Creating TAVA

At this point, I have explained my useful, but problematic “Wins Added” (WA) score as well as my equally useful and equally problematic “Points Added”  (PA) score. One places too much emphasis on whether the end-result is a win or a loss, the other places too little emphasis on the same thing. It shouldn’t kill the suspense if you realized that I did the obvious: I combined them. This post explains how. And it’s in this post that many fans will have their eyes glaze over and go “huh?” and the actual math-nerds will go “That’s really all you did? Seriously?” This gives me the opportunity to leave everyone disappointed.

The problem with combining the scores is that I wanted to give each statistic exactly equal weight. The other issue is that both statistics are cumulative, meaning that the more games you play, the more wins or points you can “add.”

CONTROLLING FOR GAMES PLAYED

First, I divided both “Wins Added” and “Points Added” for each QB by the numbers of games they played where they received scores. At this point, each QB that I am measuring has a WA/Gm and a PA/Gm score. Thus, a QB who played 8 games won’t automatically be at a disadvantage.

WEIGHTING EACH FACTOR

Second, I calculated the average WA/gm, which should be around 0. As it turns out, it’s -0.008. Then, I found the standard deviation for WA/gm, which is approximately 0.152. I did the same thing for PA/Gm, which has an average of 0.391 and a St/Dev of 0.127.

My third step is to give each QB a “weighted” WA/gm and “weighted” PA/gm. This is done by simply calculating how many standard deviations a QBs WA/gm is above the average and doing the same calculation for the QB’s PA/gm. Now, I have two separate statistics that are each on a standardized scale. I combine them, and the sum is that QBs TAVA. Voila!