Today's winner in Stats & Analytics:

Ron Gardenhire, Troy Polamalu, Chase Utley

Today's losers:

AFC North quarterbacks, Luis Castillo, selective endpoints

Before we get into the main subject of today's post, I want to look at the results of some attention-getting but flawed new research, where economists Devin Pope and Uri Simonsohn write: "A round number, a batting average of .300, can act as a goal and influence behavior." Pope and Simonsohn wanted to test the hypothesis that athletes are more motivated if they have a numerical goal to reach. So they looked at MLB hitters going into their final scheduled appearances of seasons from 1975 through 2008. And they found that players hitting .299 or .300 entering their last at-bats hit .463 in those at-bats. .463! As a result, hitters are much more likely to end a year batting just above .300 than just below it.

In related news, scientists have found that terrible airline accidents have a strong negative effect on travelers' plans to fly. Because zero percent of passengers involved in fatal crashes ever flew again!

Look, there's no question batters are motivated to hit .300. In fact, they are so motivated that when they get to .300 very late in the season, they often stop playing. Vlad Guerrero entered Sunday, the last day of the regular season, hitting .301. He went 0 for 2, dropping his average to .300 -- then the Rangers pinch-hit for him. Starlin Castro went into the Cubs' last game batting .300, and he ... well, he didn't play at all. "Castro was out of the lineup after improving his batting average to .300 on Saturday," The Associated Press reported, noting that Castro was the first Cubs rookie to hit .300 in 36 years.

Which means that running an experiment where you look only at "last scheduled plate appearances" will cause the reverse problem of studying airplane trips that ended in crashes: You'll include trials that terminated upon success but kept going upon failure. And that is a great way to end up with an misleadingly high number of successes, as a couple of blogs have now pointed out. To avoid predetermining what your sample will look like, you need to include everything that could be a success or failure, then see how they turn out. You need to study all airplane trips. Or all plate appearances by batters hitting very close to .300 in the last game (or week) of a season, not just those that turned out to be, in retrospect, their last plate appearances.

Pope and Simonsohn recognize the effect of pinch-hitting (though not outright benching): They report that 34.3 percent of players hitting exactly .300 are taken out for substitutes, versus just 4.1 percent of batters hitting .298 or .299. Nevertheless, they ascribe the jump in the number of players who hit .300 on the nose to hitters trying harder. "What you have here is asymmetric motivation," Pope told The New York Times, meaning batters have more to play for in these situations than pitchers.

Well, that's part of what we have here. Pope and Simonsohn found that in 61 cases where players were hitting .299, not one of them drew a walk. That's pretty telling evidence that hitters will do what they can to hit meaningful targets. And at the level of career statistics, obviously that has a big impact: From year to year, players can retire if they're hitting .300, or drag out their careers to cross important thresholds. But from plate appearance to plate appearance? Because this study examined at-bats that only retrospectively became hitters' final appearances, we still don't know how much influence batters actually have over what happens.