Prop bet - help me determine fair odds

**sharpcat** · 12-09-10, 03:42 PM

Originally posted by slatter

The italics are copied and pasted from another forum I post on:

Tell someone to pick six teams (seven if you are feeling greedy and think they'll take it) that they think will miss the playoffs. If all those teams miss the playoffs, they win the bet. If at least one team makes the playoffs, you win the bet.

An even-money prop. My sharper friends have decided they'd need me to lay odds (-150 or more) to take this bet at seven teams. One guy even told me I'd have to give him 4-to-1. But some other people I know are on-board for seven teams at +100 odds.

The rise of the Chiefs, Rams and Raiders this season probably hurts my chances of drumming up a ton of interest for next season, because people look at the standings to figure out if they could do it or not and see that these three historic losers could be playoff bound this season.

So my question is, what would you estimate the fair odds of this wager to be? It's hard because how many different winning and losing combinations this bet can produce, but can anyone help me ballpark this? Picking six teams, would 2:1 be fair? Seven teams, 4:1?

Thanks!

Odds should be different for every combination of teams.

**slatter** · 12-09-10, 04:02 PM

Right, but for me to offer the prop, assuming, say, the bettor takes the teams who finished with the Nos. 1 through 7 draft picks the following year, is 2:1 on six teams a fair deal?

**sharpcat** · 12-09-10, 05:29 PM

Assuming all teams are equal (which obviously is not the case) each team would have a 37.5% chance of making the playoffs giving the player a 0.1% chance of correctly picking 7 teams in which case fair odds would be 966.34:1

If the player were able to successfully decrease the field to 16 teams the player would have a 13.35% chance of correctly picking 7 teams in which case fair odds would be 6.41:1.

In any case I would conclude that at 4:1 this would be a good bet for you to book but a very bad bet to make.

**slatter** · 12-09-10, 06:16 PM

Thanks sharpcat. I was only wondering because I've been offering +100 to everyone for the seven-team prop and have been getting mixed reactions. Some people are trying to get me to offer +400 odds, others are taking it at +100. Of course, these people are not avid sports bettors.

**donjuan** · 12-10-10, 01:25 AM

Originally posted by sharpcat

Assuming all teams are equal (which obviously is not the case) each team would have a 37.5% chance of making the playoffs giving the player a 0.1% chance of correctly picking 7 teams in which case fair odds would be 966.34:1

If the player were able to successfully decrease the field to 16 teams the player would have a 13.35% chance of correctly picking 7 teams in which case fair odds would be 6.41:1.

In any case I would conclude that at 4:1 this would be a good bet for you to book but a very bad bet to make.

You're trying to pick 7 teams to not make the playoffs, not 7 teams to make the playoffs. Also each leg of the "parlay" is not independent since one team not making the playoffs increases another team's chance of making the playoffs.

**sharpcat** · 12-10-10, 02:26 AM

I apologize Slatter I misread and thought you meant picking 7 teams to make the playoffs not miss the playoffs.

DonJuan also raises a good point that I overlooked being that for each team that is successfully removed from the pool the probability will decrease for each of the remaining teams likelihood of not making the playoffs.

I did not put too much time into thinking this through I was just aiming to give you a rough answer. DonJuan has clearly put some thought into this maybe he will stick his neck out and attempt to give us the correct way to solve this problem???

**slatter** · 12-10-10, 09:08 AM

No worries sharpcat, and thanks Don for clearing it up. I realize there are a lot of moving parts to this bet in that you could choose 3,365,856 different combinations of teams (thanks combinations and permutations online calculator!). But I was hoping someone could tell me who's generally getting the best of it at 1:1, 2:1, 3:1, etc.

**ThaddeusB** · 12-10-10, 09:45 PM

Here's what I would suggest: Go back and look at the season over/under win odds from the start of the year. Take the 7 worst projections and assume these are the chosen teams. Figure out the implied percentage of winning an average game (e.g. projected 8-8 = 50% win/game, 4-12 = 25% per game, etc.). Now, take these per game odds and figure out the odds of this team winning at least 9 games by chance. Add the 7 percentages together and this is roughly the odds that at least 1 of them will make it. (Obviously this is not exact for various reasons, but should be close enough.) This estimate is probably below the worst possible odds of any 7-team combination making the playoffs. (Since only 1 team has to be significantly underrated/get unusually lucky, the actual odds are probably a bit higher.)

**goucla** · 12-10-10, 10:58 PM

sounds like a good prop for u, wish i would have had more intyerest myself in the local scene here, could have been a bookie myself

**slatter** · 12-11-10, 09:18 AM

That's a great idea, thanks Thaddeus!

