THE BOOK--Playing The Percentages In Baseball

Agree completely… It’s painful when people use OPS+ in articles that they intend to be rigorous or analytical. The only excuse is appealing to the masses, but if that’s the case, why not spend 2 sentences and tell them what wRC+ is.

Linear Weights it the gold standard for hitting metrics.  It’s set so that 0 is “average”.

wOBA and wRC are offshoots of Linear Weights.  Any one will let you derive any other.

wOBA sets the scale so that it matches the OBP scale.

wRC sets the scale so that it matches total Runs Scored scale.  That is, wRC has the same scale as Runs and RBIs.

wRC+ is simply wRC divided by the league average (times 100).  The end result is that the average player will get 100.  If you see 150, this means the batter created 50% more (theoretical) runs than an average hitter.

Definitely right.  How I see it:

OPS: Flawed but simple, easy to derive from commonly available stats and readily available on/derivable from mainstream media.

wOBA/wRC+: Better, more accurate stats but harder to calculate/find, especially on most media where they will not be referenced.

OPS+: Flawed and hard to calculate/find.  The worst of both worlds.

It just takes time and effort to internalize the distributions, which is what drives people to use an objectively inferior stat.  I know that wOBA = OBP, but I still have to stop and think about that every time I see a wOBA published.  Whereas I know what an 130 OPS+ represents, instantly.  I would have to look up what wRC+ scaled to.

I still prefer the triple slash line (for shape) for active players, though the recent drop in offense has thrown off my internal calibration.

Zack.  With a little experience you probably know that 130 OPS+ is very good but not great, but the derivation is counter-intuitive.  Lets say league averages for OBP/SLG = .320/.400.  A batter produces .400/.500, pretty good and each is 25% above average.  But the OPS+ is 150 not 125 because OPS+ is not an average, 150 does not mean the batter is 50% better than average.

wRC+ is on the same scale as OPS+ (at least the scale that OPS+ aspires to be on).

kds: The derivation may be counterintuitive, but it’s also correct (given the constraints that OPS+ places itself under).  An OPS+ of 150 does correspond to 50% better than league average--not at OBA and SLG individually, but at creating runs.  Standard OPS has a 2x relationship with runs (i.e. a team with an OPS of 1.1 relative to the league will score about 1.2 runs relative to the league).

I like Patriot/6’s parenthetical.

And yeah, OPS+ and wRC+ have the same scale.

It’s just that OPS+ is biased.  The bias is known, and it is even correctable.  I think I even offered a fix for that.  Something like:

1.2*OBP/lgOBP + 0.8*SLG/lgSLG

You do that, and all of a sudden, OPS+ is starting to look pretty good.

wOBA is obviously outstanding, and for people who think about baseball like the people here do, it’s easily the best shorthand offensive stat. For casual fans who don’t even know what a good OBP is, though, it can be difficult to grasp.

OPS+ is a good shorthand for dealing with those people. They can understand that Player X is 20% better at producing runs than the average player. Telling them that Player Y has a .310 wOBA is likely to make them think he’s an above-average player (since most people are conditioned to think in terms of BA). It’s just a matter of choosing the right stat for the audience.

mcsnide: the choice is not OPS+ or wOBA.  The choice is OPS+ or RC+. 

RC+ is better.  There’s no debate here.

In either case, no reader is going to calculate it, relying on B-R.com or Fangraphs to calculate for them anyway.

So, again, why does OPS+ exist?

Totally agree.  OPS+ is just people playing with numbers.  Unfortunately, it makes you (me, whoever) wonder about some of the other new stats.

OPS+ exists because B-Ref has huge reach, and it’s now part of their brand.  I can’t believe they would ever switch to wRC+.  But the truth is that very few people know how OPS+ is actually calculated, and if Sean tweaked the definition to make it more accurate, everyone would just happily use the new OPS+ numbers.  So if your goal is having people use more accurate numbers, I’d try to talk Sean into using 1.2*OBP/lgOBP + 0.8*SLG/lgSLG (or whatever you feel the most accurate coefficients would be).

I agree that OPS+ is now a brand more than anything.

And I agree that the best way here is for Sean to just use 1.2 (or whatever it should be ... 1.18 or something) for the OBP part and 2 minus that number for the SLG part.

I mentioned this on his blog a few years back, and I have alerted him to the existence of this thread.

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And, really, no one is going to notice a 2 or 3 point change here or there.

For example, if someone’s OBP component is 140 and his SLG component is 100, then the old way is:

140 + 100 - 100 = 140

The better way is:
140*1.2 + 100*.8 - 100 = 148

That’s probably as extreme as you’ll find it.  Most of the time, it’ll be a couple of points here or there.

