Question about differences of probability in a football pool

Without you providing all the league data, I don't think you can compute this since the chance of winning an individual game is so variable. If I were picking the three point games, I would pick the safest games I could possibly pick. Having less games to pick from means I'm going farther down in my line-up, so I have a greater chance of upset.

I think the best way to handle this would be to randomly select one of the five games selected by the individuals in question and downgrade it. That will likely result in a two point reduction and still won't be fully fair since not all games are created equal but it is probably the best you can do.

I don't understand. If the winner is the person with the most points, then not choosing one game would give a player a disadvantage, not an advantage. On the other hand, if the winner is the person with the best percentage, then there might be a slight advantage to picking only 15 games rather than 16. The solution, then, is just give the prize to the player with the most points. Problem solved!

Hi Joe- The slight advantage comes because the people who missed the Thursday game still get to choose 5 games worth 3 points out of 15 games (instead of 16 like everyone else). The other games have a 1 point weight. That is where the advantage is for the people who still get to choose 5-3 pointers out of one less game. The rules say that if you missed the Thursday game you should lose a 3 point chance but the computer didn't block it. The current suggestion is to take away 2 points from eveyone who got this probability advantage(i'd like to know how much advantage it was) but that seems unfair since the increased chance doesn't necessarily translate to an advantageous outcome. Any clearer or am I still sounding confused? I'm trying.

Did everyone else have to pick the Thursday game or could they pick five weekend games?

No, it's still confusing, but then I'm not very familiar with football pools, so it might just be me. I don't think the problem is that the players who missed the first game have a statistical advantage, it's that the computer didn't assess the proper penalty.

Explain this: how does a player win the pool?

Are you trying to figure out how to enforce a rule after the fact, or are you trying to figure out how to be fair in spite of the human-induced computer error?

If the former, then I think engineer's suggestion to downgrade a random 3-pointer might be the best you can do after the fact.

If the latter, then I agree with joefromchicago that the latecomers are actually at a disadvantage. First, it sounds like they've already forfeited a potential point for missing the Thursday game. Second, they've got fewer options for selecting 5 3-pointers. Under the assumption that an informed fan will do better than a random number generator, more options means a better chance of correctly picking more 3-pointers. To illustrate the point, assume they waited until there were only 5 games left for the week. They would have no choice at all, and the five remaining games might happen to be the toughest to pick a winner. And if they happened to be the easiest to pick, then it probably doesn't matter as they would likely have picked them anyway.