The narrative concerning Josh Donaldson has been established for the moment. He was a piece in the deal that sent Rich Harden from Oakland to Chicago in July of 2008. He was converted to third base from catcher gradually between 2009 and -12, taking up the former position in a full-time capacity at some point in 2012. Generally speaking, he demonstrated some promising offensive and defensive skills, but was never considered a top prospect. Then, in 2013, he produced an MVP-type season.

That Donaldson outperformed expectations is a fact. How he did so, though — like, in what skills precisely he demonstrated improvement and to what degree he demonstrated it — this sort of thing merits further consideration, I’ll suggest.

To begin that further consideration, we start with following — namely, a collection of projections for Donaldson entering the 2013 season. While the methodology for calculating each of them is different, the principles informing all four are roughly the same, including some combination of past performance, allowance for the player’s current place along the aging curve, defensive ability, etc.

Here are his projections for 2013 (note: HRC% is home-run rate on contact and is basically just home runs per batted-ball):

Team PA BB% K% HRC% BABIP BsR Fld+Pos wOBA Off Def WAR WAR600 Steamer 403 7.9% 18.7% 4.4% .279 0.1 4.0 .319 2 4 2.0 3.0 Oliver 516 7.6% 22.5% 5.0% .290 -0.3 3.0 .318 1 3 2.2 2.6 Fans 516 7.4% 19.4% 4.2% .291 0.1 9.0 .320 2 9 3.0 3.5 ZiPS 535 7.3% 22.1% 4.0% .277 -0.3 5.0 .297 -8 5 1.5 1.7 Avg 493 7.6% 20.7% 4.4% .284 -0.1 5.3 .314 -1 5 2.2 2.7

One will note that Donaldson wasn’t projected to produce an entirely anonymous season. His combination of position, control of the strike zone, and slightly above-average power suggested that, given the requisite playing time, he had a very real chance of recording an average major-league season.

Here’s how his actual 2013 season compared to the projected one, however:

Type PA BB% K% HRC% BABIP BsR Fld+Pos wOBA Off Def WAR WAR600 Projected 493 7.6% 20.7% 4.4% .284 -0.1 5.3 .314 -1 5 2.2 2.7 Real 668 11.4% 16.5% 5.0% .333 1.1 12.1 .384 37 12 7.7 6.9 Diff 176 3.9% -4.2% 0.6% .049 1.2 6.9 .071 38 7 5.5 4.2

What one finds is that, per 600 plate appearances, Donaldson was about 4.2 wins better than projected. Of those 4.2 wins, the contributions from both baserunning (BsR) and also defense (Fld+Pos) are rather obvious — about 1 run and 5-6 runs better than projected, respectively, for every 600 plate appearances. Those figures only account for rather a small fraction, however — about 0.6 or 0.7 wins — of Donaldson’s overall production relative to his preseason projections.

What I’ve endeavored to do below is account for how his performance in the four other offensive metrics of consequence — walk rate, strikeout rate, home-run rate on contact, and BABIP — contributed the remaining value to Donaldson’s excellent season.

For each of those metrics, what I’ve done is to re-imagine Donaldson’s 2013 season as if he had played exactly as projected except for the metric in question, for which I have substituted Donaldson’s actual 2013 mark. I’ve then used a combination of Bradley Woodrum’s De-Lucker and a generic WAR calculator to estimate the value, in WAR, of Donaldson’s improvement in that metric alone.

Below are the results of that exercise.

Walk Rate

In over 700 Pacific Coast League plate appearances between 2011 and -12, Donaldson walked about 10% of the time. It makes sense, then, that a projection system would produce a major-league equivalent of something lower than that. In fact, this was entirely the case: all four of the systems above projected Donaldson to walk in something like 7%-8% of his plate appearances. Surprisingly, however, Donaldson improved upon his minor-league walk figures as a major-leaguer, recording a rate of 11.4% this year — adding 12 points of wOBA in so doing.

