If IP > 0 and ER > 0, then ERA+ * ERA- = 10000

Typically, pitchers want a low ERA, but ERA+ is a metric that shows a pitcher’s performance scores better when it is higher. Therefore, it’s not as intuitive as ERA-.

Typically, people want a higher score. ERA is less intuitive than ERA+. You're just more used to it.

It seems to me you'd have to work pretty hard to convince yourself that ERA+ is hard to understand.

The upper reaches of ERA+ are hard to understand. The difference between 100 and 200 ERA+ is many more runs than the difference betwen 200 and 300. A pitcher who recorded a 400 ERA+ did not prevent twice as many runs as a pitcher with a 200 ERA+, nor was he twice as valuable. It's not nearly as intuitive as it seems, especially for the non mathematically inclined (ie, journalists).

As for a low score being better, golfers and track athletes have understood that for millennia. I'm all for ERA-.

[3] Maybe not hard to understand, but hard to interpret meaningfully, and can't be interpreted the same way as, say OPS+ A 180 OPS+ says that the batter's (adjusted) OPS is 80% above the league average. A 180 OPS+ says that the league's (adjusted) ERA is 80% above the player's.

Furthermore, since ERA is bounded by 0, and better performances are closer to 0, low ERAs are likely to produce non-linearities in OPS+ which are also hard to quickly interpret.

I like ERA-, though now that i really understand ERA+, its not _that_ hard to do enough of the math in my head.

Edit: Diet Coke to [4]

A 180 OPS+ says that the batter's (adjusted) OPS is 80% above the league average.

Nitpick: If I'm not mistaken, it means he creates runs at a rate 80% higher than the average player, which is not quite the same thing. (And, I would argue, a more useful thing.)

You can keep higher=better AND have a metric that makes sense. Just define ERA+ as 200 - 100*(ERA/LgERA).

A 180 OPS+ says that the batter's (adjusted) OPS is 80% above the league average.

Nitpick: If I'm not mistaken, it means he creates runs at a rate 80% higher than the average player, which is not quite the same thing. (And, I would argue, a more useful thing.)

It doesn't mean either of these things. It means, well, it means this equation:

(OBP+) + (SLG+) - 100 = OPS+

It is a moderate problem that a 120 ERA+ isn't 20% better than league average, but it's hard for me to get too concerned about that. I see the point, at least.

I don't think it's a problem at all that ERA+ isn't linear (that is, that the difference between 200 and 100 isn't equal to the difference between 200 and 300). That's true of most stats.

It doesn't mean either of these things. It means, well, it means this equation:

(OBP+) + (SLG+) - 100 = OPS+

Correct. But 180 OPS+ does in practice come pretty close to meaning 80% more runs than the league average. Every run means somebody reached base (OBP) and was driven home (SLG). So if a batter has OBP and SLG each 40% better than league average, he will produce 80% more runs than a league average batter. It's also roughly true for OBP 20% above league and SLG 60% above, or other such combinations. This approach is by no means exact, it degrades at the extremes (especially negative) and pretends neighboring hitters are league-average, but it is a useful approximation.

180 ERA+ on the other hand is not at all intuitive. It means the pitcher allowed 100/180 = 55% as many earned runs as a league average pitcher. It totally doesn't mean the pitcher is 80% better than league average. In fact he allowed 45% fewer runs than league average. Expressing this as 55 ERA- is so much more natural and intuitive. Expressing this as 145 ERAwhatever would also be acceptable, as post #7 proposes, although this works less well at the extremes because ERAwhatever would be on a scale from negative (allow more than twice league average runs) to a cap at 200 (allow zero runs). ERA- is scaled from 0 (no runs) to unbounded (any number of runs before you get hooked) which is how pitching actually works.

I don't think it's a problem at all that ERA+ isn't linear (that is, that the difference between 200 and 100 isn't equal to the difference between 200 and 300). That's true of most stats.

As Tango has pointed out, one problem with ERA+ is that you can't average it, since ERA is the denom. This leads to people thinking that a season with a 200 ERA+ and a season with a 100 ERA+ averages out to a 150 ERA+, and it doesn't work that way. In the same amount of innings, say 100 is 4.50 ERA and 200 is 2.25 ERA, the average is a 3.375 ERA, which works out to a 133 ERA+. This has tripped a lot of people up; enough so that I think it's preferable to seek a more intuitive number.

