Counting Rocks: There are so many statistics....which one should I use?

Surprise, Rowbots!  RockiesMagicNumber is still in Toronto slaving over his coverage of the World Baseball Classic, and I'll be "out of office" next week, so I'm subbing in this week to offer a slightly different version of Counting Rocks.

Baseball is the game for statistics junkies.  It just is.  No other sport lends itself so well to grading players with numbers - after all, no other major sport is a compilation of one-on-one battles (insert NBA joke here).  Analysts have responded to the possibilities of stats.  The glut of statistics currently floating around is mind-numbing: OPS, pLI, WPA, BABIP, TUIPOCO (I made that last one up - though I suppose it could start for Times Used Inside Pitch of Curveball Origin). 

It's confusing.  Wouldn't it be nice if you knew of one sensible, straightforward, effective stat that we could compare every hitter with? Well, there is one, and it's wOBA.

What's wrong with the traditional statistics?

• RBIs and runs are very dependent on the activities of the other players in the lineup.  It's not fair to judge a player on that. Would anyone take Nate McLouth before Grady Sizemore?  No.  FAIL. 
  
• Chicks may dig the long ball, but home runs only evaluate a hitter one-dimensionally.  Does anyone want Chris Coste instead of Ichiro?  No.  FAIL.
  
• Batting average is nice, but it fails to take into account the type of hit.  Is Clint Barmes more valuable than Brad Hawpe?  No.  FAIL.
• Slugging percentage is good.  It takes into account the total bases per at-bat.  Yet this ignores walks completely and doesn't account for how often a player gets on base (which increases his chance of scoring).  Is Aubrey Huff really more valuable than Matt Holliday?  No.  FAIL.
• On-base percentage does the opposite of SLG.  It takes into account the frequency of reaching base but doesn't award the hitter for extra base hits.  Do you want Ryan Theriot over Chase Utley?  No.  FAIL.
  

That brings us to OPS, the statistic most often cited as the all-inclusive go-to statistic.  This is simply OBP added to SLG.  It factors in two of the most important contributions a batter can make - getting on base, and moving a lot of bases when he does.  This means a player with a good OPS must be either quite good at both OBP and SLG, or exceptionally good at one.

Yeah...I understand that.  But what then is wrong with OPS?

It sounds like OPS is as good as we can get....but not so fast. 

OPS operates on a fundamental fallacy that SLG and OBP are equally important in contributing offensively.  In the complex world of statistics, what are the chances that SLG and OBP are exactly equivalent in value?  It turns out they are not, and it's not close.

In 2003, Moneyball documented that each point of OBP was close to THREE times more important than SLG in creating runs, and after all, the name of the game is to score runs.  Analysts knew OBP was more powerful than SLG, but that finding was twice what anyone thought at the time!

Here, we see the failure of OPS.  Its weakness is not as grave as other statistics, but OPS unfairly favors power hitters and penalizes high OBP hitters.  This effect can be seen in a table of Rockies leaders later in this column.   Clearly this weighting factor of three should be taken into account.

Join me after the jump to see how it all comes together.

The Derivation of wOBA

JC Bradbury, author of the blog Sabernomics, published The Baseball Economist in 2007 with more data and found that the factor found in Moneyball was actually closer to 2.33. Tom Tango, co-author of The Book, proposed 2.0.  We'll go with Tango's number, since he actually developed what is known now as wOBA (or weighted on-base average).  Using that weighting factor, we can then express wOBA as:

This looks better.  This provides two improvements over OPS.  It applies the appropriate weight to OBP for one.  Also, the 3 in the denominator scales wOBA down to a number that makes more sense to us, instead of the OPS that is often over 1.000. (what does that mean anyway?).  It is in the range of OBP, which can be seen later in the column.

This formula can be perfected further.  It turns out, the reason OPS fails is actually a faulty definition of SLG.  This statistic is based on total bases, assuming that a triple is three times as important as a single, a double exactly twice as important as a single, etc.  As was the case with OPS, these whole number coefficients don't hold water in practice. 

Tom Tango found the correct coeffiecients through extensive statistical analysis to be 0.77 for singles, 1.08 for doubles, 1.37 for triples and and 1.70 for home runs.  That's quite different than the 1, 2, 3 and 4 used in SLG and consequently, OPS.

These coefficients and a few other statistical adjustments come into play for the fully polished empirical wOBA equation.  Check out the gritty details here if you're interested.  For you ultra-nerds, you can follow this and calculate a fine-tuned wOBA on your own. The rest of you will be happy to know that FanGraphs just added wOBA to their data in November.  You could also use the shortcut formula displayed above.  It will get you within a couple points.

So there you have it.  The holy grail.  It includes your on-base skill and your power skill, meticulously defined to the last detail.  It is a rate, so you can safely compare two players with a different number of at-bats (provided they have sufficiently many).

A Case Study

Just for fun, let's look at the wOBA of Rockies players for context.  Note:  .333 is about the league average.  A wOBA below .300 is a very poor hitter, between .300 and .333 is below average, between .333 and .370 is above average, between .370 and .400 is a very good All-star caliber player, and above .400 is a superstar.

Note that the wOBA column does not sort in the same order as the OPS column.  As foreshadowed earlier, a power hitter like Ian Stewart gets too much credit with OPS and comes down a little bit with wOBA.  Also note how ridiculously close Clint Barmes and Jeff Baker are on all counts.

Extracurricular Activity

wOBA also lends itself directly to two other fun statistics.  You can calculate the exact number of runs a hitter creates (wRC).  This statistic a countable stat - players with more ABs will look better here.  The second statistic is wRAA, or the runs created above average.  This statistic is less dependent on at-bats, as you will see.  The details of calculating these statistics, I will leave to another day or your own initiative. 

Certainly, this is a sobering table, as Matt Holliday in a down year was better than any two other players combined.  It is also plain to see that Garrett Atkins created a lot of runs by wRC, but his production in wRAA was barely more than an average player - basically, his production was just a function of at-bats.  And a parting shot:  Willy Taveras had a wRAA of -12.4.  Yes.  That is negative.  He basically negated the contribution of Ryan Spilborghs.

Conclusion

wOBA is a powerful and accurate assessment of a hitter.  If nothing else, just visit the wOBA rankings every once in a while.  If you're a little more adventurous, you can look into wRC and wRAA.   And if your interest has been incredibly piqued, I recommend you read The Book, The Baseball Economist, and/or Moneyball.

I hope this was informative and not too cumbersome to read through.  Good luck on your slow conversions to becoming stat-heads!