Is Jason Heyward the biggest offseason upgrade at any position for any club?

Paul Casella wrote a post over at Sports on Earth that uses Wins Above Replacement (WAR) to measure which additions by major-league clubs this offseason have most upgraded a team at a given position. Such an exercise is a tricky proposition. There's also the reality that WAR is best used as an approximation as opposed to a black-and-white value down to the nearest one-tenth of one win.

With that reality as a backdrop, let's look at the choices Casella made in devising his list, starting with the parameters for gauging an upgrade:

This list was compiled using the Steamer projection system's projected 2015 WAR for any player acquired by a team via free agency or trade and then comparing it with the WAR posted last year by the player who spent the most time at the same position and finished the season with that team.

There are obviously some situations that were a bit murky, such as who exactly Jon Lester would be "replacing" in the Cubs' rotation or how to address Boston's complete rotation makeover. For situations such as the White Sox signing closer David Robertson, his projected WAR was compared with that of reliever Ronald Belisario instead of the club's 2014 closer, Jake Petricka, who figures to simply slot into a different role within the Sox bullpen.

There's also the decision of which version of WAR to use. Casella chose to use Baseball-Reference WAR (rWAR) instead of Fangraphs WAR (fWAR). The differences in the two are important, especially when using WAR in order to gauge the relative upgrades a club has made.

While batting runs are measured in largely the same manner, fielding runs are not. rWAR uses Total Zone; fWAR uses Ultimate Zone Rating, which is commonly referred to as UZR. For a good breakdown of the differences between Total Zone, UZR, and other fielding metrics, I recommend reading Christoper Cwik's primer on them from last winter.

The big difference between rWAR and fWAR, however, is in the way they measure a pitcher's value. fWAR uses Fielding Independent PItching (FIP), a stat that looks at a pitcher's strikeouts, walks, hit batsmen, homers allowed, and innings pitched. rWAR, on the other hand, uses an adjusted runs allowed model, which, as fully explained on the B-R site, takes into account such factors as quality of opponents, park effects, and team defensive skill. Given a choice between the two measures of pitcher performance over a given season, I'd choose fWAR. (This is not to say that rWAR isn't a decent gauge of a pitcher's performance over a longer period of time, but that's a discussion for another day.) B-R also provides some examples to contrast rWAR and fWAR for pitchers:

I've crafted some admittedly extreme cases below to illustrate situations where the approaches differ. For most situations, FIP and Runs Allowed Average (RA, essentially what we use) will be very close and are strongly correlated, but there are a number of cases each year where there are large disparities between the two metrics.

Situation #1, Pitcher A throws a perfect game with 20 strikeouts, Pitcher B throws a perfect game with no strikeouts.

FIP: Pitcher A -1.40 FIP, Pitcher B, 3.20 FIP, RA: Pitcher A 0.00 RA, Pitcher B 0.00 RA.

Situation #2, Pitcher A throws one inning w/ sequence, HR, ground out, fly out, BB, BB, BB, fly out, Pitcher B throws one inning w/ sequence BB, BB, BB, HR, SO, SO, SO

FIP: Pitcher A 25.20 FIP, Pitcher B 19.20 FIP, RA: Pitcher A 9.00 RA, Pitcher B 36.00 RA.

As I said, in the average case the two methods will arrive at similar results, but on the edge cases the differences can be quite dramatic.

Using this method, Casella found that the Cubs' upgrade of Jon Lester over Edwin Jackson (who has been bumped to the bullpen on the Chicago depth chart) was the No. 1 largest improvement of the Hot Stove, followed by Pablo Sandoval at third base over Will Middlebrooks (who had a really bad year in 2014 and has since been dealt to San Diego), and then, ranked third, the St. Louis Cardinals' addition of Jason Heyward, which displaced Randal Grichuk in right field.

The choice of rWAR over fWAR has implications up and down the top ten; however, the top five are particularly impacted. The following chart shows the differences when using fWAR as opposed to rWAR.

You'll note that the biggest swings are for pitchers with a gap between their runs allowed and FIP. This is the case for Jackson, who had a horrible 2014 with a 6.33 ERA which I'm going to use as an illustrative proxy even though rWAR takes into account runs allowed that are unearned as well as earned. But Jackson had a 4.45 FIP that was bad, just not as putrid as his ERA. Using the minus stats, which are park adjusted and scaled so that 100 is league average with the further below 100, the better and the further above, the worse, we get a good idea of how much worse Jackson's ERA was than his FIP. His ERA- was 170 last year; his FIP- was 116. Thus, Jackson had a bad season by fWAR but an absolutely atrocious season by rWAR. The difference shoots the Lester acquisition to the top of the upgrade chart.

If we reorder the list using the players' 2014 fWAR, it would look like this:

The binary nature of the comparisons further complicates matters. In the case of right field for St. Louis, Grichuk is the lone Cardinal remaining of the club's 2014 right-field group, which included Allen Craig and Oscar Taveras. With 282 and 220 plate appearances respectively, both Craig and Taveras tallied more than Grichuk's 72 as a right fielder, which were just eleven more than Jon Jay notched while playing right last season for the Redbirds. If we include Craig's -0.5 fWAR with the Cardinals (he posted -1.4 between Boston and St. Louis, by the way) and Taveras's -1.1 fWAR, the upgrade in right field Heyward embodies is approximately six wins. I think there's a very good argument that the Cardinals' upgrade in right field between 2014 and 2015 is the biggest made by any team during the Hot Stove, as approximated by fWAR.