"I agree that OPS+ is now a brand more than anything. “

That came off bad.  I mean that it’s a brand that still provides value if used to its limitation.  It’s a brand that has more analytic value, and fewer limitations, if corrected.

And changing to 1.2/0.8 would accomplish that.

Unfortunately, the park adjustments introduce significant errors for some hitters, which affects even these “accurate +” stats, so I prefer to use stats based on raw counting numbers, which include OPS (which are calculations based on them w/o any estimated parameters).

Doesn’t mean the + stats are not helpful if you are aware that park adjustments are not very meaningful for some hitters (eg LH pull hitters at Fenway tend to get hurt by park adjustments, and players like Ichiro and Tony Gwynns who played in parks that suppressed runs have + stats that may be inflated since the larger park they play in helped them, and SAFECO is not awful for LHH).

Also, OPS uses raw stats, and there are no uncertainties in the number of the various events (AB, 2B, HR, etc). For the accurate stats, even w/o park adjustments there are assumptions that go into the run value of various events which are assumed to be constants (league averages) but which in reality depend on park, team, batting order position and lineup position, game context, etc.  These numbers are in fact estimators with unknown uncertainty when applied to individual players (since we have no true value with which to compare).

OPS is simply an estimate of a players hitting ability and it is easy to understand and calculated, and is never changed once the season is over. 

I like all of the numbers really but there is no single number I trust to tell the whole story.  The accurate ones accuracy seems to be more a matter of faith than anything when applied to individual players, even if they are relatively accurate at the team level.

You ask “Why does OPS+ need to exist?” and then later answer your own question when you say “That’s why I support RC+ (though not the James version of Runs Created).”

Saying you’re using RC+ doesn’t yet specify what you’re doing, which you implicitly acknowledge.  For example, I know when I look at OPS+ that no baserunning has been factored in.  I don’t know what to think when someone gives me an RC+ number, unless they give me more information about what they are doing.

I agree that better stats give better information.  But, ironically, their continually evolving character has some drawbacks for quick communication.

Ben: you are saying that because OPS is known to not include SB and CS, then we know why it exists.  But because RC may or may not include SB and CS, then, we have more work to do to figure that out.

Fair enough.

Let me ask the question a different way: why does OPS+ need to exist as OBPcomponent + SLGcomponent minus 100, instead of a 1.2, 0.8 weighting scheme?

If OPS+ is used analytically, then why can’t the weighting be done closer to what is implied by Linear Weights?  Indeed, there is no effort at all to weight OBPcomponent and SLGcomponent in the right manner.

Indeed, there is no effort at all to weight OBPcomponent and SLGcomponent in the right manner.

That’s not entirely fair.  By weighting them equally, OPS+ represents a big improvement over OPS.  But to me, that’s an argument for Sean going the rest of the way and getting it right.  Since OPS+ isn’t OPS/lgOPS (as many fans assume it is), why not make it as accurate as possible?  The precise methodology is invisible to 90% of the users anyway.

Guy, you are right.  There is some effort to giving extra weight to OBP.

I’m presuming that Sean is relying on Pete Palmer’s original “PROD” equation (OPS+SLG) and his “Adjusted Prod” (or whatever he had called it).  So, in this case, Sean is applying a known previously published metric (from 30 years ago).

But, we’ve come a long way since then.  Going to 1.2 / 0.8 (or whatever is the best fit) is the right thing to do.

For what it’s worth, I’d be in favor of the 1.2/0.8 definition, too.

Tango enjoy your site and your analysis when you chime in on Bills site. Are Bill’s Abe Lincoln Scores credible? as in you a comparison tool or a legit stat that carries some value?

The Abe Lincoln scores are basically FIP.  I have a recent thread where I point that out.

so, how is rc+ calculated?

is the wRC+ presented at fangraphs acceptable?

Post 4 shows how to calculate wRC+

http://www.insidethebook.com/ee/index.php/site/comments/woba_primer/#4

And, of all things, I see that I said this in the main thread:

By the way, since Sean Forman is in charge of OPS+, any reason we can’t get him to change it to: 1.2*OBP/lgOBP + 0.8*SLG/lgSLG - 1, for OPS+?  If he did that, then OPS+ would be (almost always) superior to wOBA.  It gets the weights very close to wOBA, plus the added advantage of the park/league factors.  Such a simple change.  Listen, I have limited pull with Sean (indeed, in some cases, I have negative pull).  But, if you guys speak up, he’ll listen.  Write to him http://www.baseball-reference.com/feedback/ .

That was Dec, 2009, and I guess not enough people spoke up.

ok, but what version of RC? what’s the formula?