With ERA-, you could. The former would still be 4.50=100, but the latter would be 2.25=50. The average intuitively works out to 75, same as 3.375/4.50

As Tango has pointed out, one problem with ERA+ is that you can't average it, since ERA is the denom. This leads to people thinking that a season with a 200 ERA+ and a season with a 100 ERA+ averages out to a 150 ERA+, and it doesn't work that way. In the same amount of innings, say 100 is 4.50 ERA and 200 is 2.25 ERA, the average is a 3.375 ERA, which works out to a 133 ERA+. This has tripped a lot of people up; enough so that I think it's preferable to seek a more intuitive number.

I did not know that. That is a major flaw for me, as I oftentimes do a down and dirty averaging of a player's best seasons.

It doesn't mean either of these things. It means, well, it means this equation:

(OBP+) + (SLG+) - 100 = OPS+

That's why you should use wRC+...

The only reasons OPS+ hasn't become obsolete are that B-R (for some reason) continues to publish it, and that it's based on a more familiar statistic. wRC+ is actually precise, whereas OPS+ is an unholy amalgamation that generally comes close enough to the right answer to be an acceptable substitute. Unfortunately, the broad distaste for FanGraphs prevents people from recognizing the superiority of wRC+.

Actually, I suspect that the reason OPS+ is not obsolete is that sportswriters MUCH preferred OPS (without the +) to anything else in sabermetrics when it started showing up in sports journalism. The reason they preferred it is that they could compute it themselves from the newspaper without even using a calculator! Just add OBP to SLG. "Mainstream" sabermetricians (to the extent that such a term even has a meaning) found themselves going along with this because sportswriters would actually listen to it. I remember getting really frustrated with Baseball (now Sports) Weekly when it started relying on OPS, instead of something more useful, like RC/27. But sabermetricians knew that raw OPS was lacking really important things like ballpark adjustments, so they came up with OPS+, hoping that the sports journalists would buy into it as a "better" (I mean, it has PLUS in it!) version of OPS. This worked. Sports journalists thought themselves comfortable with a stat that they could compute out, except for the ballpark adjustments and/or whatever. So it started showing up in every newspaper and has become, for the casual sports fan, the big deal stat for offense. That it's mathematically tricky and misleading was not a concern because any adjusted stat looks mathematically tricky to a sports journalist who isn't good at math. - Brock Hanke

. Unfortunately, the broad distaste for FanGraphs prevents people from recognizing the superiority of wRC+.

It's a justifiable distaste, similar to baseball prospectus, they had an attitude as if their stats were obviously superior and expected everyone to jump on board....The rise and fall of WPA was a glorious thing to behold.

OPS+ is popular because it makes intuitive sense. It's on base plus slugging added together and adjusted for park effects.... wRC+ is a better stat, but it's not enough of a difference to have to deal with fangraphs site for the information.

Edit: Or what Brock said.

Fair enough. I can see why OPS+ would become reasonably widespread in writing that crosses between mainstream and stat-oriented. When I wrote the comment, I was referring mostly to nerds like us who comment on BBTF and are fairly "stat-aware;" I do think we're better than to use B-R lazily for everything. I also think B-R is better than to keep publishing this statistic just because people are so accustomed to it.

By the way, I agree with you that the FanGraphs writing is often poorly informed and occasionally obnoxious, but I'd guess you haven't read much BP lately if you think they're still that way. I don't like Colin Wyers (their main data guy, who also occasionally writes research pieces) at all; he's obnoxious even towards other statheads, and PECOTA is still a wreck even after he's spent considerable time on it, so I don't have great confidence in him as a researcher. But much of the rest of the staff is funny and enlightening and has pretty diverse viewpoints. I'm not a subscriber, but about half of their content is viewable by anyone, and I read the majority of that each day.

I love BP's book, and I like most of the writers at fangraphs, but it doesn't change the initial attitudes they projected. I personally don't read anything at BP anymore because I'm not paying for their material. I buy the book every year (It's more of a requirement than any other annual) but paying for their website falls below 1. B-ref. 2. Bill James 3. ESPN on the priority list (I'm only paying for B-ref right now)

Everytime I go over there, the only articles that seem to interest me are subscriber articles (I'm not a prospect maven, fantasy baseball player and I don't care one bit about team specific reports) I like their writers so that isn't the issue, it's just that I have to draw the line at monthly (or annual subscriptions somewhere) If you aren't careful, you might all the sudden realize you are spending a couple hundred dollars a year on internet reading.

