Greatness - How do we calculate it?
What is the greatest seasonal pitching performance ever? Bob Gibson in 1968? Pedro in 1999? Gooden in 1985? Koufax in 1966?
How do we determine it? I have been thinking about this for nigh a decade and haven’t really gotten around to solving the question. Many of you reading this will say “Who cares?” or “Which pitcher had the most runs above replacement?” Or something.
I’m not looking for “most value”, I am looking for “Greatness”. Not very clear, I know. That’s why I have been stuck on this question for a decade.
I took a diversity training class at work last week. I know, big groan. However, this training was about “Inclusion.” It’s great to have a diverse population, but if you really aren’t using the varied people, does it really matter? That’s what Inclusion is all about. So, here at BTF we have the best sabermetric minds around: math, stats, theory, creativity. I want to take what I think and see if we can expand it into something.
What is Greatness?
Greatness to me is the performance that pushes the boundaries of human capabilities. It’s 73 home runs. It’s hitting 0.424. It’s striking out 383 hitters. It’s 257 262 hits. These are accomplishments that are the very boundaries of what players can do on the field. These are the “great” seasons.
I know they aren’t the “most valuable” seasons, but they are very valuable seasons, and these great events stand out in time - for you and me and every person that follows baseball. What do we call teh unreachable boundaries of data? Asymptotes. So I want to shove us off the sand in a search for the proper definition and quantification of Greatness. I’ll be Jason; you guys be the Argonauts as we sail in search of the Asymptotes of Greatness (AOG).
Note: I know I am using hte word loosely - go with me here.
Where to begin?
For starters, I want to look at ERA. Why? Because over at The Hall of Merit, there is a lengthy discussion of Sandy Koufax. It’s 1972 there, and you should see the outfit John Murphy is wearing. At any rate, Koufax is up for election, and there is the natural concern that he will get more votes than he is warranted on his legacy of “Greatness”. He is legendary, and is commonly, right or wrong, referred to as the greatest left-handed pitcher of all time. He threw four no-hitters, including a perfect game, and was elected to the Hall of Fame even though he retired at the age of 30, with barely enough seasons to even qualify for election. Koufax epitomizes the idea of Great, as opposed to “Valuable” because he really only had six years (or so) of being a good pitcher. Okay, some of those seasons were undoubtedly Great, but how Great? And compared to what?
What’s Next?
For ERA, the perfect season would be an ERA of 0.00, in a bunch of innings, of course. But is that do-able? History says no. At the risk of offending the Deadball Scholars, I am going to work primarily with live ball seasons. At the risk of offending others, I am moving directly to post-War baseball. Why? Live ball is important. Good gloves are important. Integration is important. That could mean I should start with about 1955, but 1947 is as good as anything, and it is a well-known line in the sand. I doubt moving to 1951 is going to change things much.
Now I will offend the statheads with a blatant slap: I am not willing to adjust for the leagues. I might consider a park adjustment, but league adjustments are right out. I am not here to debate relativity with you nor Einstein. I am not interested in “relative to one’s peers” for the AOG. I want pushing the bounds of what can happen on a baseball field. If that sours it too much for you, I am sorry, but this is not about value directly, it is about Greatness.
Doing the Work
Using the fantastic Lahman database (the 2004 version), I sorted the pitchers and pulled the seasons from 1947-2004 of 150 IP or greater. There were some 4500 of them. Then I sorted by lowest ERA. Oh, by the way, the cumulative ERA over that period is 3.65. I then plotted the seasons and drew a trend line. Well, when you plot all the seasons, you get some polynomial “s” curve, so I plotted only the first 3000 points, up to an ERA of 4.00. This gave me a nice curve with an equation of y = 0.4626Ln(x) + 0.0328. That line is the basic equivalent to a 300 IP season and allowing just 1 ER. That’s approaching zero in my book.
