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Awesome.
This is one of the things about baseball statistics that trips mathematicians up. Very few baseball statistics are normally distributed. In any given year, there will be dozens of pitchers who can provide an ERA+ of 80 (ie, replacement level) and only a few who can provide an ERA+ of 120.
No, old ERA+ vastly overstates that. It curves in the same direction as Pyth, but that was really an accident; the distortions are huge. New ERA+ matches up with run value perfectly, and misses a little bit on win value, but less than old ERA+ does.
Chart again
The orange line represents a team (or a pitcher who throws CGs every time); the green line represents a SP (whose impact on the runstowins converter is dampened a little because he doesn't pitch the whole game). For relievers, they pitch such a small part of each game that I don't think going to Pythagenpat makes much difference.
Sure. Without a normal distribution, you can't do things like estimate that 66% of data points are within one SD, etc. The SD is still useful, though. We can still use standard deviation to measure the spread in a metric, and to adjust for that spread by expressing things in terms of SDs.
Huzzah!!!
Pedro's >200 ERA+ seasons are back!
Eckersley's ERA+ is 17, that makes sense, he's 6 times better than the league, 17*6 = 102.
Eckersley's ERA+ is 20017 = 183, you basically have to convert it back to the "17" to make it a useful stat.
He did not do "83%" better than league average. He did 600% better. The only way that is reflected in the number "183" is that 200183 = 17 * 6 = 100.
Using simply the number "183", there is no direct route to show that Eckersley allowed 6 times less runs on average than the rest of the league. You have to do the "200  X" part before you can demonstrate that.
So why bother with the 200 at all? To make the numbers "look" like old ERA+? That's dumb.
That's not exactly what I meant. Most fans  like me, for instance  would think that a 100 ERA+ is average, a 120 is good, a 150 should put you up among the league leaders, a 200 is historic. I would guess that most fans think of it in broad parameters like that, rather than percentages.
And as we've seen, when it comes to what "twice as good" means in terms of ERA, there's no easy answer.
I think that with any composite metric, like ERA+ or WAR or VORP or whatever, you use the numbers long enough and you gain some sort of inductive sense of what's good and what's not, and you learn (if you listen up here on Primer) how to use the numbers in arguments. Or not, if you're invincibly ignorant like me.
The 200 is very intuitive to me. It is impossible to prevent runs at a better rate than 100% under league average, by definition. So just as 200 OPS+ means creating 100% more runs than average, 200 ERA# will mean preventing 100% more runs than average. 200 is the natural top end of the scale by definition. (A few percent more is possible if parkadjusted, but the 200 cap conceptually holds, and it's academic as real stats won't exceed 200 ERA# anyway.).
Or if we flip the scale as I wholeheartedly support, we get a 0 ERA% as preventing 100% more runs than average, and a 200 ERA% as allowing 100% more runs than average.
The phrase "twice as good" is really confusing things here; that concept doesn't really apply to preventing runs. Instead phrase it in terms of "100% better" or worse and the mechanics become clear.
Classic ERA+ is simple:
lgERA (with park adjustment)/pitcher ERA*100
New Coke+ goes through more machinations with an artificial cap.
The new formula is basically the inverse of the old one with a cap of 200 artificially thrown in there.
If the new formula is used, it should be just pitcher ERA/lgERA, so that Eck's great season is 17....with a different name for the stat (ERA+inverse?)
Neither way to do it scales with OPS+ as they are measuring different things...however, the new formula makes pitchers look much worse than hitters to someone casually looking at it.
As I've saif: ERA is the answer.
He did not do "83%" better than league average. He did 600% better.
Says you. I disagree. He allowed 83% fewer runs than the league average.
So why bother with the 200 at all? To make the numbers "look" like old ERA+? That's dumb.
No. To make allowing 83% fewer runs show up as 183.
Before calling things "dumb", you might try reading the thread to understand why.
Works fine on numbers over 100, under 100 not so much. The ERA+ version works on both sides of 100.
The main advantage of the new formula seems to be the ability to simply average ERA numbers.
I believe that this could also be done with the old ERA+ if one used ER instead of IP to weight each ERA.
The rest of the arguments seem to be about semantics on how much better (or worse) a certain ERA is in relation to the league average.
ERA+ has been virtually the same for over 20 years.
I know Bill James has tinkered with Runs Created over the years, but he hasn't changed the way it is basically calculated.
It's still based on the ratio of league ERA to the pitcher's ERA. It's a different number, but it means exactly the same thing.
