Batting Averages Puzzler

From the soon to be retiring Car Talk radio show, a fantastic new baseball puzzler.

RAY: As you might guess, I’m a baseball fan. And now that the season is in its waning days, I thought I’d use this baseball Puzzler I’ve been saving.
There are two rookie players, Bluto and Popeye, who started the season on opening day and made a wager as to which one would have the best batting average at the end of the season.
Well, the last day of the season arrives, and not much is going to change–especially considering that neither one of them is in the starting lineup.
Bluto says, “Hey, Popeye, what did you bat for the first half of the year?”

Popeye answers, “I batted .250.”

And Bluto responds, “Well, I got you there. I batted .300. How about after the All-Star break?”

Proudly, Popeye pipes up, “I batted .375.”
Bluto says, “Pretty good, but I batted .400. Fork over the 20 bucks that we bet.”
The bat boy, Dougie, saunters over and says, “Don’t pay the 20 bucks, Popeye. I think you won.”
TOM: Why is someone who batted .375 not playing in the last game of the season? That’s what I want to know!
RAY: Good point. But the question is this: How could Popeye have won?

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