So, I have the equation that I can use. Yes, I could push it a little lower, but round numbers are fun (4.00 ERA, 300 datapoints, 1 ER in 300 IP - you get the idea).
Maybe this isn’t the best approach. I think the basic idea makes sense to me, and I am pretty sure this will work for all stats, but generating the Magnitude of Greatness (MOG) is tricky.
Where do You come in?
Right here. Now what do I do? Annnnnnnnnnnnnnnnd, go!
Chris Dial
Posted: March 19, 2006 at 10:09 PM |
122 comment(s)
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*K/9: about 10.8. Has been surpassed 21 times (all since 1994 except a few N. Ryan seasons).
* HR: 61. Nope.
* Wins: 31. Certainly too high for 5-man rotation--no one will ever be "great" again
From post 6:
"I am also operating with complete knowledge that we may have to pucsh out the boundary once it is met.
A year ago, I would have set the hits AOG at 255. Now it has to be set at 263 (ooh, one more than demonstrated)."
Chris finds that interesting. Some of us, not so much. To each his own....
I understand that.
From the original writing:
"I am not interested in “relative to one’s peers” for the AOG. I want pushing the bounds of what can happen on a baseball field. If that sours it too much for you, I am sorry, but this is not about value directly, it is about Greatness."
I understand, Guy. I also understand there are only "practical" limits. We don't know what they are, so we are going to have to make some assumptions.
Yes, HRs may move. Will they get higher? Maybe. But for now, I think we can draw the line at 75.
But how does "the math" say that? Gibson's hardly the only pitcher to have an ERA like that. Dutch Leonard, 3F Brown, Christy Matthewson, Walter Johnson… they all managed it. By excluding them, you're conceding the point that context matters. But then you try to deny it.
What I can't figure out, Chris, is why you deny that what you're looking for is "here's what a great pitcher can do under near-optimal conditions for pitching." In post 31 you deny it -- but in every one of your other posts, you implicitly endorse it.
why you deny that what you're looking for is "here's what a great pitcher can do under near-optimal conditions for pitching." In post 31 you deny it -- but in every one of your other posts, you implicitly endorse it.
I deny it because it isn't true - and it isn't anywhere near true. Because that's a silly notion. Is 2006 "near-optimal conditions for pitching"? Do you think my opinion would change of the AOG if Pedro threw a 1.10 ERA this year?
Why or why not?
Was 1968 NL Busch Stadium the best conditions? I'd say no. he wasn't in Dodger Stadium. No one else was within half a run. Where were all the Dodgers? The second best guy in 1968 has been beaten twice since, and once in this high scoring era.
I am also much more interested in the guys behind Gibson, because Gibson really shook it down.
OK, but this raises two issues you need to deal with:
1) is greatness additive? When you raise the bar, do previous great performances remain great as well, or become "ungreat"?
2) Will you push back the boundary as well as move it forward? This isn't track and field, where peak performances only get better. Or are you OK with the idea that there will never again be a great Wins performance by a starting pitcher (for example)?
It doesn't matter which park ... but it does matter which year. 1968 produces a lot of great years. 1964-1972 produces most of the great years. 1936 produced a lot of great years for doubles and that era produced a lot of great years. 1998-2001 produced a lot of great seasons for HR.
You say we can't explain these, but to a large extent we can. The 60s were a pitcher's era -- the mound was higher, the strike zone was big, the Astrodome came around. The late 90s were a HR era -- smaller parks, Coors field, weight training and of course possibly significant impact of PEDs.
These are certainly more satisfying "explanations" than that, somehow, for some completely unknown reason, the great doubles seasons, the great pitching seasons and the great HR seasons all happened at the same time. I see absolutely no way in which you can argue that this clustering supports your argument. This clustering screams "dude, your measure of greatness is context-dependent."
And c'mon, no matter how much you want to ignore context, you can't include the war years. You talk about equipment changes ... well, the basic equipment (i.e. talent) was vastly inferior during those years.