Yes he did. I just checked my old copy. He has, for example, Eck's 1990 ERA+ as 605.
This is completely incorrect. The new metric scales almost perfectly with OPS+: both compare a player to the average in terms of runs created/prevented, a higher number means better performance, and both are symmetrical around 100 (120 is as good as 80 is bad).
To me, this is in fact the best argument for the new metric (whatever it's called). I think OPS+ has more/wider recognition, and there is a benefit to having them work the same way. Certainly a benefit for BR. So I get why Sean prefers a scale where higher=better (though I agree "ERA" is also a perfectly valid way to measure the same thing).
At very elite levels, yes. But as has been explained repeatedly, that is because it's true. Shouldn't that matter, at least a little?
Yeah, that's easy and intuitive! In any case, there are several other advantages to the new metric.
Not correct. A 79 means a pitcher gives up 21% more runs than average, just as 183 means 83% fewer runs than average. It means exactly the same thing on both sides of 100, which is not true of old ERA+. (Again, I have no quarrel with ERA/LgERA  but I think Sean has valid reasons for wanting higher=better. That's a totally subjective question.)
After all these comments, this remains the only reasonable argument for old ERA+ IMO. Basically, "I'm comfortable with the old scale, and don't feel like learning a new one." Will that be enough to prevent people from gravitating to the new metric? I don't think so, if both are easily available on BR. Eventually, the strengths of the new metric are sufficient that people will use it much more in analysis and debates, as post 206 suggests. Time will tell.....
That's kinda my point, you still have to get from the 79 to 21. Now obviously this is extremely easy, but you still have to do it manually. It's not first glance obvious (and more so once you get into negative numbers), whereas ERA is always first glance obvious: 17ERA is 17% of league average ERA; 121ERA is 121%. It's a slight complication, where none need be.
Basically, "I'm comfortable with the old scale, and don't feel like learning a new one." Will that be enough to prevent people from gravitating to the new metric? I don't think so
How's that DVORAK keyboard working out for you?
Also known as the Rants Per Canto ratio.
Okay, but maybe you could fit the season's ERA+ distribution (perhaps for pitchers who hit a minimum IP threshhold) to a Weibull distribution, generate parameters and use the cumulative distribution function to estimate the percentile for a given pitcher's ERA+.
A 200 ERA is the best one can get under the new formula right? While OPS+ can be over 200 and could even be over 300 if someone was good enough.
Maybe it's semantics, but to me that means they don't scale the same.
<the new formula makes pitchers look much worse than hitters to someone casually looking at it.>
"At very elite levels, yes. But as has been explained repeatedly, that is because it's true. Shouldn't that matter, at least a little?"
A 200 ERA in the new formula is the same as a 0.00 ERA in a neutral park right? Do you think a 0.00 ERA from a pitcher is not as good as someone putting up a 250 OPS+?
ERA+ and OPS+ were never meant to measure the same thing. That is why Total Baseball converted everything to runs to compare pitchers and hitters.
This is a reason for not changing it. It doesn't add additional knowledge to the statistic.
It seems like some people want to change it because the new formula looks better to them. I don't think that is a good enough reason to confuse a lot of nonhardcore people who are used to the current ERA+ on Baseball Reference. Interestingly, I think many of those who want to change it are statistically savvy enough to understand ERA+ whichever way it is calculated.
Because Baseball Reference and the Baseball Encyclopedia are for a more general audience, I think they should be consistent in the general way they calculate stats.
This is because there is no bound on the number of runs scored whereas there is a bound on the number of runs allowed  zero. It is not possible for a pitcher to be as much better than average as a batter who never makes an out. The upper limit in a batter's performance is to produce an infinite number of runs, which means an infinite number of runs above average and an infinite number of runs above replacement. The best that a pitcher can do is to allow zero runs, which, in a 5.0 run environment, for example, means a pitcher can't be more than 5 runs above average or, say, 7 runs above replacement (if a 7.00ra pitcher is "replacement level"). Which ties back into, yes, a pitcher with a 0.00 ERA is not as good (on a per PA level) as someone putting up a 250 OPS+.
Barry Bonds in 2002 had an offensive winning percentage of .938 (that was his best)  i.e., a team of 9 Barry Bonds and average pitching/defense would have a Pythagorean winning percentage of 0.938.
