Over 6 weeks ago, Craig Brown wrote about Nick Swisher's unlikely batting average. At the time, Swisher was hitting .299. Craig crunched the numbers, and concluded that "Swisher’s days as a .300 hitter are likely in the rearview mirror as his BABIP and line drive rate normalize." Fast-forward to the present. After going 1-for-5 with a double last night against Mitch Talbot and friends, Swisher's average currently stands at—drumroll, please—.299. Contrary to Craig's expectations, the jovial right fielder with the .251 lifetime average remained a .300 hitter as recently as this time yesterday.

I'm not here to quibble with Craig, who came to what was (and probably still is) the most logical conclusion. I'm just curious about what it might take for a skeptical sabermetrician to believe in an improbable performance over a fairly small sample. After all, if there's anyone whose unlikely improvement might not be a mirage, it's Swisher, who started tinkering with his batting stance during the 2009 World Series (of all times), and completed his extreme stance makeover last winter. Not only that, but he reported to camp in the proverbial best shape of his life. So why can't we take the numbers put up by the "new" Swisher on faith?

As a species, we're wired to see a cause for every effect, even where one doesn't necessarily exist. For our early ancestors, it came in handy to suspect a predator behind every rustle in the bushes. Of course, as jaded analysts of a game in which randomness plays a prominent role, we've trained ourselves to resist the temptation to see a mechanical tweak or change in approach behind every fluctuation in batting average. How many times have we heard a simple mechanical explanation advanced for a fleeting improvement, only to watch as the player in question sinks back to his established level, taking his self-assured explanations for success with him?

However, Swisher hasn't just boosted his batting average; along with his look, he's changed his style. The Moneyball draftee has never walked or struck out less frequently in extended action than he has in 2010; according to FanGraphs' plate discipline statistics, Swisher's swinging 9% more often than he did last season, and still making significantly more contact. As a result, he's seeing only 4.04 pitches per plate appearance, compared to his career rate of 4.23. The aforementioned alteration in stance was conceived in order to make Swisher less susceptible to breaking balls; according to FanGraphs' pitch-type values,  Swisher has posted positive values against both sliders and curveballs this season, two pitches against which he's been a below-average performer over the course of his career. It would be easy to attribute these changes to a more closed-off stance, which might have enabled Swisher to commit to swinging earlier and more often. Of course, this could also be little more than a blip; at 29, Swisher is on the old side for a drastic reinvention as a player.

Swisher's BABIP and line-drive rate have fallen since Craig's post (though they remain elevated over their levels in recent years), but his average has not. Moreover, we've long since passed the points at which Russell Carleton discovered that some of the statistics mentioned above stabilize (unsurprisingly, BABIP and batting average aren't included among them). So what say you, constant readers? Do you buy the notion that Swisher's true-talent batting average is higher with one stance than another? How much more likely are you to believe that his improvement this season can be sustained because of the convenient cause with which we've been supplied? And if Swisher's recent success can be traced back to the new way in which he prepares for pitches to arrive, do we need to credit Kevin Long with a win above replacement hitting coach?

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I'm not sure where the "line of significance" gets drawn, but I wanted to add that the same phenomenon took place with Cliff Lee in 2008: he fundamentally changed the WAY he pitched, shifting from extreme flyball stuff to moderately groundball stuff. I'm not sure at what point the NUMBERS would reflect his real, repeatable newfound command.
I don't know how useful this is, but personally, I recently found that a changed stance has allowed me to hit the ball harder and in the air more often in my adult league. Whether or not this is germane I don't know, but I feel like, if Swisher altered his stance and was able to maintain the alteration, i.e. not return gradually to his old ways, there could be some level of real change there.
I think Long deserves a win above replacement hitting coach, look at his work with Cano's stance at the end of the '08 season and coming into the '09 season... might Kevin Long be emerging as the Dave Duncan of hitting coaches? I think Swisher could be a .280 - .290 hitter from here on out since he's made such strides against breaking balls.
Superficially I see what you're saying, but how do we know that it was Long who came up with Cano's new stance? I mean, sure he's the hitting coach and all, but couldn't it have been Cano who did it? Or maybe Cano's newfound MVP form has more to do with him maturing as a player. I think we have the same problems here that we do when analyzing managers or pitching coaches: just not enough information to go on.
"I'm just curious about what it might take for a skeptical sabermetrician to believe in an improbable performance over a fairly small sample."

Statistical Process Control (SPC) theory tells you when to conclude that the recent observed behavior of a time series is from a different generating distribution (e.g. a new "true" batting average) than the historical/expected distribution.

Bayes' Theorem (and associated inference methods) tell you what the most likely new distribution is, given the evidence. There are also hypothesis tests based on Bayes' Theorem that can be used in lieu of SPC if you aren't dealing with time series per se.
Kevin Long or no, Swisher is so much quieter at the plate all he does now is drop the bat head on the baseball. He's hitting like a new age Paul Molitor lite with more power. I miss the walks, but since he's hitting 50 points higher I'm sure his OBP is in line with his career numbers. I'm very happy for Nick. He's really turned his career around after that lost season in Chicago. He's turned himself into a tough out and that wasn't always the case. I wasn't sure he'd be able to hold that RF job down last year when pre-injury Xavier Nady was still on the team. He's proven everybody wrong and stands today as one of Brian Cashman's best trades ever. Good for him. He's having so much fun playing in New York it's contagious.