Applying game theory to playoff confidence pool (1 Viewer)

Curious to hear others' thoughts on this scenario:

Playofff confidence pool, you pick the winner of each game straight up and assign points for each game. You can only use each point value once, but unlike an NCAA pool, you don't have to submit a pick until right before each game (ie, no losing your championship pick in the wildcard round). Payouts are $500/$250/$100.

Here are the standings heading into the Super Bowl:

• Player A: 41 points (max points: 50)
  
• Player B: 41 (max 46)
  
• Me: 41 (max 46)
  
• Player C: 40 (max 51)
  

I am almost certain to lose the tiebreaker to Team B, which means if all of us pick the same team and that team wins, I would finish out of the money.

Here's what I'm thinking: Player C is in the driver's seat. If she gets the pick right, she wins the whole thing. So she is almost certain to take the Pats.

As for A and B, they have a choice to make. Knowing that C will likely be choosing Pats, they could either pick NE for the best shot at finishing in the money, or go for glory and pick the Eagles.

So that leaves me. If I knew A and B were taking the Pats, then it would be a no-brainer to take the Eagles, because it would be my only shot at winning. By contrast, if I knew one or both were taking the Eagles, I'd be better off taking NE for a better shot at second/third place.

If were them, I'd take the Pats. As a result, I'm planning on taking Philly.

What would you do if you were A or B? What would you do if you were me? Are there any other factors I should be considering?

Not sure why you're making this so hard.  Pick the winner.  Eagles are going to win so pick Philly. 

Snotbubbles said:

Not sure why you're making this so hard.  Pick the winner.  Eagles are going to win so pick Philly. 

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Thank you for offering that completely unbiased perspective! 

I have had this dilemma many times in regular season confidence rating pools going into Monday night games.  I have tried all kinds of ways and usually when I overthink it causes problems because you outsmart yourself.  Bottom line is you have to pick the winning team no matter what.  By trying to guess what the other people are going to do you can end up making a pick you aren't happy with because "it seems like the best chance to win". 

The first thing you need to do is analyze who you think it is going to win.  If you are confident in a certain pick then you might as well go with that because you really don't have any way of knowing who the others will take.  If you honestly think it is a toss up and can go either way then it makes more sense to really delve into your opponents to try and figure out what way they are going to go and then choose according to that (going opposite the way you think they will pick). 

None of this matters if you don't get it right so I would spend my time trying to figure out if you have confidence in one team or the other and go from there.

You can solve this by assigning values of probability to the game outcome, and to each choice by your competitors. 

Vegas gives the Pats a 63% chance of winning. 

Give Player C a 90% chance of taking the Pats.

A/B, are they football people or numbers geeks? Because if A is a numbers geek, he can do the same calculation and figure that he wins overall only if he's right and C's wrong about the outcome. So his probability of winning overall by taking the Eagles is 0.37 * 0.90 = 0.33, while his probability by taking the Pats is 0.63 * 0.10 = .063. So it's not close, if you think C is 90% likely to take the Pats. So give A a 90% chance of taking the Eagles if he's a numbers geek, but way less than that if he's a football geek.

B's calculation is that he can't win in the scenario where A and C choose different outcomes, but he's guaranteed second place if he chooses correctly. So he should take the Pats, which loses only when the Pats lose, and A and C both choose the Pats (0.37 * something less than 0.10). So give B a high chance of taking the Pats, probably whether he's a football geek or a math geek, unless he's a football geek from Philly, or really hates the Pats.

So your scenario is that if everyone's a math geek, it's most likely that A chooses the less-probable outcome, and B and C choose the more-probable. So you can finish alone in second by choosing the Eagles (if they win), or tied for second if you choose the Pats (if they win). The right choice there depends on the differential payout between being alone in second ($250) or tied for second ($175, presumably) So (0.37 * 250 = 92.5) vs. (0.63 * 175 = 110.5). So taking the Pats is slightly better, based on those assumptions.

I suppose there's also a scenario where everyone chooses the Pats, and they lose, and then you wind up in a three-way tie for first, making 283.33. 

So you probably should take the Pats.

Except they're awful human beings, so you should take the Eagles.

Throw all the probabilities out.  From the data posted prior to the selections, you appear to be in the worst position.  A and C can both outscore you and B wins a tiebreaker with you. That indicates that you should go with the contrarian pick and select the Eagles.  Selecting NE would give you little chance at finishing first or second, whether you are right or wrong.

Went Eagles. Everyone ahead of me went Pats. FLY EAGLES FLY!

zftcg said:

Went Eagles. Everyone ahead of me went Pats. FLY EAGLES FLY!

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You chose wisely. Good luck!

Thanks to everyone for their advice. It was interesting that you all made good points in different ways. @CalBear was right that it was possible to map out the decision tree with expected values (I put together a crude one, which, depending on certain assumptions, indicated that picking the Eagles had the highest EV). @Gally was right that it's possible to overthink these things, and it's best to go with the team you actually think will win (I didn't have a strong opinion, but I did think the Eagles had a good shot to pull off the upset). @Bronco Billy was right that, given my position, the Eagles were a strong contrarian play. Hell, even @Snotbubbles was correct in his blatant homerism. 

If I'm really being honest, though, what may have drove my decision as much as anything was the fear that if I picked the Pats, I would realize 5 minutes after kickoff that I had already been eliminated (and in fact, that's exactly what would have happened.) Picking the Eagles made watching the game more enjoyable ... especially at the end 

So thanks again. And congrats to @Snotbubbles and all the other Eagles fans! Cheesesteak emojis on me!