# Algebraic Baseball Puzzler

RAY: Let's assume that they both had 600 at-bats.

TOM: Is that a lot?

RAY: That's about average for a guy who plays the whole season except for the last game.

TOM: OK. He had 600 at-bats.

RAY: OK?

TOM: Yeah.

RAY: If Bluto batted .300 for the first half of the season...

TOM: Mmm-hmm.

RAY: And he had 500 at-bats during that first half of the season -

TOM: Oooh. Yeah.

RAY: He got 150 hits. One hundred fifty over 500 is .300 average, right?

TOM: Mmm-hmm. So he would have gotten 150.

RAY: Yeah. OK? If Popeye batted .250 and had 100 at-bats, he would have had 25 for 100.

TOM: Mmm-hmm.

RAY: OK? You with me so far?

TOM: I'm with you.

RAY: The second half of the season, Bluto bats .400. How does he do that? Well, we know he had 500 at-bats in the first half.

TOM: So he's only been up 100 times in the second half of the season.

RAY: And he got 40 hits.

TOM: And he got 40 hits. Got it.

RAY: Popeye bats .375.

TOM: But he's up 500 times.

RAY: And he gets 187 and a half hits. One of them was a chuck-swing single over the infield. They only count that as half a hit.

TOM: Yeah.

RAY: So now, let's...let's figure it all out.

TOM: So we got...

RAY: Bluto batted 600 times. How many total hits did he get?

TOM: 190, I have.

RAY: Right. How about Popeye? How many hits did he get?

TOM: 212.

RAY: 212 and a half.

TOM: And a half.

RAY: And when you figure that out, Bluto batted .316 for the season.

TOM: Yeah.

RAY: Right? Even though he batted .300 and .400 in each half.

TOM: Yeah.

RAY: And Popeye bats .353 and wins the batting title.

TOM: No kidding!

RAY: Pretty good, huh?

TOM: Pretty darned good. A good little example of the arithmetic mean and what it means to me.

RAY: And how statistics can lie, more importantly.

TOM: Wow! That's good. Now, you know that every fifth-grade teacher in the country will be using this problem next week.

RAY: I hope so.

TOM: I hope so.

RAY: Because it's a good one.

TOM: And what they should do is take bets. Teach the kids about betting.

RAY: Right!

TOM: And they should give odds, teach the kid about odds. That's good.

RAY: They can cover all the bases, so to speak.

TOM: Cover all the bases, so to speak.

RAY: So, who's our winner?

TOM: The winner is Mike Bennett from Dallas, Texas.

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