Quick summary for those who have no idea what the hell I'm talking about:

Over in the thread about how great Hanley is, the use of OPS to justify Hanley's greatness came up. At which point, some of us began pointing out the shortcomings of a stat like OPS http://www.marlinbaseball.com/forums/index...t&p=1484337 .

 

Then, I originally posted a presumably more accurate ratio after crunching some numbers and testing correlations. The post can be found here: http://www.marlinbaseball.com/forums/index...t&p=1484576.

 

In short the whole point behind all of this is that there is some value of X out there where (X*OBP) + SLG = A better OPS stat. I'm trying to solve for X.

 

/end summary

 

So I've run the numbers for the 1997-2006 era, which gives me a sample size of 327 full seasons to work with instead of the 30 partial season I used in the last thread. When I run a multiple regression on this data, I get a different coefficient. Previously, we had 1.342. With more data, I get 2.094. That means that an increase of say .010 in OBP is roughly 2x as valuable to a team as a .010 increase in slugging percentage, and a more valuable OPS stat can be derived from the formula (2.094*OBP) + SLG as opposed to the standard OBP + SLG.

 

With this data, my R-Squared value also went up to .908. An R-Squared value is simply a score from 0 to 1 that measures how well two sets of data correlate with one another. If you were to compare something like the number of thunderstorms there were in Moscow last year to the number of times I went to Burger King, the correlation would be close to, if not actually, 0 because the two events are about as unconnected as it gets. On the other hand, something like the number of left shoes you own compared to the number of right shoes you own would be a perfect correlation (R-squared of 1.0) barring the loss of a shoe or something. As it is, .908 is a really good correlation and indicates a strong connection between this new OPS formula and the number of runs a team's offense scores.

 

I put all of this information in a chart like the one I used in my earlier post, and included some other stats just for reference. Unlike the last time, I didn't supply 4 different variations of OPS with different coefficients. I only included an OPS stat with the coefficient I derived and the standard OPS stat (OBP+SLG). Instead of multiple OPS numbers, I included batting average and EqA.

 

I included batting average to give everyone an idea of just how bad it is as an independent measure of total performance. (The R-Squared value for batting average is .6678.) I included EqA because it's one of those all-encompassing stats and I was curious to see how well a modified OPS stat matches up to something like EqA. To clarify, EqA is a stat that tries to take into account everything a player can do as a hitter (hit for power, steal bases, get on base, etc.) and quantify that in a statistic that looks a lot like batting average so it's easy to understand. Interestingly, really big numbers (like team totals for a season) seem to drive EqA values way out of whack. The relative values remain consistent (i.e. good run scoring teams have higher EqAs than low run scoring teams) but the actual values range in the .700s. I very well may have made some mistakes in my analysis, but I think it may just be that EqA, since it's not a true average in the mathematical sense, stops looking like batting average values once you throw in big numbers. With all that said, EqA, as I calculated it, still has a strong correlation (R-squared of .9038).

 

Here's the chart:

 

 

 

I'll wait until other people start discussing this to mention some other things as this is already a novel of a post.

Awesome work. Any chance you can try out the expression Fox mentioned in his post: (1.8)OBP + SLG/4?

Awesome work. Any chance you can try out the expression Fox mentioned in his post: (1.8)OBP + SLG/4?

 

Just ran the numbers. The GPA stat Fox mentioned (1.8*OBP)+SLG/4 gives you an R-Squared value of .9073 compared to the .9038 of EqA and the .908 of (2.094*OBP) + SLG. I didn't expect much difference from the GPA stat because the divsion by 4 doesn't alter anything. As I understand it, the divsion by 4 is to the whole amount (not just SLG) and it's just to have it more in line with a batting average value. So, it's no different than testing out (1.8*OBP) + SLG alone.

Yes. The division of 4 is just to make a batting average esque number. GPA is just a quick, handy reference tool and a bare bones way at deciphering OPS and comparing two player's similar or different OPS.

 

Great work CC as always. I'm enjoying this.

