# Expanded Four Factors: The Average Player

In case you missed it, this morning I went over the mathematics necessary to take the four factors of hitting to the next level. Now, it’s time to put it to good use.

As Eric pointed out in the comments section, the way that the math is done, we could figure out how much a change in one of the factors changes a player’s wOBA by taking the derivative of the new formula for wOBA derived from the four factors equations. However, that’s a lot of work, so instead, as he suggests, I’m going to do this analysis numerically using a little program called Microsoft Excel.

Let’s test run this method on the simplest of targets: the league average player. In this case, we’ll use the league average player from 2009 MLB. In 2009, the league average BB% was 8.9%, the league average K% (K/PA) was 17.9%, the league average POWH (XB/H) was .595, and the league average BABIP was .299. The following chart shows how changes in each variable changes the player’s Four Factors Equivalent wOBA (ffwOBA).

In order to more easily visualize these on the same scale, I looked how changing each statistic by one standard deviation impacts ffwOBA. In this case, one standard deviation for BB% is 3.7%, for K% it’s 7.3%, for POWH it’s .257, and for BABIP it’s .049 points.

The slope of these lines tells us how sensitive wOBA is, at least as predicted by the four factors, to changes in each stat. BABIP is the steepest, as changing BABIP by one standard deviation changes wOBA by 41 points. Next is POWH, which although it isn’t perfectly linear, it’s close enough that we can treat it as such. Changing POWH by one standard deviation changes wOBA by 33 points. One standard deviation change in K rate changes wOBA by 26 points. A player’s wOBA is by far least sensitive to BB%, as a one standard deviation change in BB rate only changes wOBA by 13 points.

My explanation for the small changes in wOBA brought upon by BB rate changes is that increasing BBs, at least in this model, reduce all favorable outcomes (all hits) as well as reducing outs. The reduction in outs is enough to mean that an increase in BB% is a good thing. However, decreasing K% only means decreasing outs, increasing POWH means increasing 2B, 3B, and HR at the expense of 1B, which is a high net increase, and increasing BABIP means increasing all hits at the expense of outs, which is clearly the best of all results.

Through the rest of the week, I’ll be taking a look at some interesting players, hopefully examining how this method performs at the extremes.

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