Pedro Martinez in 2000 had an ERA of 1.74 in a 5.06 earnedrun environment (1.74*2.91  the latter being his oldERA+ divided by 100). Using PythagPat (so, coeff = (RS+RA)^.28 = 1.71 in this case, ignoring unearned runs), that works out to a winning percentage  given an average offense  of 0.861, which actually overstates Pedro's dominance because it ignores his bullpen. For example, in reality, the Red Sox actually went 218 (0.724) in games started by Pedro that year.
Looking at Bonds's OPS+ of 268 v. Pedro's oldERA+ of 291 makes it look like Pedro was more elite than Barry. But Barry's influence was more extreme as you see in their relative winning percentages (0.938 v. 0.861).
Yes, that's an excellent analogy: ERA+ is definitely as well established as the qwerty keyboard, and adjusting to ERA# would be just as difficult as learning a new keyboard. In fact, ERA+ is more like a keyboard in which some letters are always capitalized while others are always lower casewhich is worth fixing.
The scale is the same. What is true is that a hitter can produce more than 200% as many runs as the average hitter, while it is impossible for a pitcher to give up more than 100% fewer runs. That's just a function of how baseball is played, not a scale problem.
I don't really care, because there are no 200 ERA# pitchers. But in fact, a 200 pitcher would prevent 4 runs per game (if lgERA were 4.00), while a 250 OPS+ hitter would contribute 6 runs per game (38 PAs). More realistically, a 150 pitcher and a 150 hitter both contribute 2 runs per game, and are in fact equivalent on a per PA basis. (And yes, it's true that each run saved by elite starters is worth a bit more in terms of wins than hitters' runs created  and I think metrics like WAR should take that into account.)
Correct, which allows us to understand that the old version is a misleading and poorly constructed metric (and also widely misunderstood, it turns out). That we can "understand" it either way doesn't make them equally useful or valid.
OK, but a pitcher who never allows an earned run will have an ERA+ of 200, much less than 268. A team which never allows an earned run will have a better win% than .938 (152 wins in a 162 game season). How many times a season is a team shutout allowing only unearned runs? Once every 10 years? At any rate, it's a lot less than 10 per year.
Sure, but at that point (hell, at the point of Bonds and Pedro) you're getting into extremes that simply aren't approached. A single pitcher who allows no runs will nevertheless see his team lose some games either because he isn't playing or because his bullpen allows some runs after he leaves. As Guy says, it's possible for a batter to be 6 runs better than average in a league where the average team scores 4 runs per game. It's not possible for a pitcher to be 6 runs better than average in such a league. Barry Bonds, in 2004, was more runs away from an average hitter than it is possible for a pitcher  no matter how good they are  to be better than an average pitcher.
If I ran it right, BBREF play index says 38 times from 20002009
EDIT: So a little over 1 time per team per decade.
To sort of expand on this, at the extremes, you start to get into distortions in moving from runs to wins  the conversion is nonlinear and, in fact, I think even Pythag starts to fall apart at these sorts of very extreme extremes (as well as how one translates individual performance into team wins  what do you assume about the other hitters or about the bullpen or the other starters, etc.). But that's moving beyond the issue being challenged by Mr. ERA+. OPS+ and newERA+ have a common scale: RUNS relative to average. And here, as Guy and I said, there is a natural limit to the number of RUNS better than average that a pitcher can be whereas there is no such limit to the number of runs better than average that a hitter can be.
Yeah, and the 2002 Giants lost one or 2 as well. I understand the concept, and I agree it's trivial because no pitcher will ever have a 200 ERA+. But if a team with and OPS+ of 268 will lose only 10 games, a team with an ERA+ of 200 will lose at most 1.
This is wrong, at least in a discussion about OPS+, which is a rate stat. OPS is capped at 5.000, and therefore OPS+ is also capped. You can go the infinite PA approach, but that won't change that cap.
This whole argument about trying to conflate rate stats with runs per game is nonsensical. You have no way of knowing how valuable somebody with a 100 ERA+ or OPS+ was, without accounting for playing time. Starting pitchers, relief pitchers, starting position players and bench players are not magically all of equal value, because they have a 100ERA+/OPS+. Hell, two starting pitchers aren't equal just because they both have 100 ERA+. If you are trying to make a stat that equates value of offense and pitching, then what you are making is not ERA+ and OPS+.
The cap on OPS is a flaw in using OPS as a measure of runs generated on offense (albeit a fairly minor one relative to some other flaws).