Obviously I haven't done any of this research myself like you have, but this seems like a reliable way to assess the connection between the two statistics:

 

http://danagonistes.blogspot.com/2005/08/d...ta-and-ops.html

 

It talks a little bit about the famous depodesta claim in moneyball that a point of obp is 3X as important as slugging and discusses one study that says the weight should be a point of obp is 1.7 times more important than a point of slugging. Maybe you could use 1.7 as your coefficient and run the r-squared again to see if we are closer. Also, even though this sounds stupid considering you looked at a lot of seasons, maybe you should expand your search a little outside of the recent power era.

Obviously I haven't done any of this research myself like you have, but this seems like a reliable way to assess the connection between the two statistics:

 

http://danagonistes.blogspot.com/2005/08/d...ta-and-ops.html

 

It talks a little bit about the famous depodesta claim in moneyball that a point of obp is 3X as important as slugging and discusses one study that says the weight should be a point of obp is 1.7 times more important than a point of slugging. Maybe you could use 1.7 as your coefficient and run the r-squared again to see if we are closer. Also, even though this sounds stupid considering you looked at a lot of seasons, maybe you should expand your search a little outside of the recent power era.

 

If you use 1.7, you get an R-squared value of 0.9066. Still below what you get when you use 2.094. Maybe if I describe what I mean by regression I can clear up some of the confusion about other possible coefficients. When I run the data through data analysis software, I basically tell it: Take the formula A*OBP + B*SLG + C = Runs Scored and find the best values for A, B, and C. Since I'm not looking to accurately predict actual runs scored totals, the only important values for me are A and B because B/A gives me the OBP:SLG ratio I'm looking for. What regression and the software allow me to be certain about is that there is no better coefficient for the provided data I give. As far as predicting runs scored from OBP and SLG from 1997-2006, there is no better coefficient than 2.094; that much I can be sure about. That's why I included EqA which includes things that OPS doesn't (steals, hit by pitch, sacrifice hits, etc) to see if stats outside of the OPS world are more suitable.

 

You raise a good point with the time period of my study. As large as my sample size may be, I've obviously focused on a particular era of baseball (The Home Run Era). That was intentional. Places like Baseball Prospectus and other SABR blogs out there have run the same regressions I've run for all season since like 1871 til the present day. When they do that, they get slightly different numbers than the ones I'm using. Check here for an idea: ( http://www.baseballprospectus.com/article.php?articleid=2596 ).

 

However, I think that including such a big sample size is potentially hazardous as well. With their stats for instance, batting average is a much more reliable predictor than I gave it credit for. There's a reason for that. In the early eras, power hitting wasn't all that common. You had Babe Ruth and then you had alot of slap hitters. (Gehrig and Co. notwithstanding). So, slugging percentages were much closer to batting averages than they are today. For example, if baseball was comprised entirely of Juan Pierre like players, batting average would be a fine measure for performance because there isn't a whole lot of difference, normally, between his slugging percentage and batting average nor does he walk a whole lot. However, in the era we're in right now, those differences exist and they're significant. Therefore, you can find figures and coefficients which may be more accurate on average for all eras and my formula is probably less reliable if you use it to measure performance in the 1960s, for example, but I think that it's more accurate than those other formulas if you want to assess the performance of today's players.

Was this using the "raw" eqa formula or is it era adjusted?

Was this using the "raw" eqa formula or is it era adjusted?

 

Raw EqA. Which would explain the values in the .700s, thanks.

I'd be interested in seeing how era-adjusted EqA adds up in correlation to runs scored, but I have no clue how to calculate that, as I can only find the formula for the raw EqA.

 

Also for those interested, top-15 with the adjusted OPS (parentesis = their standing in normal OPS)

1-Bonds-1.58(1)

2-Cabrera-1.49(2)

--Chipper-1.49(4)

4-Ortiz-1.48(5)

5-ARod-1.47(3)

6-Mags-1.46(7)

7-utley-.145(6)

8-Pujols-1.44(9)

9-Howard-1.43(8)

10-Posada-1.42(12)

11-Holliday-1.41(10)

---Thome-1.41(15)

13-Pena-1.39(13)

1--Hanley-1.38(14)

15-Fielder-1.38(11)