Fangraphs has this post:

http://www.fangraphs.com/blogs/index.php/wrc-and-wraa/

And I show the run values of OPS+ here:

http://www.insidethebook.com/ee/index.php/site/comments/abso_lutely_not/

OPS+ is, under the covers, something like 1.25*OBP+SLG.  Here is what those Linear Weights give you:
event 1.25*OBP+SLG
1b 0.46
2b 0.81
3b 1.16
hr 1.50
bb 0.26
out (0.28)

The gap between 2b and 1b should be .30 runs, not .35.  The gap between the 3b and 1b should be .58 runs, not .70 runs.  And the HR value should be 1.40 runs, not 1.50.  The BB walk should be .16 runs less than the 1B, not .20 runs.

As you can see, OPS+ is biased toward power hitters, notably HR, and biased against guys who walk.  Any study that uses OPS+ and doesn’t account for this bias is flawed if it is trying to distinguish between power and walks.

And if you use the 1.2 / 0.8 coefficients, you get something alot closer to Linear Weights.

what’s RC+?
-it’s the adjusted RC compared to the league.

ok, what’s RC?
- it’s a version of wOBA that’s scaled differently.

next question: what’s wOBA?
- got that one:(0.72xNIBB + 0.75xHBP + 0.90x1B + 0.92xRBOE + 1.24x2B + 1.56x3B + 1.95xHR) / PA

so, is wRC and wOBA the same thing, just scaled differently to look like something else? why scale at all?

why include reached base on error, but not intentional walks?

wRC and wOBA are the exact same thing as the tried-true-tested Linear Weights, but set to different scales.

LWTS is “runs above average”.

wOBA is scaled to OBP

wRC is scaled to total runs

wRC+ is scaled to total runs divided by league average

They are all the exact same thing.  It’s all based on whatever scale the fan prefers.  If wRC+ didn’t exist, and a fan WANTED a scale-to-100, then what’s he to do?  Well, go to OPS+.

If he wanted runs above average, and LWTS didn’t exist, then what?  We give the fan what he wants, but we make sure it’s the best that it can be.

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As for your other question:
http://www.insidethebook.com/ee/index.php/site/comments/reader_mail_of_the_minute_apparent_vagaries_in_woba/

As a side note in terms of comparing Linear Weights to wOBA: even though they are identical at its core, and the difference is just the scale (i.e., presentation), wOBA is much better for the masses.  Why?  Because I have never, ever, (EVER!) needed to explain the “average = zero = useless” that the detractors of Linear Weights have hammered over it for the last 30 years (and counting).

I say “wOBA = .333, PA = 600”, and people say “ok”.  If I say “LWTS = 0”, then people are like “???”.  And even if I say “LWTS = 0, PA = 600”, that only helps a little.

People are just not ready to see these two players:
LWTS PA
-5 100
-10 600

Listed in that order.  They just can’t.  They see that -10 may be worse than -5, but that -5 was done in only 100 PA.  They WANT To see -10 as the better hitter.  And they are probably right!

The above players in wOBA would be:
wOBA PA
.310 600
.270 100

And that is so much more appealing.

In wRC+, they would be:
wRC+ PA
86 600
42 100

too many stats.  Can we put Tango in charge of picking one and getting rid of the others?

I’m quite happy that we have ONE stat presented 4 ways:
- runs above average
- total runs
- runs along OBP scale
- runs indexed to 100 scale

Really, if all you care about is one scale, then just ignore the other 3.  That’s why the little “w” is there.  Pick one, and ignore the other three:
wRAA, wRC, wOBA, wRC+

There’s no need to push one over the other.  Everyone can be happy here, just as surely as rum, vodka, whiskey, and tequila can all co-exist, even if you always drink rum & coke.

comparing the career OPS+ leaders to the career RC+ is interesting. not much of a difference unitl you get to Dan Brouthers: 8th overall by OPS+, drops to 16th with RC+. anyone know what happened here?

I guess.  But if I didn’t read this blog and therefore know what wOBA is, I’d probably say, “screw it, OPS is close enough.”.  How many different brands of rum to serve might be a closer analogy....

Maybe wine would have been a better analogy for the various Linear Weights scales.

Continuing with the wine analogy, OPS+ is what happens when you don’t let the wine ferment long enough.

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The weird part is that Pete Palmer created both Linear Weights and OPS+, and used both in The Hidden Game, a sabermetric staple if ever there was one.

I actually had a long email talk with Pete on the issue of OPS+ two years ago.  He said the argument was about cleanliness over accuracy.  He cited as another example the runs to win conversion.  Most of us are happy with using “10”, even though a Pythag construct would be more accurate.

And, yes, he’s right.  If someone ELSE is going to figure out it, I would rather he do the tough job of figuring it out the more accurate way.  As long as I have a decent shortcut to use in a pinch, then when it comes time for the best thing, then do it the best way.