The rate stat would be runs per PA, which is what both OPS+ and ERA+ purport to measure, albeit imperfectly in both cases. Guy and I are just speaking in terms of runs per game because it's a more familiar scale. As a rate stat, if the average R/PA is, say, 0.1, it is possible for a batter to have an R/PA that is more than 0.1 greater than that. It is not possible for a pitcher to have an R/PA value that is more than 0.1 less than that.
This is an argument against all rate stats: OBP, SLG, BA, ERA, everything. If that's what you believe, fine, but then you should logically have no opinion about how best to calculate ERA+.
No it's a limitation of rate stats, that does not mean that they are completely useless, or that I can't have oppinions about them. The point is that attempting to scale them according to some arbitrary amount of IP and PA, so that OPS+ and ERA+ may or may not in some cases be comparable does not in any way, shape or form "improve" those stats. In fact it encourages people ro abuse these statistics. Nobody right now is using OPS+ and ERA+ to compare hitters and pitchers, and nobody should be using them to do so. Making a change that will encourage people to use the stats in an incorrect way is IMHO wrong
There are plenty of stats that can be used to compare hitters and pitchers, but ERA+ and OPS+ are not suitable for that. Trying to force a change that makes them comparable in an extremely imperfect way distracts from the actual value these statistics provide.
The cap on OPS is a flaw in using OPS as a measure of runs generated on offense (albeit a fairly minor one relative to some other flaws).
Which would be totally relevant, if the proposed fixes changed this.
The rate stat would be runs per PA, which is what both OPS+ and ERA+ purport to measure, albeit imperfectly in both cases. Guy and I are just speaking in terms of runs per game because it's a more familiar scale. As a rate stat, if the average R/PA is, say, 0.1, it is possible for a batter to have an R/PA that is more than 0.1 greater than that. It is not possible for a pitcher to have an R/PA value that is more than 0.1 less than that.
Which changes nothing about what I said. You can't get to value from R/PA, without removing the PA part. Value is not the valuable information you get from ERA+ and OPS+. If you are interested in a value stat there are plenty available to choose from, why bother about these "imperfect" stats in the first place, in the words of GuyM:
"This is an argument against all rate stats: OBP, SLG, BA, ERA, everything. If that's what you believe, fine, but then you should logically have no opinion about how best to calculate ERA+."
I honestly don't understand what you're arguing at this point. Yes, value = rate stat * playing time. I thought everybody understood that. I only jumped in because you seemed to be bothered by the fact that hitters can accumulate higher OPS+ than pitchers can accumulate newERA+. But that's just because runs are distributed asymmetrically  whether as rate stats or as absolutes (although, runs per game is a rate stat). It hits pitchers at their peak and hitters at their floor  i.e., a pitcher who fails to record an out would have a lower newERA+ than a batter who made an out every time up. We just don't care about hitters and pitchers that crappy.
Barry Bonds in 2004 created more runs per PA relative to average than Pedro2000 saved relative to average. That Pedro has a higher oldERA+ than Bonds has an OPS+ is therefore an example of the weakness of oldERA+ as a rate stat. To move from that to how many wins each of these guys were worth requires moving far beyond OPS+ and ERA+ and is, hence, largely irrelevant to this discussion and to the extent that I'm the one who brought up wins, I apologize if by doing so I unnecessarily confused the issue.
They're not arbitrary amounts  they're approximately the same amount. Which was Tango's point, if I understood it correctly  a batter and pitcher who go through the same number of PA with the same OPS+/ERA# now have roughly the same value in terms of runs created/saved. Which is kind of neat, for metrics as rough as these are. (Yes, the best hitters now score higher than the best pitchers  but the best pitchers go through more PA.) However...
In fact it encourages people ro abuse these statistics. Nobody right now is using OPS+ and ERA+ to compare hitters and pitchers, and nobody should be using them to do so. Making a change that will encourage people to use the stats in an incorrect way is IMHO wrong
It seems like people were doing that, since one of the complaints about ERA# in this thread has been that its top scores are much lower than the highest OPS+es. Regardless, I'm not under the impression that this was what motivated the change  it was prompted by a desire to have ERA+ be linear, and therefore easier to use in secondary calculations. The fact that OPS+ and ERA# are now more comparable is simply a nifty little feature that you are free to ignore if you want to.
Everyone here maybe. You'd be surprised how many people there are, that use ERA+, that are not us
I only jumped in because you seemed to be bothered by the fact that hitters can accumulate higher OPS+ than pitchers can accumulate newERA+.