Ultimately I really miss Robb Neyer Articles. Daily articles in newspaper size format that did a good job asking and at least attempting to answer a nagging question, and was oftentimes a great starter conversation for more research or even a basic "primer" for a newbie to delve into the stat pool.

player/wRC+/OPS+

Trout 176/170
Cabrera 163/162
McCutchen 161/166
Braun 160/157
Posey 160/166
Encarnacion 154/151
Stanton 152/150
Melky 149/157
Fielder 146/143
Wright 143/148

Rank in ERA-/ERA+
Sale 1/1
Price 2/4
Dempster 3/5
Verlander 4/3
Weaver 5/9
Kershaw 6/7
Dickey 7/6
Cueto 8/2
Lohse 9/10
Miley 10/8

Yes these differences are incredibly important.

The important differences between ERA+ and ERA- have nothing to do with the differences in ordinal ranking. It has to do with other uses for the stat - ERA-, as has been pointed out above, allows for much more intuitive comparisons between players and between seasons.

In fact, there actually should be zero differences between the ordinal rankings produced by ERA+ and ERA-. It should produce the exact same list. I'm guessing that you took ERA+ and ERA- from two different sites, which use different park factors, and that caused the differences. The underlying stat, so long as you use the same input, should output the exact same ordinal rankings.

(I'm not a huge ERA- booster, but it misses the point entirely to post ordinal rankings as counter-point.)

Austin - I was completely aware of what you were saying, and I also agree with it completely. I was just trying to give my take on the history of OPS+, not give you a hard time for saying something that I think is absolutely true. I imagine that BB-Ref is stuck with OPS+ and ERA+ because their audience is wider than BBTF, and most of that audience has become acclimated to OPS+ and ERA+. I, personally, use them when I need a serious database reference, which is what BB-Ref provides. If there was any serious agreement as to which version of WAR or Win Shares was "best", I'd use that, and BB-Ref no doubt would, too. But there is no consensus about the stronger stats, so I end up falling back on OPS+ and ERA+, and BB-Ref's choice of WARs is as good as any, and they had to make a choice. I don't LIKE it, any more than you do. It just happens. I can't blame BB-Ref or anyone else. You take a serious research community's work and put it out there to the general public, you end up with watered-down versions. I mean, everything I know about string theory comes from TV shows. The actual math is beyond me. I'm part of the general audience in that field. What's important to me is that I remember that I'm not part of that research community and not talented enough to ever become a part of it. So I do the best with what I think I can understand. That's what sportswriters who are bad at math have to to with sabermetrics. Of course, neither my ego nor my income are affected by my lack of understanding of string theory, so I'm not as cranky about that as many sportswriters are about sabermetrics.

And Shoewizard: I have to know. Wins above which Willie? McGee? Davis? Mays? It won't change the ordinals, but it would sure be fun to see a set of WAR that were almost entirely negative, because it was Wins Above Willie Mays. - Brock

The important differences between ERA+ and ERA- have nothing to do with the differences in ordinal ranking. It has to do with other uses for the stat - ERA-, as has been pointed out above, allows for much more intuitive comparisons between players and between seasons.

In fact, there actually should be zero differences between the ordinal rankings produced by ERA+ and ERA-. It should produce the exact same list. I'm guessing that you took ERA+ and ERA- from two different sites, which use different park factors, and that caused the differences. The underlying stat, so long as you use the same input, should output the exact same ordinal rankings.

(I'm not a huge ERA- booster, but it misses the point entirely to post ordinal rankings as counter-point.)

MCOA, less intuitive for whom ? The only reason I gave ordinal ranking is because you can't compare them side by side, like you can for OPS+ and wRC+. I was actually comparing the hitting stats first, and then did the same thing for ERA+ and ERA-.

If you look up any 20 hitters, 15 of them are going to have wRC+ and OPS+ within 3 or 4 points of each other. The ones that aren't close are always going to be guys that either don't walk much or walk a lot. It's an easy adjustment for me.

Baseball reference is easier for me to use and navigate, and fangraphs is too slow. I still go there every day, but the differences between the metrics here is not all that great.......good enough for the purpose 90% of the time, if not more. Would I prefer BB-REf to use ERA- and wRC+ ? Sure, if you true statheads convince me they are better metrics, and there is a real consensus in the community they are better, then I'd like to see Sean adopt them. But looking at it from Sean's perspective, there may not be enough upside to go through the work to make the change and cause all the loyal readers of his site to have to adapt.

