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Tuesday, January 13, 2009

The game before the games

The betting lines are out for this Sunday's pro football games, and in the underdog pool in which I have been playing, lo this entire season long, it's time to call a final winning 'dog. Here are the choices -- if you had to pick one of the underdogs (in caps) to win its game outright, which one would it be? If I pick correctly, I get the number of points listed next to that 'dog:

6 BALTIMORE at Pittsburgh
3.5 ARIZONA vs. Philadelphia

Readers, as ever, your predictions are welcome:

Will the underdog teams win in this weekend's pro football playoff games?
Neither underdog will win
Baltimore will win in Pittsburgh, but Arizona will lose at home to Philadelphia
Arizona will win at home over Philadelphia, but Baltimore will lose in Pittsburgh
Both underdogs will win
pollcode.com free polls

While the actual games should be fun to guess about and watch, the last week of the underdog pool is as much about gamesmanship in wagering as it is about which underdog team is going to win. To have a shot at moving up in the standings -- top four players get cash shall we say, rewarded -- you have to pick the underdog that the player ahead of you isn't choosing. If both you and the other player pick the same team, your positions in the standings relative to each other won't move. And so one of the first hurdles is choosing the team that the player ahead of you will decide not to go with.

Assuming you get that right, you have two ways to move up:

1. Your 'dog wins, the pick of the person ahead of you loses, and the point earnings on your game are greater than the distance between the two of you in the pool standings.

2. Both 'dogs win, but your point earnings exceed the other player's point earnings by more than the distance between the two of you in the pool standings.

Of course, on the other side of the ball is defense. If one of the games has a smaller point potential than the other, by choosing the game with the larger spread you can insure that the person behind you can earn only the smaller points at most. If the smaller points are less than the distance between you, you thereby insure that the person behind you can't catch up.

If you've got people both in front of you and behind you, there's sometimes a tough choice to be made between offense and defense. By trying to move up, you may risk falling back.

Not to overlook the obvious, in order for either of you to go forward, you or the person behind you has you pick a team that's going to win. But there's a good chance that it won't matter -- that the pool could be decided before kickoff on Sunday. For example, if we all pick the same 'dog, the current standings automatically become final at tailgate time.

With that, I'm sure most readers will have had their fill of the internal drama of the final act of the pool -- if not more. But if you've been following the action over the last 19 weeks and care to hear about how it's all coming out, here's the preview of the final week's throwdown:

I currently stand in third place, and there's enough of a gap between me and second place that there's no chance of me making it to second. But the guy right behind me could sneak into third place if I let him. And so for me, the game is defense. Meanwhile, he's got both sides to think about, because there are two players behind him that could catch him if certain events transpire.

Here are the top six players left in the pool (not their real names), and their point totals. Nobody else can take home a prize:

66 Samantha
64.5 Endora
57.5 Me
54 Mike
49 Chuck
48 Greg
Samantha and Endora will battle it out for first. Samantha finishes first and Endora second in all of these scenarios: (a) neither 'dog wins; (b) they both pick the same 'dog; (c) they pick different 'dogs and only Samantha's 'dog wins; or (d) Samantha takes Baltimore, Endora takes Arizona, and both 'dogs win. Endora prevails only if: (e) they pick different 'dogs and only Endora's 'dog wins, or (f) Endora takes Baltimore, Samantha takes Arizona, and both 'dogs win.

For third place, it's me against Mike. I finish in third ahead of Mike unless we choose different 'dogs, Mike's wins, and mine loses. Interestingly, though, if I choose Baltimore, the most Mike could pick up would be 3½ with Arizona, which would leave us tied for third place. If I select Arizona, and Mike takes Baltimore, then if he's right and I'm wrong, he would pick up 6 points, leaving me in fourth. Hmmmm.

Right behind Mike is Chuck. Chuck needs 5 points to catch up with Mike. The only way Chuck can get there is if Chuck picks Baltimore, Mike picks Arizona, and only Chuck is right. In that case, Chuck is fourth, and Mike is out of the money. If Mike takes Baltimore, Chuck can't catch him.

In sixth place is Greg. The only way Greg could get to fourth place and a prize would be to get ahead of both Mike and Chuck. And the only route to that outcome would be Greg winning with Baltimore, and Mike and Chuck losing with Arizona. In that case Greg and Mike would split fourth prize.

