First time with an image, so I will fix it if it is not correct. Anyway, I have picks from all 17 weeks. There was some concern regarding collusion between 2 player recently, and I wonder if it can be proven. Seems tough, but some of you stats folks could probably tell me for sure. The thought is that 2 players take all the medium to large favorites, and take opposing teams in games that are close calls. Possible edge. Forbidden in the rules to do so; but, after doing an eyeball test, it seems very possible. Will go into it a bit more if there is any interest. Gonna see if so for a few days before dropping it. Thanks in any case.






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Oops! Minor mess with the image text, but I won't worry about that. Will improve in the future.

Is collusion forbidden by your pool? I know a pool I was involved in certainly did not prohibit it.

I don't know if the OP could have said it more clearly.

Anyhow, I don't understand this table the OP has given us. None of the rows or columns have any names. Who are the two players who are suspect? For now it just looks like a table of professional football team abbreviations.

NFL football is kind of set up that way. If you watch a preview show you'll see a lot of games where the panel agrees across the board, a few with maybe a single dissenter, and maybe a game or two that are tough picks.

In that kind of scene you're probably going to be able to find a lot of stuff that looks like something if you just keep trying to make connections. An oddity like the one I think you're mentioning could be something as simple as two guys who take a lot of chalk with one preferring some variable (say defense, or home team, or red zone offense) and the other another (say offense, or 3rd down efficiency, or momentum) in the toss-ups. It's just not hard to legitimately have a set of data that looks like that in an NFL pool w/ a lot of common ground and then some fairly consistent divergence.

The pools I play in have all gone to point-spread (plus confidence) to combat this. If you have a pick straight games, even in a confidence pool, you just get a lot of similar entries I mean everybody can open up USA Today and put a big number next to whoever is playing the Colts so obviously many do. From just a brief look I'm not even sure this has that element (does it?). I mean if it's just straight pick every game for a point of course there's going to be a ton of chalk and then some dissent (which depending on player bias could be very consistant and still far from malicious).

I mean if they cheated I hope you catch them, don't invite them back, whatever...but I'd want a whole lot of at least circumstantial evidence outside of what you've got to even think about asking the question.

I could see where teaming up could be a fun way to play, but that behavior was explicitly forbidden in the rules of my pool.

Sherman, the names are on the left. This is just an example of what I have. I have all 17 weeks. Right, I did not point out the suspects, yet. If good statisticians are interested in this, I will be happy to move it along. Wasn't sure about the traction, though.

Phew! I just typed you a wall of text, but it was blown away when I tried to post. Anyway, let me condense it. The pair are suspected because of information exchange between one of them and a number of people, including me. They are mother and teenage child. When the child won one week last year, the mother asked me to pay her without informing the child. That raised a flag, then I started getting wind of other conversations. I then installed rules forbidding collusion. Again, though, they overperformed when considering their perceived knowledge compared to some pretty seasoned pool vets. I always attributed their succes to variance, or maybe a little savantism. I am skeptical now, though. That is why I would like to know how much of a nightmare it would be to try to prove that something was amiss.

What's the payout structure of your pool?

$5/player per week. Weekly winner gets $4 and $1 goes into the kitty for the yearly winner. Both weekly and yearly winners are determined by outright most wins unless a tiebreaker is needed in the weekly which is Monday night points scored. Yearly tie is a split pot.

18 players:
weekly winner gets 4 X 18 = $72
yearly winner gets 17 X 18 = $306

Thanks for the interest, 2p2. Gonna watch the games now, but will check back in afterwards.

There are other guys who know more about stats than me but...

I think it's very hard to prove because the data points aren't random. If they were you could show the probability of certain similarities happening. Since they aren't there can be "intentional" similarities that are just part of the element of choice given to each participant. I mean a simple way to put it is there is no number that can say whether or not they just see a lot of games similarly and a few differently in a fairly consistant way. It'd be like if me and you very much agreed on the merits of large segments of literature but had certain consistant biases in certain small segments. That can happen quite naturally and doesn't really ever have the ability to be boiled down to a math problem (which we could do if the selections were supposed to be random).

With all that said the circumstantial evidence is what I'd think you look at. What your particular burden of proof is I don't know. Sucks if you're in a bad situation because I know it's a tough spot.

After the fact and it doesn't help you here but it is why it's easier to look at the system and make it less exploitable than to try to police the individual situations, i.e. make the system in a way where the benefits of collusion shrink.

I think OP is arguing that some of the games can be treated "as if" they are random. A simple way to do it would be to look at all even money games in the NFL last season. Theoretically, one could argue that picks on those games are random (or close to it). Then you could see if those two people match up more than would be expected by chance if they were picking at random.

It isn't perfect, but the answer to that question could help you determine whether further investigation is warranted.

It's reasonable for it to have happened, but it's always going to be +EV for people to do it, so.. if you're sure everybody else is playing fair, then don't invite the person back, or just allow people to run as many entries as they want, etc, in which case everybody knows what they're in for.

Yes, to withhold funds, I would have to be able to see and understand calcs showing cheating with a probability of near 100%. It is a little bit of a tough spot because many of the players in the pool feel there was something going on. Some would not accept variance, or a knack. I did inform the pair that one would have to forego participation next year, and it didn't go well. Mostly ok because they are not people I am close to, but all a bit stressful especially when considering I run the thing for free and do not take any kickbacks from the weekly, or yearly.

