On Tuesday, Jay sent us a link to a news story about the Seattle Mariners’ last game of this year. In the story, one of the sportscasters, Mike Blowers, makes an amazing prediction. During the pregame show he predicts to his radio partner that a Mariner rookie, one Matt Tuiasosopo or Tui for short, will hit his first ever major league home run. He then goes on to elaborate that the homer will occur during Tui’s second at bat in Sunday’s game. The kicker was that he called the count at which the homer was to be hit, three balls and one strike. Egged on by his radio partner, he continues on with the prediction that the home run will land in the second deck of the left field stands. Finally, when his partner asks which row in the stands the ball will land in, he begs off with a statement about fans standing up trying to catch the ball and not being able to tell in which row it would land.
I posted the link that Jay sent us as a postscript to Wednesday’s post. I showed it to Tom, who I know is a baseball fan. Tom is also a bit of a statistician. Tom said there are five variables in Blowers prediction: 1) What are the chances of Tui hitting a home run?; 2) If he hits a homer, what are the chances that it is on his second at bat?; 3) How would he get the home run on a 3-1 count?; 4) In which field would the homer be made?; 5) Which deck will Tui hit the homer into?
Here is my take on Tom’s analysis:
1) Pujols has about 47 homers this season. The question is, is Tui another Pujols? Since Blowers made the prediction, I’ll assume best case and that Mike thinks that Tui is another Pujols. Assuming an average of 400 at bats in a season, then the probability of Pujols and by inference Tui, hitting a homer at any given at bat is about 47/400. Since we were doing the math in our head, we called it 50/400 or 1/8. [I can hear the groans.]
2) This one is easier, we assumed that Tui had a likelihood of four at bat in the game. Hence, if he was going to hit a homer, he had a 1/4 chance of hitting one at his second at bat.
3) This one is the kicker, the 3-1 count. The way we figured it, on any given pitch there are three possible outcomes, a ball, a strike or a play. We weighted each possibility evenly [groan again, if you will]. This calculation required more probability theory then I could dredge up, but Tom was up to the task and came up with the number of 4/81, which we promptly rounded up to 1/20.
4) We pretty much figured that any homer hit by Tui and scouted by Blowers was going to be into the left field. So we gave this prediction the Duh! response and gave the probability of this happening as a certainty or a 1.
5) Finally, which deck will the ball fall in was the last variable. I’ve rated the first deck of having a 2/3 chance of receiving any homers that were hit there and the second deck , the predicted one, of only a 1/3 chance of recieving a homer. [Before you groan again, I’m giving him this one.]
So according to probability theory you just multiply the preceding blue numbers together:
1/8 × 1/4 × 1/20 × 1 × 1/3 = 1/1920 or about ~1/2000.
One in two-thousand are prodigious odds. Tom’s and mine back of the envelope calculation could be off, but the odds are not Powerball odds. Winning Powerball goes off at about one in sixty plus million. As incredible as Mike Blowers’ prediction was, maybe he should have gone for the actual seat number or maybe he should have just bought a Powerball ticket? 😉