Anyway, that clustering _might_ be context dependent. Such events often don't follow a normal distribution but rather something closer to a power law, which has a thicker tail. For reasons I certainly don't understand, these outlying performances apparently do happen in clusters. Some research I was exposed to recently noted that massive power failures (think that huge blackout) happen more often than you'd expect under a normal distribution ... and there happened to be a number of massive blackouts around the world in a couple year period. There is a literature on this ... and there was an article posted here a few months ago in which someone applied these distributions to the HR record and concluded (I'm not sure correctly) that the late 90s HR surge was fit just fine under this distribution. So I'm not gonna say you're wrong ... I'm just gonna say that I think that "context" impacts the mean and variance of the distribution of baseball stats which will impact the likelihood of specific outlying point values occurring and I need to see proof otherwise.
Beyond that, you do still have the probably minor problem that you're looking at season. Who's to say the lowest ERA for a season's worth of pitching is 1.13? Let's start with a crude example. You bring up Eck .61 in 1990 (73 IP). For June/July 1968 (108 IP), Gibson threw 108 IP with a .50 ERA, which blows Eck away. That was also his RA for those months while Eck's RA was nearly double his ERA.
Now back to Gibson. Take out his April and you get 272.2 IP with a 1.02 ERA. So why isn't that our lower bound? Take out April and May and you get 216 IP with a .96 ERA -- that would seem to be the "asymptote" for today's game (if you believe context doesn't matteer). His Sept 67 was an ERA of .96 ... if we add that to 1968 we get a slightly lower ERA ... or replace Sept 68 with Sept 67 and we get a "full season" with a slightly lower ERA. Anyway, I think Gibson puts your asymptote at 1.
From August 1993 through August 1994, Maddux threw 294.1 IP with an ERA of 1.53 -- I think that's an MOG of 209.8 and second place on your post-47 list.
In Sept 1984, Gooden threw 42 IP with a 1.29 ERA. In April 1986, he threw 43 IP with a 1.26 ERA. That pushes him up to 361.2 IP and an ERA of 1.47. I believe that's an MOG of 269 which is pretty close to Gibson.
Maybe what you want (ideally at least) is something like the lowest ERA ever pitched over any 50/100/150/200/250/300 consecutive innings pitched.
Yes, they become "less great". I think this is obviously true in regular evalutaions as well. Cal Ripken's offense for a SS was unreal, and so was Larkin's. Then we got Jeter, Nomar and ARod. Pie Traynor and all that. Okay, SHs didn't think Pie was ever that great, but the GREAT 3B are *all* post Mathews. And we don't even put those other guys in the conversation *even though some claim context is everything*. It simply isn't. The game itself hasn't changed that much (since 1920).
2) Will you push back the boundary as well as move it forward? This isn't track and field, where peak performances only get better. Or are you OK with the idea that there will never again be a great Wins performance by a starting pitcher (for example)?
No. Bob Welch got 27 wins in 1990 - in 238 IP. That's pretty close. As discussed, we may set the boundary for ERA *higher* than Gibson's - why? RA+.
Besides, sooner or later, someone else is going to win 31. Yes, they are, *AND THEY CAN DO IT IN 2006*.
Every offseason we talk about going to a 4-man (or at least pushing starts back towards 40). Somebody is going to do that. Or someone is just going to win all their starts. It happens.
In fact, one of my issues with this era cliam is that you use wins as an example, when right there is Bob Welch with 27 Ws in 238 IP.
In teh last 8 seasons, we have seen two teams set all time high seasons for wins (98 NYY, 01 M's). You mean to say in a season like that - a pitcher can't win 31? Hogwash.
We are in an era of extremes. Not one simply defined by "high RS".
Yes, that does matter - some. But even in these seasons where the odds of a boundless performance occur, we still see very few performances like that.