Yes, different pool structure is not a bad idea. Most in are family and friends, though, so it will be disappointing if I ever have make the move, especially because both of the people in question are now out for good.

Yes, I think you have put it in a good way. For a time, I was taking pairs of players who are close to each other, making them good candidates as colluders; and I was using them in comparisons. I would look to see if their choices in toss-ups were similar in number to the duo in question. Unfortunately, this eyeball test did not yield anything that was useable as evidence. In other words, they were mostly similar. Hardly scientific, though. Also, another part might be what they might've been doing with the Monday night tiebreaker points. When I would look there, I was not always happy that there seemed to be a little strategy going on.
This all could have been due to just dumb luck. Maybe they were even colluding before this year and winning; and it all just went there way this year while they were obeying the rules. That would be ok because previously there weren't really any limitations although there might've been were I a little less naive.

agree!

I agree that's a method it just seems tough to do for the NFL. I mean I like road dogs/pick 'ems. I think Vegas over-values home field advantage. You always go with the home team in games that are supposed to be close. We both pick a whole lot of chalk otherwise. Isn't that very reasonable and aren't we going to look like we're colluding under this method though we've never met? Having played a lot of (legitimate) pools I just know you can look at data and find that stuff that's why I think any action is going to have to be on stuff other than #'s. JMO.

Whoops. Attention to detail fail.

Every pool I have ever been in, you could always just enter yourself twice and collude with yourself. I don't see the problem here.

The pool is for family and friends, and collusion was forbidden in writing before the season started. It is cheating in this case, so it is a big problem. I now see I need to be more selective when allowing people in. Also, as some ITT have suggested, I can consider having it be more than just straight pick 'em.

Could you clearly explain the edge? Anybody can take all the big favorites and randomly guess on the others.

If there's three close games you could pick: ABC, ABc, AbC, Abc, aBC, aBc, abC, abc. Assume the capital letters are the home team and small letters are the away team.

How can two people cover all eight possibilities if they're random and how can two people collude and gain from doing so?

I won the football people at my company. It was very simple. Most people seemed to pick random favorites that they loved: Big Ten/SEC/Notre Dame etc. Plus a lot of people didn't look at the last minute line for their picks. The last minute line is always the most accurate.

http://www.twoplustwo.com/magazine/i...osing-line.php

I think the people who have posted so far think there is an edge derived from 2 entries, but no one has shown the math. Part of the reason I'm here, really. I have a somewhat technical background, but not in statistics. I thought a math guy might come along to enlighten me. OK if not, though. I appreciate all respectful replies. In general, as was previously stated, there is an overperformance here. It has gone on for about 6 years now. Variance? Not completely out of the question; but not the most likely explanation, I think, at least. Quick example of how it might work. Player A and B take the same picks in which the spread is something like greater than 3, or 4, with those picks being the favorites. Let's say that totals 11/16 games in a given week. Now they decide how they want to approach the last five. Player A takes all home, Player A takes all faves, Player A takes all away... In any event, Player B takes the opposite. Edge? I am not sure by the numbers, but sounds reasonable. Of course, they do have to win twice as much to break even; but they have, and more. That's as well as I can explain it. Hope that gives you an understanding. Thanks!

Two person collusion usually doesn't really give edge so much as it just decreases variance. That's not an overly technical way to explain it but is basically what happens. That said, if it's against the rules it's against the rules and presence or amount of edge gained really isn't the issue.

Do think it's smart to at least make it a confidence pool (where you rank with numbers). Maybe it already is it didn't look like it from what I saw of the chart. I think you'll have more fun with that too.

People over-performing really isn't that uncommon especially if it's just a straight pick pool. There's so much information out there now there just isn't that much edge to be had. It's kind of like fantasy football anybody with an up to date magazine has about as much chance as the next guy no matter what the football knowledge or whatever. It's part of the reason those pools are so popular, the possibility for skillful play to gain edges but the size of those edges usually being small enough to insure luck has a lot to do with any short term (and short term can be relatively long the way we look at things) results. Kind of like poker...

OP, did the winners win the weekly more than anyone else, and then win overall as well?

picking teams without spreads is fun?

I was in two this season and they both used spreads and confidence but just confidence is still fun. Spreads is a little tougher on the organizer as you can't just have all your materials pre-prepared especially if it's got a brick and mortar aspect to it. It also scares off some potential customers like if you're just doing it as a thing for the people to do in the office more people will join if they think it's simpler and some will even look at it less like gambling if it doesn't have Vegas spreads (weird but true).

There are still a lot of spots where it's interesting just confidence. Do you pick the opponent of a big favorite who you think is vulnerable and put a 1 on the game (which will often be a big swing in points)? Do you go straight big chalk for your high totals and just try to outperform everybody on the tougher games. If you're playing for yearly do you start putting some big numbers on dogs as a hail mary catch-up attempt? There's strategy even without spreads. Now the straight pick every game straight up for a point to me that lacks a little. Basically you're supposed to go a ton of chalk and that's about it.