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: If Bluto batted .300 for the first half of the season...
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.
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.
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?
RAY: 212 and a half.
TOM: And a half.
RAY: And when you figure that out, Bluto batted .316 for the season.
RAY: Right? Even though he batted .300 and .400 in each half.
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.
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.
[ Car Talk Puzzler ]