Why only Gibson? Yes, the conditions were enhanced for a great pitching season (and several occurred), but why isn't the second or third best ERA season from 1968 (okay, the fourth is there)? And why is Gibson so far out in front? Because it takes more *MOSTLY* something else.
I'm just gonna say that I think that "context" impacts the mean and variance of the distribution of baseball stats which will impact the likelihood of specific outlying point values occurring and I need to see proof otherwise.
I agree. I want to see the math out of curiousity. I have seen other calculations regarding how likely DiMaggio's season was, but they disagree all the time. Also the likelihood of Hideo Nomo throwing a no-hitter in Coors.
And c'mon, no matter how much you want to ignore context, you can't include the war years. You talk about equipment changes ... well, the basic equipment (i.e. talent) was vastly inferior during those years.
I agree, but I'm not convinced it's worth the effort to sort the data out. It's three seasons out of 80+. Are there any critical events in that time? Newhouser was awesome, but he was awesome in 1946 too. Then Stan Musial...
(all your Gibson stuff)
I think an asymptote of 1 is about correct.
And within a season is important because of fatigue. And so is "completeness" of a season.
And there's almost no chance I can properly sort every 50 inning stint in MLB history (or any other portion).
No, it's not "close". When you get to these levels, each incremental improvement is incredibly difficult to achieve. 4 more wins is huge. McLain got a W in 76% of his starts. To win 31 today, you'd need 86% (no one gets more than 36 starts). I doubt very much that has ever been done by a pitcher with 30 or more starts.
Every offseason we talk about going to a 4-man (or at least pushing starts back towards 40).
We talk about it, but it won't happen in MLB. Almost no one can make that many starts and throw as hard as today's game requires. The odds of a team assembling a staff with 4 such starters is very unlikely.
* * *
Also, does Greatness require at least some value? If someone gets 140 SBs, but also 60 CS and thus does nothing for his team, is that great? Why or why not? What's the minimum value required to be great?
You are correct - if we are talking about asymptotes, it's a steep slope.
We talk about it, but it won't happen in MLB. Almost no one can make that many starts and throw as hard as today's game requires. The odds of a team assembling a staff with 4 such starters is very unlikely.
Well, you really just need one guy, and make sure he starts every fifth day, and then a few short starts. the otehr guys don't follow hte strict roatation. A horse as it were.
And it's *supposed* to be unlikely. ;-) (mmeting to attend)
When Ichiro! got his 262, it didn't just break the record, it was 20 more hits than anyone else had gotten in 70 years. Similarly, Rose just barely edged past Cobb, but he was almost 500 hits ahead of anyone who was even remotely contemporary.
That's greatness -- smashing records that no one else is coming close to. It's as if someone came out of nowhere and hit 37 triples.
No doubt about it. But the issue of context is that it would be very nearly as impressive if someone came out of nowhere and hit 35 triples. Because of the inescapable relevance of environmental context, that would be a more impressive feat than Wilson's astonishing 36 of 1912.
I agree.
Because of the inescapable relevance of environmental context, that would be a more impressive feat than Wilson's astonishing 36 of 1912
As i have stated repeatedly.
And which is precisely why I (and others, I think) are pretty fully confused. By stating this, you clearly acknowledge the crucial nature of relativity/context/environment, whatever we wish to label it as. Yet in the next breath you insist that you don't want to hear about relativity/context/environment, from me or Albert or anyone else.
But Pedro hasn't thrown a 1.10 ERA this year (*). I think you miss my point. I'm not saying that your conscious desire is to ask that question; I'm saying that, empirically, your question leads to that answer. You're not getting Pedro in 2006 as the answer to your question. You're getting Gibson in 1968 as the answer to your question. And no matter how you twist your head, you'll keep getting that. And if you don't factor in context, you're guaranteed to get your AOG-HR answer as being a HR-era season. Etc., etc.
(*) And if he does, I think based on this thread that you'd still discount it compared to Gibson because of the IP difference.
