate clutch. When I get back to my laptop, I’ll take a look to see which relievers are adding the most context neutral wins.

  16. Pizza Cutter says:

    I used total context neutral wins (WPA/LI on an AB-by-AB basis) in a game, in games where a save was recorded. This eliminates some of the bias that Dan brought up in #13, by telling what the change in win probability would have been (roughly) if this were an “average” event in the game. How often was it the case that the man who recorded the save was also the man who recorded the most context-neutral WPA for the game? 22.3%.

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