He agreed with me that it would be an improvement to OPS+ to modify the formula.

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I TOTALLY forgot I did this:

http://www.insidethebook.com/ee/index.php/site/article/proof_of_the_modified_ops/

Since what we REALLY care about is Linear Weights per PA, but what we ONLY have is SLG and OBP, then how can we convert SLG and OBP into LWTS per PA?  Well, we perform a simple regression:

LWTSperPA = x * OBP + y * SLG + z

And when we run a regression of the above data, we get a correlation (r) of .999.  What does that mean?  Well, if you have r=0, that means the variables (OBP, SLG) bear no relationship to the output (LWTSperPA).  If r=1, then we have a perfect relationship.  r=.999 is about as close as you could ever hope for.  We have, therefore, found a relationship that links OBP and SLG to Linear Weights.  So, what is that equation?

The core was this:
1.73*OBP+SLG

is 1.73*OBP+SLG the same (relatively) as 1.2*OBP+.8*SLG?  At first I thought no, but maybe it is…

To me, the only argument against this (and it’s a weak one) is that folks have developed an intuition around OPS (e.g. 1.000 = Manny Ramirez, etc.).

It’s not
1.2*OBP+.8*SLG

It’s:
1.2*OBP/lgOBP+.8*SLG/lgSLG

Once you realize that lgSLG=lgOBP*1.2something, then you get:
1.2*OBP/lgOBP+.8*SLG/(lgOBP*1.2)

So, now you have 1.2 as the coefficient for the first term, and .8/1.2something as the coefficient for the second term.

Or, 1.2 for the first and 0.65 for the second.  And 1.2/0.65 means a ratio of 1.85 to 1.

So, something like 1.17 and 0.83 might be a better balance (instead of 1.2 and 0.8).

Thanks.  Good to know.  I thought 1.2*OPS+.8*SLG= wOBA (relatively).  But this is not what you were saying.  1.2 and 0.8 “fix” OPS+, not OPS.

Right, the fix is to OPS+.  And the fix of changing to 1.2 / 0.8 (or 1.17 / 0.83) is going to be so buried deep in the process that no one is going to see it as anything other than an improvement.

So a co-worker of mine, that manages our accountant league slow pitch team, and myself have decided to use OPS+ (with the above corrections) and wOBA on our spreadsheet that tracks our teams stats (we’re geeks). He thinks that OBP is more valuable in slow pitch than slugging (even more so than the 1.2 and .8 weightings suggest). My question is this: to those of you that play in a beer league low talent slow pitch league (or anyone else), what weighting would you suggest using for both OPS+ and wOBA? Or would you leave them unchanged?

I understand there are far more issues than the weighting, but let’s leave those aside for now. Especially the ones relating to what the hell is wrong with us for calculating OPS+ and wOBA for a beer league slow pitch team.

Put your league stats here:

http://tangotiger.net/markov.html

Hit Calculate.

And then cut/paste the last chart.  Then I can give you your answer.

Sorry about the formatting, I can’t seem to get it to space out neatly.

Thanks Tom!

(Ed note: use the tags {code}...{/code}, but use the [ and not { characters, for better formatting)

First off, as you can see, BaseRuns does a fantastic job of capturing the league environment.

Anyway, we see the gap between a walk and a single is .10 runs (instead of the .16 we are used to).  And the gap between singles and extra base hits is about .15 to .20 runs (instead of the .30 we are used to).

In short, instead of 1.7*OBP+SLG that you’d have in MLB, you’re probably looking at 3*OBP+SLG in your league.

I don’t see any point in dividing by lgOBP and lgSLG, because you are not doing cross-era comparisons, are you?

You can also try to get more specific by following the steps here:

http://www.insidethebook.com/ee/index.php/site/comments/why_does_17obpslg_make_sense/

Thanks Tom (I’ll read the suggested post this afternoon). We now have the most complicated stats spreadsheet in our league!

Actually it is likely we have the only stats spreadsheet in our league.

As for comparing across eras, I will probably be working at the firm for the next few years and we may want to do this in the future

Now all we need to do is higher a few full-time stringers to collect batted ball data and we can get started on evaluating defense!

Thanks again.

By the way, if you want to do wOBA, it would look something like:

wOBA
= 0.90 * BB
+ 0.95 * 1B
+ 1.05 * 2B
+ 1.10 * 3B
+ 1.20 * HR

Thanks, we now have wOBA and OPS+ (correctly weighted) tracked on our spreadsheet.

All of this has led me to one clear fact: I am a terrible slow pitch (and all other forms of baseball) player.

Tango/45: I should note that that’s the numerator.  The denominator is PA.