UPDATE: J.J. has given me a macro. See the random results below.

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A lesser man would hope you've forgotten my NFL picks for the year.

Let's talk about how bad they were.

While my preseason Super Bowl pick of San Diego is still alive, they're almost the only one. I only predicted four of the 12 playoff teams. Only 2 of the 8 division champs.

When you take the records that I predicted for the teams and compare them to their actual record, I was 108 games off for the 32 teams.

Do the math. I was an average of over three games off! Seriously. There's a hell of a difference between 7-9 and 10-6, and that difference is on the low end of my picking abilities this preseason.

For the sake of comparison, I hunted down Mike and Mike's preseason picks, mostly because they, like me, predict records and not just standings. It confirmed that I was very off.

Golic was 89 games off...an average of just short of 3 per team. Greenberg was the best at 82 games off, a shade over 2.5 per team. Golic had half the playoff teams; Greenberg had 9 of the 12.

Better than me...but 2.5 per team is still awfully far off. How do I know?

If one of us had simply predicted every team would go 8-8, we'd have beaten us all. He/she would have been a total of 77 wins off, which is under 2.5 per team.

To be fair, nobody--and I mean nobody in the whole world, including their mothers--had Miami or Atlanta in the playoffs this year.

But I still feel like I must be better than a random number generator. So I'm wondering if one of you computer programming types could do me a favor.

I need a quick and dirty computer program that will give me 32 random integers between 0 and 16, with a catch: the total of those integers must be 256 (such that it all adds up to the proper number of wins in the NFL in a year). When I crank out those numbers, then assign them randomly to teams, will I do better than that? Surely, I think, I would have. But I leave it to one of you to manufacture and send me the program.

(I'll owe you an ice cream for your troubles.)

UPDATE: I owe J.J. an ice cream for his kick-ass Excel macro. The random computer program picked 4 undefeated teams this year. Man, that'd have been AWESOME! In part because of that, the random-wins-generator was off by more than me, Mike, Mike, or everybody's-eight-and-eight. It averaged nearly 5 wins off per team.

HOWEVER, the random wins generator picked six of the 12 playoff teams! Better than me, and the same as Golic.

That's pretty scary.

I used to know how to write an equation to figure out what the odds are of getting a certain number of these teams right. 16 teams in a conference, 6 go to the playoffs. If I pick randomly, what are the odds of getting exactly none of them? Probably pretty slim. The odds of randomly picking all? Probably even slimmer. What are the highest odds that a random picker can luck into?

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## 3 comments:

This problem is actually harder than stated, because in a conference of 16 NFL teams, you can’t have *any* combination of 6 teams getting into the playoffs. Specifically, there’s no way you can have all 4 teams from the NFC West get into the playoffs. And, there's no way that the 2 wild card spots could be given to the 2 lowest performing teams in a conference.

However, the solution likely involves the function COMBIN in Excel. Check it out in the Excel help topics. To get the number of different combinations of 6 from a group of 16, I believe the formula for the cell is =COMBIN(16,6) But, that’s only the right formula for your problem if any 6 teams can get into the playoffs, which isn’t correct.

My very quick first guess is that there are 7168 total playoff combinations among 16 teams, following the NFL's rules. Thus, the chance of randomly choosing the 6 correct playoff teams is 1 in 7168.

Are the math teachers from your building reading your blog? :-) Or maybe you can give it as a bonus problem to some of your students. This should be easy stuff for students learning about probabilities, permutations, and combinatorics, which was nearly 20 years ago for me...

Hmmm.

(dusting off the neglected left half of my brain...)

Eight division winners. The computer has a one-in-four chance at each of those. That means four to-the-eighth chance of nailing all of those. Sixteen times four. 256 times two. One in 512 chance of nailing the division winners.

To get two of the remaining 12 teams as wildcards. There are 66 combinations. So multiply by 66. Twice (once for each conference). 512 times 66 times 66= 2,230,072.

So there's a one in 2,230,072 chance of getting all the division winners and all four wild cards randomly.

HOWEVER, that's not the question I asked. I asked for the odds of getting all twelve playoff teams. So we'd have to reduce that number by the number of instances where the computer might have had two correct playoff teams, but picked the wrong one as division champ (i.e., this year, had the computer picked Tennessee as wild card and Indy as division champ). I'm not sure how to determine the number of ways to reduce the number thusly. Do I just figure out the number of combinations within a division? I guess that'd work. So we can remove 12 instances per division (the different first/second combinations for each). Twelve times eight is 96. So divide the above number by 96 and I land at the following answer:

Shit. Wait. That won't do. That'd only be the number of ways that the computer could swap wild card and division leader ONCE. In reality, the computer could swap them as many as FOUR TIMES and still name all the playoff teams. So we'd divide by a lot more than 96.

It's at this point that I need to, rest, or to defer to your superior problem-solving ability...

Duh. 4 to the 8th power is 65,536, not 512.

65536*66*66=285,474,816. That's the odds of the computer nailing division winners and wild cards, not the paltry 2 million from before.

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