**sharpcat** · 12-12-10, 03:14 PM

...............

**slatter** · 12-13-10, 09:49 AM

Originally posted by ThaddeusB

Here's what I would suggest: Go back and look at the season over/under win odds from the start of the year. Take the 7 worst projections and assume these are the chosen teams. Figure out the implied percentage of winning an average game (e.g. projected 8-8 = 50% win/game, 4-12 = 25% per game, etc.). Now, take these per game odds and figure out the odds of this team winning at least 9 games by chance. Add the 7 percentages together and this is roughly the odds that at least 1 of them will make it. (Obviously this is not exact for various reasons, but should be close enough.) This estimate is probably below the worst possible odds of any 7-team combination making the playoffs. (Since only 1 team has to be significantly underrated/get unusually lucky, the actual odds are probably a bit higher.)

Assuming the binomial distribution calculator is what I'm supposed to be using (I think it is), here's what I came up with:

Detroit o5 2.30%
St. Louis o5 2.30%
Tampa Bay o5.5 4%
Buffalo o5.5 4%
Cleveland o5.5 4%
Oakland o6 6.20%
Kansas City o6.5 8.90%

Total: 31.70%

I'll run through these with the past 10 years or so, but wanted to make sure I was on the right track. Detroit o/u 5 wins means they're 2.3% to win nine games. That sound right? But how's it possible there's only a 32% chance that one of these teams wins at least nine games? Then it would seem like I'm getting the worst of it.

**slatter** · 12-13-10, 10:04 AM

Here are the 2009 numbers:

Detroit o5 2.30%
Oakland o5.5 4%
St. Louis o5.5 4%
Cincinnati o6 6.20%
Kansas City o6 6.20%
Tampa Bay o6.5 8.90%
Cleveland o7 11.90%

Total: 43.50% of one team making the playoffs (Cincinnati did).

Does this seem right?

**ThaddeusB** · 12-13-10, 10:36 AM

Originally posted by slatter

Assuming the binomial distribution calculator is what I'm supposed to be using (I think it is), here's what I came up with:

Detroit o5 2.30%
St. Louis o5 2.30%
Tampa Bay o5.5 4%
Buffalo o5.5 4%
Cleveland o5.5 4%
Oakland o6 6.20%
Kansas City o6.5 8.90%

Total: 31.70%

I'll run through these with the past 10 years or so, but wanted to make sure I was on the right track. Detroit o/u 5 wins means they're 2.3% to win nine games. That sound right? But how's it possible there's only a 32% chance that one of these teams wins at least nine games? Then it would seem like I'm getting the worst of it.

Seems we have discovered the weakness of my simplistic model. I assumed it would be sufficient to show an edge, but obviously that isn't the case. In my model there are two crucial assumption here that are both false.

1) Every game has the same probability, which is clearly false. Why does this matter? Say Detroit has 30% to win on average. If the season was 2 games long, they would have 51% to win at least 1 game if they had 30% in each game. But, if they had 50% and 10% instead, they would have 55% to win at least 1 game. Over a course of 16 games this variation could make a significant difference.

2) Each game is independent. This is also false. First, sometimes two "bad" teams will play each other. When they do, one of them has to win so they have a total of 100% to win but the model implies the teams only have a combine ~70% to win that game. Second, winning one game has a positive correlation toward winning more games. Thus, if a "bad" team gets off to a good start their expectation for the remaining games will rise even if they started off doing well mostly by luck (the emotional/confidence factor). I alluded to this in my first post - this is likely where much of your edge comes from.

Removing these assumptions make coming up with a number more difficult, but I'll see what I can do later today...

In the mean time, an even more simplistic model would be to simply count how many of the lowest 7 projections made the playoffs each each. Then use whatever ratio you come up with as the odds of any given bad team making it and figure the odds of at least 1 making it in any given year. (If you can't find the actual data, you can probably just use the 7 worst teams from the previous year without much problem.)

**slatter** · 12-13-10, 11:03 AM

Yeah, I've been coming up with win percentages of each game, running them through the binomial distribution calculator, and adding up the odds of the lowest seven teams making the playoffs. Dating back to 2002 (so far), I've got at least one and as many as four teams making the playoffs from that bottom tier every year, except in 2002 when there were none.

Also slightly flawed I think is the fact that nine wins doesn't guarantee you a spot in the playoffs. But I'm just trying to figure out how frequent this is, and your initial post has steered me in the right direction for sure.

As a sidenote, it's a pain in the butt trying to find some of the win totals dating back to 2001 and before. Damn!

**slatter** · 01-11-11, 02:24 PM

Bump, would love to hear any other opinions/ideas on this.