Not being great pitchers. You're being as silly as those people who say, "How can you say Coors Field is a great home run park? Nobody hit more than 20 (!) home runs there last year." Nobody said the conditions were a substitute for a great performance; merely a complement for them. Busch Stadium had the second lowest park factor, in the best pitchers' year in the live ball era. That's pretty near optimal.
As people have already pointed out, all the great doubles years were in specific eras. You can't pretend that's a coincidence. (I should say, you can't rationally pretend that was a coincidence.)
What you (and others, I think) seem to not be reading is that I have said repeatedly *some* relativity/context/environment is crucial, while other relativity/context/environment is NOT (or may not be).
You assert that all relativity/context/environment is crucial. I disagree with that position.
I don't need asymptotes for LHB vs LHP, or RHB vs GBSP, or anything else.
Well, I don't want them anyway.
The was more different in 1968 than most others, but not, IMO, enough to seperate it. And as I've said *Gibson's* season may require an asterisk (or whatever). Was 1985 "different"? Would you be happier if I were claiming RA+ (Gibson comes in around 1.4 it's been posted)? The mound wasn't higher than it was in 1967 was it (maybe it was)?
I'm not saying that your conscious desire is to ask that question
Well, you wrote:
What I can't figure out, Chris, is why you deny that what you're looking for is "here's what a great pitcher can do under near-optimal conditions for pitching."
I deny it because it isn't true. Can you figure that out?
You're not getting Pedro in 2006 as the answer to your question. You're getting Gibson in 1968 as the answer to your question. And no matter how you twist your head, you'll keep getting that.
Well, I assume I would too, but that's BECAUSE THAT"S THE LOWEST ERA.
Based on your "1968 theory", who would I have as the second Greatest! season (free hint, you'll get this wrong)?
And if you don't factor in context, you're guaranteed to get your AOG-HR answer as being a HR-era season.
Really, the highest spike of a given activity most likely occurred at a time when the ebb and flow of the game was that way.
I don't think that's critical in the definition. YOU (and Steve) are welcome to.
Not being great pitchers.
Wow. Two of the five starters are in the HoF. And a couple more were outstanding in 1969.
Nobody said the conditions were a substitute for a great performance; merely a complement for them.
That's the same thing I am saying! I'm saying they aren't all critical to control for and you are saying they are. For that matter, depending on how you want to evaluate a season of peak (quality) and career (IP or whathaveyou, depending on the stat), Gibson still has the highest. See my post on the previous page.
Busch Stadium had the second lowest park factor, in the best pitchers' year in the live ball era. That's pretty near optimal
Actually it was closer to being a hitters park than it was to being "optimal".
We didn't just meet, so I know you know using simple rankings as a description of how much a park affected performance is a no-no. So try that trick with someone else.
(*) And if he does, I think based on this thread that you'd still discount it compared to Gibson because of the IP difference.
Only if Pedro threw fewer innings and whatever method comes out of this demonstrates it to be as much.
As people have already pointed out, all the great doubles years were in specific eras. You can't pretend that's a coincidence. (I should say, you can't rationally pretend that was a coincidence.)
The eras these doubles spanned represent 45% of all the time of the liveball era. Why should that matter? Are you kidding me?
I can't pretend that half the time it's a hitters era and half the time its a pitchers era, and the hitting records will be set in one half of history and pitchers in the other half, so I have to control for every context tightly? I don't think so.
Low ERAs are set in every era (demonstrated). High HRs are set in every era (demonstrated).
People are saying you need to control for one tiny little bit of context called "era". You do this by tossing out pre-47 or pre-20 baseball. You seem to think you should do this by tossing out the war years, except maybe that's not worth the trouble. So it's hardly unforeseen that some might call for further adjustments and you can't just dismiss it with "I don't want to."
You seem to be arguing two different things.
