## GPA: A Better OPS

"When someone asks me how much change I am carrying, I don't reply, 'eight coins'." - Paraphrased F.C. Lane quote from 1916 on why numerical weights are important in baseball.

Fortunately, OPS has surpassed batting average over the past five years as the quick and dirty single number most often used to judge a hitter's worth. It has even gained acceptance amongst the mainstream media and semi-educated fans. There are plenty of more sophisticated measurements out there, ones that paint a nearly 100% picture of offensive contribution, but these statistics are just that; much more sophisticated, hard to grasp intuitively and sometimes impossible to calculate by hand, much less on the fly. That's why OPS is so useful, it relies on information, on base percentage (OBP) and slugging percentage (SLG), that is easy to find and the math involved, adding the two numbers, is basic enough for anyone to do.

However, OPSs greatest strength is also its greatest weakness. By just adding on-base and slugging percentages, OPS puts them on equal footing; but we know from the more advanced statistics that on base ability is more crucial to run scoring than slugging. We already have enough complicated measurements, so what we would like to see is a simple measure like OPS but one that incorporates a better balance between OBP and SLG. This is where GPA comes in.

Lets steal borrow some stuff from Tango and examine six prototypical players all specially designed to contribute equal projection (according to linear weights). These players will range from all-power and no walks to no-power and all walks.

What we would like to come up with is a simple measurement that would mirror the equality that we see here in BaseRuns (a run modeling system generally regarded as the best measurement for offensive production). As it turns out (read Tango's article if you want the full treatment), we can improve our OPS metric significantly just by upping the factor on OBP. OPS as it's known can be written as: 1*OBP + 1*SLG and what we want to do is increase the 1 in 1*OBP until we hit upon the proper coefficient to create an equal weighting. Stealing again from Tango, his conclusion: I would expect the best-fit equation to fall somewhere between 1.5 and 2.0. If you must rely only on OBA and SLG to establish a player's current run production, it would probably be easiest to do 1.5*OBA+SLG.

I agree Tom, 1.5*OBP + SLG is still simple enough to do in your head or back of the envelope, but we also care about figuring out that exact number between 1.5 and 2.0 that gives us a golden ratio, if you will, of OBP to SLG. Lucky for us, other people have already done this work independently and the number they all tend to settle on is 1.8; meaning that for run scoring purposes, OBP is 80% more valuable than SLG. OPS is already on a bit of a weird scale, and adding another 80% weight to OBP is just going to make it weirder since we're not used to it. It turns out that we can scale this weighted version of OPS by dividing it by 4 and the result leaves us close to a very familiar scale, the one we use to judge batting averages. This new metric,

(1.8*OBP + SLG) / 4

is the creation of Aaron Gleeman which he coined Gross Production Average (GPA), and is available for every player at The Hardball Times. Below I list some handy information concerning GPA from 2007 data.

AL Average GPA: .258
NL Average GPA: .256
Observed Standard Deviation (sigma-hat): .037

So .257 (you can call it .260 for ease of use) is a good approximation for league average with a standard deviation of 37 points. That means 2/3 of players in 2007 had a GPA between .220 and .294 giving us some guidelines for classifications of GPA thusly (note these do NOT account for position):

> .331 = Possible MVP
.312 - .331 = Star
.294 - .312 = Great
.275 - .294 = Good
.257 - .275 = Above-Average
.239 - .257 = Below-Average
.201 - .220 = Horrible
.182 - .201 = Black Hole
< .182 = You play for the Giants

Finally, some positional averages, again from 2007, which you should combine with the above rankings to properly weigh a player:

C:  .242
1B: .276
2B: .257
3B: .265
SS: .250
LF: .269
CF: .257
RF: .271
DH: .271
PH: .227

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