(... I think. Man, somewhere in here is a math term paper for some youngster.)

So what should Mike do? Mike knows that Greg and Chuck are going to take Baltimore. If Mike takes Baltimore, they can't bump him out of the money or even get a piece of fourth. Moreover, if Mike takes Baltimore, there's a chance he could knock me down to fourth and take third himself. So from both a defensive and offensive standpoint, Baltimore looks like the better bet for him. But I know that. He knows I know that. I know that he knows that I know... Oh, the drama.

What would you do if you were Mike?

Which team should Mike pick?
pollcode.com free polls

Anyway, we'll all be watching the players' selections when they're announced Sunday morning. As mentioned earlier, the pool could become final right then and there. The games will both be fun to watch regardless, but if there are still prizes at stake for us players, they'll take on that little extra edge that the pool has given the league all season.

UPDATE, 1/18, 12:45 p.m.: All the top players took Baltimore, and so we wound up in third place, with $60. Not bad! Couldn'ta done it without the blog commenters. Thanks, everybody.

Comments (7)

Everyone outside of the top 2 spots has to take Baltimore. Because the difference in the reward between 3rd place and 4th place is not worth the risk to Mike of falling into 5th place and getting no reward whatsoever.

Sounds right to me.

FWIW, the bookies say that Arizona has a 35% chance of winning, and Baltimore has a 29% chance. An Arizona win and Baltimore loss together are therefore a 25% shot. Baltimore win and Arizona loss are 19%. Philly and Pittsburgh prevailing are at 46%; Arizona and Baltimore winning, 10%.

And I've just been picking my underdogs the last few weeks based on who has the ugliest quarterback.

The only scenarios you care about are the 25% and the 19%. I presume a 3rd/4th tie pays $47.50? Anyway, since this all depends on who he picks, and it's a solvable problem, let's just do it.

If you pick Arizona, your expected value is $60(p) + $60(0.81)(y) + $35(0.19)(y), with p and y being the probabilities of Mike picking AZ and Bal respectively.

($60 when he picks Arizona, $60 when he picks Baltimore and you both win or he loses, $35 when he picks Baltimore and wins while you lose).

If you pick Baltimore, your expected value is $60(y) +$60(0.75)(p) $47.50(p)(0.25).

(%60 when he picks Baltimore, $60 when he picks Arizona and doesn't gain from it, $47.50 when he picks Arizona and wins while you lose).

p = 1 - y, y = 1 - p, so let's just do the math.

EV if you pick Arizona:
60(1 - y) + 60(0.75)y 35(0.19)(y)
60 - 60y +45y + 6.65y
60 - 8.36y

EV if you pick Baltimore:
60(y) + 60(0.75)(p) + 47.50(p)(0.25).
60(y) + 45(1 - y) + 11.875(1 - y)
60y + 45 -45y + 11.875 - 11.875y
15y +56.875 - 11.875y
56.125 + 3.125y

Again, with y being the chance of him picking Baltimore. Want to find out when you have an advantage? Set them equal to each other.

60 - 8.36y = 56.125 + 3.125y
3.875 = 11.485y
y = 0.3374 = 34.74%.

What this means is if you think there's better than a 34.74% chance he'll pick Baltimore, you also should pick Baltimore. If you think there's worse than a 34.74% chance he'll pick Baltimore, you should pick Arizona. For simple reasons outlined above, that makes your choice pretty clear.

By the way, from his perspective, picking Baltimore is the right move even if you're picking Baltimore 100% of the time (as Chuck and Greg are). His EV from that is $35, whereas by picking Arizona, he has a 25% chance of moving up $12.50 and a 19% chance of moving down $35. Basically he's burning money by picking Arizona no matter what you do. At the least, it's definitely better than 35% that he'll pick Baltimore.

Trivial! Go with the ravens and enjoy the weekend.

Weren't you the guy who told me to take San Diego last weekend?

Weren't you the guy who picked San Diego last weekend?

Math doesn't like results-oriented thinking. San Diego and Arizona were far better plays by the numbers than Baltimore and Philly. You got unlucky, so it goes.

How many weeks are you gonna doubt Kurt and the Cards? Besides, god is on his side.

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