First, you are arguing that no matter the context, there's a limit to how low an ERA can go. I don't actually believe that, but fine it's certainly a defensible position. And if you're right, context might impact the probability of seeing a perfomance close to the asymptote, but won't affect (much) where the asymptote lies. To make another asymptotic analogy, you can't have a probability less than zero. If the overall probability is .2, we're much more likely to see an individual probability below 1 in 1,000 than we are if the overall probability is .5 but we're still not going to see one below zero (and maybe not even at 0).
But then you take the step of identifying the "greatest" performances. And this is where you're running into all the criticisms. Your own numbers clearly demonstrate that it was much easier to achieve a "great" performance in 1968 than in any other year; it was easier to do so from 1964-1972 and during the war years. It's been much easier to hit lots of HRs in the last 10 years. It's simply not likely to be coincedence that 4 "great" seasons happened in 1968. It is far more likely that your measure does not measure what you want it to, that it is highly dependent on context contrary to your desires and that your measure should not be interpreted as providing sufficient grounds to say that Luis Tiant's 1968 was "greater" than the best seasons of Maddux, Clemens, Johnson, Pedro, etc.
Frankly, for almost everything except for ERA and to a much lesser extent other rate stats, your proposed measure of greatness would essentially just be the leader board. By the logic you've argued, the greatest HR season is 73; the greatest hits season is 262; the greatest doubles season is 66. Even for hitter rate stats, given that the number of PA for top hitters hasn't changed much over the years and doesn't vary much within, we can just go to b-r's leader board to find our measure of "greatness." Adjusting for PA might lead to slightly different rankings, but nothing major.
"Greatness" by your definition is difficult for ERA only because, ironically, pitcher usage today is vastly different than it was 20/30/50/80 years ago -- i.e. context matters. You feel it's necessary to adjust for era by coming up with some weighting for innings pitched -- of course, if anything, your adjustment gives an even greater 'advantage' to the 1960s pitchers.
Now, as I cleverly alluded to with my "greatness thrust upon them" comment, there's clearly a logic to that latter argument ... even IF they weren't greater, those pitchers were given more opportunity to display their greatness. We can't ignore that. But there's still a contradictory notion here -- the argument for not granting Maddux et al "their due" is an argument that's essentially based on regression to the mean -- i.e. a distributional argument. I'm fine with such a distributional argument because it's the same argument that I and others are making, but you should not be so comfortable with it.
Low ERAs are set in every era (demonstrated). High HRs are set in every era (demonstrated).
Ummm....so what? A normal distribution with mean 0 and standard deviation 1 will produce values below -2. So will a normal distribution with mean of 1 and standard deviation 1. Of course such values are far less likely to occur in the latter case. Maybe you think "greatness" and rarity are completely unrelated. Seems some of us don't.
The clustering of "great" seasons suggests one of two things ... there was a clustering of great players (though some may have been great for only that season which seems odd ... Earl Webb hit 40% of his career doubles in one season) or it was a "great" time for such performances. Or some mix of the two.
Anyway, the bottom line is that no matter what your belief and arguments are, your measure is highly context dependent and really tells us little/nothing more than if you're a great pitcher who happens to pitch in a pitcher's era (in terms of both quality and quantity), you will put up some great raw numbers and rate stats -- just like the guys in the deadball era did except that (and keep this to yourself) the deadball guys pitched in an even greater pitcher's era.
I think this is what I am striving for.
What is killing me, in all the "gotta have context" posts, everyone seems to have ignored post 51.
Using ERA+, Gibson's 68 still just dusts everyone considering IP.
I personally find the approach of adjusting pitching records for "how many innings pitchers were throwing in the era" extremely distasteful.
I agree with this. But we never do that (adjust for chances). The Statheads discount IP far too often.
And I am interested in more than the greatest. I'm interested in the 2nd and 3rd, and a general ranking.
Yes, on both counts.
If not, then there must be a difference in context which explains why.
But since they can/are, then there isn't.
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