Why the Rays Underperformed Their WAR numbers I: Intro to wRAA, wOBA, RE24 and WPA

Last week DRB user _David_  questioned if bad luck with strand rates was the reason the Rays won 84 games in 2009 vs. their Fangraph's WAR total of 51 which would equate to about a 98 win season. I'm going to attempt to look at some descriptive (not predictive) stats to add some context. If anything looks incorrect, please speak up and we can all use this as a learning experience.

The batting component of WAR consists of park-adjusting wRAA (runs above average) based on wOBA (weighted on-base average). wOBA consists of using linear weights of each type of event where a batter reaches base successfully  relative to the total plate appearances. Per the Book, the formula is:

 (0.72xNIBB + 0.75xHBP + 0.90x1B + 0.92xRBOE + 1.24x2B + 1.56x3B + 1.95xHR) / PA

The next step is to figure out how far above/below average a player's wOBA is using the formula: (wOBA – lgwOBA) / wOBAScale * PA, where the wOBAscale typically is around 1.15. This gives a pretty idea of the player's value at the plate, hence why park-adjusting wRAA results in the batting component of WAR values. What this stat does not do is tell us anything about how the player fared situation-ally based on the 24 possible base/out states or situational leverage based on the score margin and inning. For that we have two more stats; RE24 and WPA.

RE24 is a player's aggregate runs above average based on the 24 base/out states. It marks the change in the team's run expectancy for the inning before the plate appearance and after.  

Per Tango:

To begin an inning, a single or a walk will raise the run expectancy from .555 to .953. The player would be credited with an RE24 of .398. If a player came up with two out and the bases empty and draws the same single or walk, they would be raising the inning's run expectancy from .117 to .251. The payer would be credited with a RE24 of .134. Is the player who walked with no one on superior to the player who walked with two outs? No, but it describes to us the significance of the event.  What aspect does RE24 fail to describe? It does not account for how much change in run expectancy impacts a team's chance of winning. Hitting a solo home run in the 4th inning down 10-0 provides the same RE24 as a walk off solo-shot in the bottom of the 10th inning.

That's where WPA comes in. It involves the same base/out states as RE24 but it also takes into consideration the margin of score and the inning through the use of a leverage index. Again, we aren't measuring player's ability so much as telling a story of what happened. There is little difference in skill between a solo shot in the 3rd vs. a walk-off grand slam, but the relative magnitude is captured by WPA.

How can we apply these stats to the 2009 Rays?  Move forward to part II. In the meantime, if any of this looks incorrect, please speak up. Or feel free to ask additional question you may have. If no one on staff has an answer I'm sure R.J. can dig through is little blackbook and find someone who does.