##### Oct 07, 2000

**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?

**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.