In 2016, despite playing for the hapless Minnesota Twins, Brian Dozier was a bona fide down-ballot MVP candidate. He finished 13th in American League MVP voting and was 8th among the league's position players in Baseball Reference Wins Above Replacement.
Although Dozier has been a good player for a while, his big 2016 breakthrough was his power: he hit 42 home runs, 3rd in the AL, and while he is an average at best defensive second baseman (his 2016 Ultimate Zone Rating was slightly above average and his career mark is below average, though not catastrophically so), his ability to hit so many home runs while fielding a competent second base made him, on a team whose hype mostly surrounded top prospects Byron Buxton and Miguel Sano, easily Minnesota's best player in 2016.
Even if you believe that Brian Dozier peaked in 2016, and it's not an unreasonable hypothesis (his 28 home runs in 332 second half plate appearances wildly exceed his generally good but not "literally better than Babe Ruth" career pace), he has a strong track record. He is certainly one of baseball's better second basemen, and all signs point to him being an upgrade over existing options if the St. Louis Cardinals were to pursue him, as had been rumored on Monday (although Tuesday comments suggested the pursuit may not be an actual thing).
But this isn't just about Brian Dozier. It's about Jedd Gyorko and Kolten Wong.
There is no more irritating form of analysis (sorry for the nonzero times I've done it myself) than "add a player's WAR to a team's win total and presto, that's the team's probable new win total". The inherent problem isn't so much that WAR is theoretical, though it is: it's that a player's replacement, particularly on a relatively good team like the Cardinals, is rarely at exactly the “replacement level” threshold.
Some, for instance, criticized the Jhonny Peralta signing in 2013 as an overpay, but in this case, he was replacing a very poor starter in Pete Kozma. In practical terms, Peralta was more valuable than if he were replacing a league-average (think 2 WAR, if that is your preferred exchange rate) shortstop. Dozier is (probably) a better player than Peralta was by true talent, but second base incumbents Wong and Gyorko, while flawed enough players that the team would at least consider an upgrade, are also valuable enough parts that it slightly suppresses Brian Dozier's projected impact.
I'll start by comparing Dozier and Gyorko, as the two are similar types of players: each had an above-expectations 2016 built largely on 2.5 true outcomes-y stat lines (lots of home runs, lots of strikeouts, walk rates that aren't Matt Carpenter levels but also aren't Randal Grichuk levels) and extremely okay defense. Gyorko even made occasional turns at shortstop, where he would make weird-looking plays like these.
However, Dozier had an undeniable edge in baserunning (he had 18 steals in 2016; Gyorko has four in 492 career games) and while Gyorko did some things very well, Dozier did them better.
On one hand, Gyorko had a low batting average on balls in play (.244) and arguably got somewhat unlucky. But like Dozier, Gyorko's career home run high was largely inflated by an unusually strong second half. And while the second half counts too, it must at least be considered that it could be an outlier. Regardless, it would take a convergence of two factors—that Jedd Gyorko, though perhaps not the kind of speedster that would tend to be a high-BABIP guy, should improve upon his .244 mark and come closer to his career BABIP of .270 going forward, thus improving his non-home run offensive acumen (believable), and that Gyorko is truly a “30 home runs in 438 plate appearances” type of power threat (less believable)—for Gyorko to approach the levels of offensive production we know Brian Dozier can attain.
This could be a somewhat moot point, though, if indeed Jedd Gyorko is used predominantly at third base alongside Jhonny Peralta, as MLB.com’s Jenifer Langosch has conveyed. Whatever level of production Gyorko reaches over the next several years would be more or less also possible at third base. Kolten Wong, however, despite his grand experiment in the outfield in 2016, appears to be the player the Cardinals want at second base, at least among the internal options.
And while Wong has a prospect pedigree, his actual MLB production has been..well, it’s been fine. By UZR, Wong has been an above-average defensive second baseman, better than Dozier or Gyorko, and he figures to be the best defensively of the trio going forward (while Wong feels dramatically younger, he is just two years younger than Gyorko and 3 1⁄2 years younger than Dozier; he is, however, by definition, still younger). He has been, persistent mentions on national broadcasts notwithstanding, an above-average base runner, and given these factors contributing to his all-around game, his career 87 wRC+ is, to use a word from earlier in this paragraph, fine.
The Cardinals, however, are built on a foundation of “fine” players—few gaping holes, but few standouts among their ranks. And while no team should shun a player who averages just over 2 WAR per 600 plate appearances without reason, “acquiring a player who has, since 2014, been more valuable by FanGraphs WAR than all but 14 position players, including such players as Andrew McCutchen, Robinson Cano, and Yoenis Cespedes” is more than sufficient reason.
Kolten Wong could very well be a part of a Brian Dozier trade. I hesitate to use the term “centerpiece” because while Wong likely still carries some prospect cache, it would probably take several prospects on top of Wong to seal the deal (the “several” part could probably be circumvented by parting with Alex Reyes, which I would not do, but is technically a thing the Cardinals could do).
And while there is a limit on what the Cardinals should be willing to trade for Brian Dozier, he certainly would improve the team in the short term, and he’s probably a safer bet than current internal options in the medium-to-long term as well. Dozier probably doesn’t mean that the Cardinals would catch the Chicago Cubs (though it does improve the odds some degree), and thus I would be hesitant to sacrifice the entire future for him, but he represents a large enough improvement that he may be worth sacrificing some future returns.