Wasn't me, doesn't bother me, because ERA+ and OPS+ are completely disjointed.
Barry Bonds in 2004 created more runs per PA relative to average than Pedro2000 saved relative to average. That Pedro has a higher oldERA+ than Bonds has an OPS+ is therefore an example of the weakness of oldERA+ as a rate stat.
No this is an example of the fact that OPS+ and ERA+ are not comparable.
Let me demonstrate an example of what you are going to see when new ERA+ hits:
Justin Verlander: 2009 NewCokeTM+ 125
Jason Bay: 2009 SecretOPS+ 133
Hey look, Jason Bay's offense was worth more than Justin Verlander!
Do you agree with that comparison, do you think it's accurate? If not, then why are people touting this as a feature!
HAH! See, my point. It's not a faeture, it's a lie wrapped in insincerity shrouded in deception masquerading as a feature. 162 IP is comparable to 700 PA in the same way as my Labrador is comparable to a wolf.
There were 16 NL pitchers between 152 and 172 IP last year. Those pitchers averaged 164 IP and 706 PA against.
You have a fierce labrador.
There were 46 pitchers in the NL with at least than 162 IP. The NL leader had 233.
There were 46 pitchers in the NL with at least than 162 IP. The NL leader had 233.
Nobody said that those amounts of playing time are identically impressive, or difficult to accumulate.
A hitter with 700 PA and a 140 OPS+ has the same value, give or take, as a pitcher with 162 IP and a 140 ERA#. The hitter's playing time may be more impressive, just like the pitcher's performance rate may be more impressive. But the values are (roughly) identical.
"I do wonder, though, why folks who find these stats to be so inadequate and imprecise are spending so much time trying to improve them in ways that can never actually remedy their overall deficiencies"
"A hitter with 700 PA and a 140 OPS+ has the same value, give or take, as a pitcher with 162 IP and a 140 ERA#. The hitter's playing time may be more impressive, just like the pitcher's performance rate may be more impressive. But the values are (roughly) identical."
Doesn't this imply that a fulltime pitcher (around 200+ innings) with a 140 NewCokeERA# is more valuable than a full time hitter (700+ PA) with a 140 OPS+? If so, then it seems like NewCokeERA# and OPS+ shouldn't be compared directly either.
In any case, ERA+ isn't hard to understand, and I never thought it could be directly related to OPS+, even 20 years ago when I knew very little about baseball statistics (OK, I don't know that much about advanced stats now either).
Yes.
If so, then it seems like NewCokeERA# and OPS+ shouldn't be compared directly either.
Why? I mean, obviously they shouldn't be compared as a measure of overall value unless you account for playing time. That's not exactly unique. But in a backoftheenvelope level calculation, I don't see any particular reason not to treat ERA# and OPS+ as generally equivalent rate stats.
Anybody who knows enough about sabermetric stats, to know that you need to adjust for playing time, is not going to bother using ERA# vs OPS+ in any comparison hitting and pitching. There are plenty of statistics that can do this far more effectively. Heck, you'd be better off using frickin' VORP to do this. What you are going to see, is a bunch of people, who are not well enough informed to this, and have been told that "ERA# and OPS+ are now equivalent", drawing faulty conclusions from their comparisons.
And riddle me this. Do pitchers now get a place on the positional spectrum? Is a 162 IP, 120 ERA# pitcher now equivalent to the 700 PA, 120 OPS+ first baseman, or to the 700 PA, 120 OPS+ catcher. This whole thing is a complete mess.
Who's been told this? People reading this thread and the one on Tango's blog, right? I don't know that Sean is going to advertise the equivalence we're talking about here, because it's not the main reason to make the change.
And riddle me this. Do pitchers now get a place on the positional spectrum? Is a 162 IP, 120 ERA# pitcher now equivalent to the 700 PA, 120 OPS+ first baseman, or to the 700 PA, 120 OPS+ catcher.
Well, since we're evaluating pitching, and pitchers are (pretty much) the only people who pitch, there's not really much need for a positional spectrum beyond starters vs. relievers. So starters get a bump of a few runs, maybe like second/third basemen, and relievers are docked a few runs, something like an outfielder who splits time between center and the corners. A 162 IP, 120 ERA# pitcher (presumably a starter) would be right around the midpoint between the first baseman and the catcher (who is a freak of nature, by the way, unless he's DHing a lot).
This whole thing is a complete mess.
Again, you are free to ignore this potential use for ERA# if you want to.
Eggsactly.
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