And Shoewizard: I have to know. Wins above which Willie? McGee? Davis? Mays? It won't change the ordinals, but it would sure be fun to see a set of WAR that were almost entirely negative, because it was Wins Above Willie Mays. - Brock

Brock, it's a reference to something Tango posted

MCOA, less intuitive for whom ?

For certain kinds of comparisons between players and seasons. See the points made in this thread by Shock at #11, for instance.

The only reason I gave ordinal ranking is because you can't compare them side by side, like you can for OPS+ and wRC+

I get that. But the point I'm making is that there aren't actually any differences at all, in ordinal rankings, between ERA+ and ERA-. If you found a site that calculated both ERA+ and ERA- using the same park factors, you'd see that they produce identical ordinal lists. The ordinal lists have nothing to do with the issue at hand.

(The ordinal lists are relevant for comparing OPS+ vs wRC+. There are meaningful differences, but they're surprisingly small. For quick reference, the superiority of wRC+ has probably been overstated in this thread.)

Would I prefer BB-REf to use ERA- and wRC+ ?

I would treat these as separate issues. OPS+ is in fact nearly as accurate as wRC+, it measures what it purports to measure (players' contribution to run creation), it is functional (for example, you can take a straight average of several OPS+ ratings and get the right answer), and the scale makes sense (the difference between 110 and 120 is the same as the difference between 140 and 150). And unlike wRC+, OPS+ has already been adopted by many non-saber writers, a huge breakthrough (ironically, this is probably because people think it's based on OPS, which isn't true). Sean would be crazy to drop OPS+.

ERA+ is different. It's structure is fundamentally illogical, it doesn't tell you what you would naturally think it does, and it is very difficult to work with. To the extent it has a brand value like OPS+, Sean could continue that simply by changing the calculation to make LgERA the denominator (just as LgOBP and LgSLG are the denominators in OPS+). Everyone who uses ERA+ now would continue to do so. Alternatively, he could move to ERA-, which is arguably even better. But I can see the value to B-Ref in maintaining its own brand....

Wasn't this dealt with 2 years ago?

http://www.baseball-reference.com/blog/archives/5159

We Goofed: ERA+ numbers

Right now on the site you'll see different ERA+ numbers from what you are used to seeing on the site. The old formula was 100*(lgERA/playerERA). The numbers you see now are 100*(2- playerERA/lgERA). This changes the numbers somewhat and bunches the top end a bit more, but doesn't change the ranking of players. The two lists of league leaders are the exact same.

Current

Old

I had not intended to roll out this change just yet as I was mulling a change in name to show that we are presenting a different formula. I was testing the change and ended up rolling it out to the site unintentionally. I apologize, and I am embarassed by the confusion this has caused.The reasons for making a change are a bit esoteric, but I find them compelling. The old formula is a power equation. The independent variable is in the denominator, so you get a 10% change in the player's ERA showing up as any of a variety of percentage changes in ERA+. It depends where on the curve you are. For example, if you have a league ERA of 4.50 and one pitcher at 3.50 and one at 3.00 and one at 2.50, you get ERA+'s of 129 and 150 and 180. The changes aren't linear.With the new formula, the equation is linear, so if the league ERA is 4.50 and you have one pitcher at 3.50, one at 3.00 and one at 2.50 you get ERA+'s of 122, 133 and one at 144 (one is 22% better than the league, one is 33%, and one is 44% better). It seems to me the numbers make a little more sense this way.That said, I've rolled this out in about the worst possible way, so for now, I'm going to take the day to figure out what to do and then implement it tomorrow. I apologize again for the confusion this caused.

UPDATE: As I said above, it was not my intent to roll this out at this time. I still believe this to be a good idea, but it needs to be done in a MUCH more organized manner, so I'll be rolling back to the old stat tonight or tomorrow and then taking a more measured approach going forward. I apologize again for the confusion. ...

Posted by Sean Forman on March 25, 2010.

So it was changed, and then changed back.

Was anything more ever posted than this?

"ERA+ update: yesterday, I mentioned that we erroneously changed the definition for ERA+. I am still considering a long-term change, but for the short-term have changed it back. I apologize for the confusion."

http://www.baseball-reference.com/blog/archives/4718

There was a thread here about it, although I don't know how to find it. People totally freaked out. There even was a poster never seen before or since named something like "Change back to the old ERA+", which might have been the only personal crusade stranger than cardsfanboy's dozens of simultaneous weird crusades.

which might have been the only personal crusade stranger than cardsfanboy's dozens of simultaneous weird crusades.

Weird crusades? Which one is weird?