Type PA BB% K% HRC% BABIP wOBA Off WAR WAR600 Proj 493 7.6% 20.7% 4.4% .284 .314 -1 2.1 2.6 BB% 493 11.4% 20.7% 4.4% .284 .326 4 2.7 3.2 Diff — 3.8% 0.0% 0.0% .000 .012 5 0.5 0.7

Value Added: +0.7 WAR per 600 PA

Strikeout Rate

It’s almost always the case that a minor-league hitter will both walk less often and also strikeout more often after graduating to the major leagues. As one will note above, Donaldson was able somehow to improve upon his recent minor-league walk rates this season with the A’s. A nearly similar thing happened with Donaldson’s strikeout rates, as well: the third baseman, who struck out in 17.9% of his 2,302 minor-league plate appearances, recorded a slightly better rate this season in his first full-length major-league season, adding nearly a win per every 600 plate appearances.

Type PA BB% K% HRC% BABIP wOBA Off WAR WAR600 Proj 493 7.6% 20.7% 4.4% .284 .314 -1 2.1 2.6 K% 493 7.6% 16.5% 4.4% .284 .328 5 2.8 3.4 Diff — 0.0% -4.2% 0.0% .000 .014 6 0.6 0.8

Value Added: +0.8 WAR per 600 PA

Home Runs on Contact

Generally speaking, if a plate appearance hasn’t ended in a walk or strikeout, then the result is a batted-ball in fair territory somewhere. A certain percentage of these batted balls become home runs — about 3.5% of them in the major leagues, it appears. That Donaldson was projected to produce a home-run rate on contact of about 4.4% (i.e. about 0.5 standard deviations above the mean) while playing half of his games in rather a pitcher-friendly environment suggests that there was some optimism already among the four systems here regarding his power. Donaldson still managed to outperform his projections, hitting 22 (as opposed to 19) home runs for every 600 plate appearances, adding about half a win per 600 plate appearances above what might most reasonably have been expected.

Type PA BB% K% HRC% BABIP wOBA Off WAR WAR600 Proj 493 7.6% 20.7% 4.4% .284 .314 -1 2.1 2.6 HRC% 493 7.6% 20.7% 5.0% .284 .321 2 2.5 3.0 Diff — 0.0% 0.0% 0.6% .000 .007 3 0.3 0.4

Value Added: +0.4 WAR per 600 PA

Batting Average on Balls in Play

On the 96% of occasions when a batted ball doesn’t leave the park, it becomes a ball in play. Of the ideas which have most impacted baseball research over the last 20 or so year, among the most important is the discovery that balls in play are converted into hits at a pretty regular rate — about 30% of the time, that is. That said, it’s also apparent that batters exercise some degree of control over batted balls — just not necessarily in such a way as can be measured reliably over the course just of one season. Probably in part due to Oakland’s wide expanse of foul ground, Donaldson was projected to record a slightly below-average .284 BABIP — a figure which he surpassed by a considerable amount, producing nearly two extra wins per 600 plate appearances as a result.

Type PA BB% K% HRCon% BABIP wOBA Off WAR WAR600 Proj 493 7.6% 20.7% 4.4% .284 .314 -1 2.1 2.6 BABIP 493 7.6% 20.7% 4.4% .333 .347 13 3.6 4.4 Diff — 0.0% 0.0% 0.0% .049 .033 14 1.5 1.8

Value Added: +1.8 WAR per 600 PA

Summary and Totals

As stated above, the objective here has been to understand more clearly in what ways the 2013 version of Josh Donaldson outperformed expectations and how that performance might be understood, on a slightly more granular level, in terms of WAR. Also as stated above, the value of Donaldson’s baserunning and defense in wins is apparent (even if the calculation of defensive runs remains an inexact science). What has been less clear is the precise value of Donaldson’s improvement in the four other offensive categories that inform WAR — namely, walk rate, strikeout rate, home-run rate on contact, and BABIP. Below is a table which summarizes both Donaldson’s raw improvement in each metric (relative to his projections, that is) and also the estimated value of that improvement in terms of WAR per 600 plate appearances.

I noted above that Donaldson outperformed his projections by about 4.2 WAR per 600 PA — for which baserunning and defensive improvements accounted only about 0.7 WAR. Rounding errors aside, the following table provides reasonable estimates for Donaldson’s improvement in four other metrics.