Wednesday, January 2, 2013

Happy New Year... And Hall of Fame Relievers

It's Baseball Hall of Fame season, which is typically a very active time for me on this blog.  Well, it's been a really, REALLY busy few weeks, so I haven't done as much as I'd like.  But suffice it to say that I'm disappointed that it's likely no one will get election to the Hall this year.  I mean, I'm not the kind of person who says that Jack Morris should make the Hall of Fame.  But here's the thing:  Jack Morris was better at baseball than most people are at ANYTHING, and yet people scream and shout about how he doesn't belong.  Now, if I had a ballot, I would not vote for Morris.  I don't think he's good enough to make the Hall.  But if he did, I'd be very, very happy for him and for all the Tigers fans out there who have seen so many players who are above the Hall benchmark fail to be elected.

But anyway, today, Poz posted an article that discusses the candidates he didn't vote for, but who merit more consideration.  Well, I'm happy to say that one of the sections struck a chord with me:  the section on Lee Smith.  I thought to myself, would I vote for Lee Smith?  Now, with a ballot as crowded as this year's, the answer is "no."  But, if there were unlimited slots, would I?  I don't know.  So, I devised a way to figure it out.

People (like Poz) talk about how saves are too one-dimensional a stat.  I agree.  Especially when we're comparing people to starters (as we do in HOF voting).  So how do we account for this?  I think it's actually pretty easy.

First, we look at only two statistics for the pitcher:  ERA+ and Innings Pitched.  Normally, I'm more of a fan of ERA-, but I'll use the more commonly-known baseball-reference stat (speaking of which:  all stats courtesy of that wonderful site).  And I use Batters Faced for most of the silly little things I do with pitchers, but in this case, IP is necessary.

Anyway, we first convert ERA+ to ERA-, which is easy, and necessary.  ERA+ measures how much higher the league ERA was than the pitcher's (adjusted for ballpark).  What we need to know is the inverse (in other words, how much lower was the pitcher's ERA than the league, adjusted for ballpark).  Here it is:
10000/ERA+
It's that easy.  So we then have that number.  And we'll figure out a Pythagorean winning percentage, based on an average offense.  It looks like this:
100^2/(ERA-^2+100^2)
Now, we have a winning percentage.  Let's keep that in our back pockets.

Next, we take the innings pitched, and we divide by nine.  Why?  Because, roughly every nine innings, there's a decision.  Look at individual pitchers (starters, preferably), if you want.  Divide their career innings by nine.  Usually, you'll find that they have roughly nine times as many innings pitched as decisions.  If that's not good enough proof for you, go ahead and pick a random team in history.  Divide their number of Innings Pitched by the number of Games Played.  You will usually find that the answer hovers between 8.8 and 9.2 - which is good enough for me to just call it nine.

So anyway, we now have a number of "decisions" and a "winning percentage."  Now, just multiply them together.  That gives us a number of "pitcher wins" for these players who usually don't really have those to look at!

This gives us a nice starting point, actually.  But we can go a step further, of course.  We simply take the decisions, and subtract the wins.  That gives us losses, because that's important to know, too.  Then, we use one of my favorite Bill James tools:  Fibonacci wins.  We take:
Wins*Winning%+(Wins-Losses).  This helps us account for both the raw total of winnings, and the percentage of the time the player won.

Anyway, I did this for eleven relievers, who are considered among the best of all-time.  Why eleven?  Because these are the eleven relievers who are either in the Hall of Fame, or I have heard an argument for belonging in the Hall of Fame.  Here they are, presented with their "record," as well as Fibonacci wins (and ordered by the latter).

Hoyt Wilhelm:  171.2-79.2; 209.1
Dennis Eckersley:  209.4-155.6; 173.9
Mariano Rivera:  109.7-25.8; 172.6
Goose Gossage:  123.3-77.7; 121.3
Billy Wagner:  78.0-22.3; 116.4
John Franco:  90.8-47.7; 102.6
Rollie Fingers:  111.6-77.5; 99.9
Lee Smith:  91.0-52.2; 96.6
Dan Quisenberry:  78.9-37.0; 95.6
Trevor Hoffman:  80.5-40.5; 93.6
Bruce Sutter:  75.1-40.6; 83.3

Obviously, this is overly simplistic.  It takes a lot to say that you can boil things down to one number (as much as we all try to do it).  But at the end of the day, when it comes to the Hall of Fame, there are only two options:  in or out.  That's a binary decision.  Binaries are numbers.  So you have to be able to put a number on it.  And this is a pretty good place to start, if you ask me.

As you can tell, innings pitched is skewed for Eckersley because of his years as a starter.  But so what?  He did that pitching, as well.  And when you factor it all in, he's roughly as good as Mariano, which sounds about right to me.  Wilhelm's HUGE number of innings keeps him at the top of the group, which sounds about right to me.  And frankly, I'm not sure if I could vote for anyone below Mariano - the gap seems to be in roughly the 150 Fibonacci win area.

But, back to the topic at hand, which is Lee Smith.  Fingers' induction has been much-maligned by many people.  But seeing Fingers, Wagner, and John Franco atop Lee Smith makes me fairly certain of this much:  I don't think I could vote for him.  He deserves to be remembered, so, like Jack Morris, I would never begrudge his election.  But, also like Morris, I just don't think the Hall of Fame is big enough to include not only Lee Smith, but all of the players who were better or roughly his equal.  I just don't think anyone wants a Hall of Fame with 10 relief pitchers - not yet, anyway.  Maybe in another 50 years, but not right now.  And if Smith is still one of the 10 best relievers of all-time in 50 years, then we can talk about it.  But for now, it's a no.

2 comments:

  1. Can you show the derivation of the formula converting ERA+ to ERA-? How would you go the other way? The inverse? Where does the 10000 come from?

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  2. So, in its origin, ERA+ is the formula:

    LgERA/PlayerERA

    (PlayerERA adjusted for ballpark, of course)

    ERA- realizes that there's a flaw in this, because every single player has a different denominator. When we're neutralizing stats, we want to have the same denominator, with a moving numerator. Thus, ERA- is the formula:

    PlayerERA/LgERA

    (again, with PlayerERA adjusted for ballpark)

    Then, both of them are multiplied by 100. So, what ERA+ is telling you is that if a player's ERA+ is 125, that means the league allowed 25% more runs than the player (in math, that's 125/100). But if we want to know how many fewer runs the player allowed than the league, we just need to take the inverse (which would be 100/125). But if we do 100/125, that will give us .8 - but we don't want .8, we want 80. Thus, we have to multiply by 100. So the real formula is 100*100/ERA+, or 10000/ERA. If I had just stuck with the 100, it would be obvious that I'm just taking the inverse; but that would have given us a decimal centered around 1 instead of a large integer centered around 100.

    Going the other way, we'd just do the reverse. If the player's ERA- is 80, we'd take 10000/80 - and you'd get right back to 125. It's really just taking inverses of fractions.

    That being said, there's not a DIRECT 1:1 in baseball-reference's ERA+ and Fangraphs ERA-, because they use different park factors. Take Nolan Ryan (the first pitcher I just chose randomly). ERA+ of 112, ERA- of 90. If you do the formula starting with ERA+, you'll see that it should be 89; if you try to convert ERA- into ERA+, you'll get 111. Frankly, that's close enough for me. So it's pretty much spot-on. And that difference of 1 percentage point we see with Ryan comes from different park factors from the two different sites.

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