1. Stop calling an automatic double a ground rule double.
2. Stop using k/9 and go with k/27 (or strikeout percentage whichever is easier to find) since k/9 can be helped by pitchers who aren't that good and walk a lot or allow a lot of hits?
3. Judge Tlr by his actual actions, instead of what you think he is thinking when he says or does something?
4. Keep Jack Morris out of the hof?
5. End WPA....
6. Judge players by performance and not theoretical performance?
7. Instant replay done right(other words not the NFL way)
8. NFL is not vastly(or even demonstably more popular than MLB....TV Ratings isn't the only measure of popularity)

I was all for the proposed change in ERA+ at B-R, which would have meant a pitcher with an ERA+ of 125 was 25% better than park-adjusted league average, and therefore more akin to OPS+. I wish Sean had gone ahead with it, because there would have been a year of grumbling but everyone would have adapted by now simply because of the power that B-R has in the stat marketplace.

Thank you for the feedback. I know this discussion will never go away, but where I'm at now is that I'm not going to make a change to how ERA+ is calculated. I agree that something averageable is better, but I'm very loath to change stats once they've been on the site for 11 years.

Here are a couple of reasons.

1) I didn't create the stat, so changing the definition away from Palmer's original seems a bit out of my pay level.
2) The thousands of earlier references to ERA+ all become antiquated if I make a change.
3) There are probably a thousand or so people who would understand why we are making a change and take time to sort it out.
3b) I'm very loath to change how metrics are calculated, we get a lot of feedback when things get tweaked that we are essentially making things up, so making changes that aren't super, super necessary I think undermines our and by proxy sabermetric credility in the wider baseball audience.
3c) As an example in the past month, our internal web analytics show well over 1 million unique visitors, while only a small percentage are interested in OPS+ and ERA+ (10%), that's still 1,000 general fans for each hard core stathead.
4) They say in web servers it is impossible to be fast, cheap and super-reliable, so you have to focus on 2 of the 3 and do your best on the other. I would say for sabermetric websites it is hard to be consistent over time, cutting-edge and usable/understandable by a broad audience. We have chosen to focus on the first and third and do our best on the second one.

In terms of adding something new to the site. We could go in that direction, though the pages already have so much, jamming a whole lot more in there is not necessarily the best idea. FIP or real-live dips ERA would probably be the next thing to add.

1. Stop calling an automatic double a ground rule double.

This is the Jon Miller Crusade, and a noble and admirable one to be sure.

2. Stop using k/9 and go with k/27 (or strikeout percentage whichever is easier to find) since k/9 can be helped by pitchers who aren't that good and walk a lot or allow a lot of hits?

This is my own personal crusade, and thus even nobler and more admirable than the first.

EDIT: except that hey, wait a second, K/9 IP is the same as K/27 outs; you mean K/some number of BF, right? But that's going to be kind of arbitrary and confusing. So K% is the way to go.

I would treat these as separate issues. OPS+ is in fact nearly as accurate as wRC+, it measures what it purports to measure (players' contribution to run creation)

Aside from properly weighting OBP/SLG, wRC+ also includes SB/CS.

EDIT: except that hey, wait a second, K/9 IP is the same as K/27 outs; you mean K/some number of BF, right? But that's going to be kind of arbitrary and confusing. So K% is the way to go

I haven't seen it in a while, but it was k/27 plate appearances instead of outs. Agreed that it's confusing which is probably why it hasn't caught on, or why I can't find any mention of it in the past two years. The theory I guess is that it would look somewhat similar to k/9 in format, but be a more accurate measure...27 was probably arbitrary number to represent the minimum to face in a perfect game.

#28: Yes.

#30: Sean, that's fine in any given case, but I'm sure I don't need to point out to you that the reductio ad absurdum of a "we can't change how a stat is calculated because it'd be confusing, and we can't add new stats because there's no room" position would be the site failing to reflect future improvements in sabermetrics.

If BB-Ref changed it, I would definitely recommend renaming it. Put it where ERA+ is currently located. You can even keep ERA+ for a while, sticking it in the minor stat category.

If BB-Ref changed it, I would definitely recommend renaming it. Put it where ERA+ is currently located. You can even keep ERA+ for a while, sticking it in the minor stat category.

I think a while back, couple of years maybe, Sean did change ERA+. And it brought on a shitstorm of protest.

i have tried to make era plus hard to understand and failed. methinks people got way too much time on their hands

and if you have this much time how about finding a better option b before tossing out option a

key rule in management