500 Level Fan Cheat Sheet: Advanced Offensive Statistics

In yesterday’s “Weekly Things” post, I made note that despite the wonderful seasons being had by Josh Hamilton, Miguel Cabrera, and Paul Konerko, the leader in Baseball Reference’s WAR stat in the American League is none other than our own Brett Lawrie.

Not too long after posting, the Blue Jay Hunter noticed that Lawrie’s Fangraphs WAR is much lower than that of Baseball Reference.  He posted the reasoning behind the discrepancy in a great write-up on his site this morning.

But all of this talk about WAR, bWAR, and fWAR got me thinking heavily about advanced baseball stats, and really drove home the fact that I truly know very little about them.  I was an old school guy for so long, relying heavily on Batting Average and RBI’s.  It’s only recently that I have become converted to the wonders of WAR, OPS, and OBP.  But since there are so many other stats out there that I really don’t understand, I thought it would be educational for both myself and any readers out there in the same boat as me, to take a tour around some advanced stats.

Today I’ll start with a few offensive statistics: OPS, wOBA, wRC, and WPA.  Pitching and defense will be left for another day.


As I said, I was a traditionalist for a long time, relying heavily on batting average to get me through the wonderful world of baseball stats and player valuation.  And why not?  It had been the acceptable methodology for years, and the numbers were pretty straightforward.  An average of over .300 was great, .250 was usually pretty average, and .275 was good enough.  Plus there was a lot of mystique around certain numbers, like .400 and of course .200 – the Mendoza line.

But batting average is inherently and obviously flawed, and it doesn’t take a rocket scientist to figure out why.  A batter receives no credit for a walk.  A single is worth the same as a double, triple, or home run.  Quite clearly that is wrong and unfair.

OPS (which stands for On-base Plus Slugging) attempts to remedy that.  The formula is simple (obviously sum a players OBP and Slugging percentage), and it is easy to understand.  Anything above .900 is considered great, .700-ish is average, and under .600 is awful.  It is much more fair to a batter because a home run receives more credit than a single, and reaching base via walk or hit-by-pitch is also included.  Looking at the top-10 in OPS this season gives us a prety good indication of baseball’s top hitters:

It can also show us baseballs’ worst:


wOBA stands for Weighted On-Base Average, and was created by author Tom Tango for The Book: Playing the Percentages in Baseball.  It attempts to measure a player’s offensive contributions per plate appearance by giving a weight for each type of offensive event and scaling it to map to the same scale as OBP.  In other words, it is a modified OPS – a home run counts for more than a single, and walks and hit-by-pitch are also included.  The major difference is that each outcome is mapped to a pre-determined weight, a weight that is updated each and every season, and that is in proportion to the event’s actual run value.  The weights are different than those applied to OPS.  In OPS, a double is worth twice as much as a single (i.e. two total bases vs. one), but in reality a double isn’t twice as valuable.  For a better and more detailed definition of wOBA, please refer to the Fangraphs page.

In short, using the 2011 version of the formula, the weights were:

Unintentional Walks = 0.69

Hit By Pitch = 0.72

Single = 0.89

Double = 1.26

Triple = 1.60

Home Run = 2.08

Stolen Base = 0.25

Caught Stealing = -0.50

Using wOBA, here are this season’s best and worst hitters:


wRC stands for Weighted Runs Created.  It attempts to measure the number of runs created by each player for his team.  Obviously, since baseball games are won by scoring more runs then the other team, the higher the number the better.  It uses wOBA as a starting point, adjusts it to the league and scales it using a wOBA scale.  The final number is an estimated number of runs.  For example, a wRC of 10 means that the player alone was worth 10 runs to his team over the course of the season.  Again, Fangraphs has the formula in much more detail.

Once again, let’s look at the best and worst hitters in baseball thus far in 2012 ranked by wRC:


WPA, or Win Probability Added, takes wOBA one step further – and it is one crucial step.  The weights associated with each outcome in wOBA are fixed, meaning every double, every triple, every home run is worth the same amount.  WPA attempts to tie the outcome of the at-bat to the game situation, meaning a hit that has a greater impact towards helping a team win is worth more.  For instance, while in wOBA a home run is always worth more than a single, in WPA, there is a chance that a single might be worth more, if the single occurs in the bottom of the 9th with the bases loaded down by a run, and the HR is a solo shot in the first inning while trailing by five.

Makes sense right?

So how is it calculated?  I’ll save some space and refer you to Big League Stew, but in a nutshell, there is a large database that calculates the win expectancy of every game context, from being down by 30 to being up by 30, from the first to 30th innings.  Whatever play a batter makes to increase (or decrease) his teams win expectancy is attributed to him.  Say, for example, the Jays had a 25% chance to win a game.  Then say Brett Lawrie hits a solo home run, increasing Toronto’s chances to win up to 29.5%.  Lawrie is attributed a WPA of 4.5%, or 0.045.

When accumulated over an entire season it can give you a rough idea of how important a player is to any individual team.  However, since it is a counting stat, it should be interpreted with caution – players with more at-bats have the chance accumulate more plays.

Here is one final look at the best and worst hitters this season, this time based on WPA:



There are a few morals to this story.  One is that all of these stats are quite different, especially WPA, in comparison with WAR, as they don’t take into consideration the defensive side of the game.  That explains why Brett Lawrie is nowhere to be found, and also explains why Yunel Escobar is on the worst 10 hitters list in terms of WPA.

Second – and most important, is this:

Joey Votto is good.

Feel free to share any comments in the section below.  I’d love to hear about other stats you want to see discussed.

5 thoughts on “500 Level Fan Cheat Sheet: Advanced Offensive Statistics”

  1. Good writeup. Note, it’s “WPA”, not “wPA”. The little w in wOBA and wRC stands for “weighted”. WPA is Win Probability Added.

  2. Thanks for the clarification. I have amended the mistake (except for in the table – can’t find where I saved it!!!)

  3. Is that really Tom Tango commenting on your site? Impressive if so.

    When you look at the pitching side, if you can figure it out, I’d like to see an explanation of SIERA (“Skill-Interactive Earned Run Average”) I think that it takes the type of batted ball into consideration and maybe even how well the ball is hit in its newest iteration.

    Advanced stats are the best. They’ve really increased my appreciation of the game. That’s not to say I don’t still see the joy in going to a game, getting drunk and ripping on Adam Dunn for hitting .210 and striking out 250 times. But educated smack talk is best.

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