NFL math
Quote: ChodempoleAny math that supports this kind of problem?
Quite a bit:
1) three-team parlays at +600 have a lower commission than single game bets at -110
2) Starting with $1,000 and betting full Kelly against every NFL side and total someone who is a 65% winner will end the year with around $16 billion (I think, expected growth of 1.033% according to online calculator means 1000 x 1.033^512. Someone please correct me if that's wrong).
That means you will run into limit bets very quickly, parlays are a great way to get around that.
3) If you win nine out of 14 games (64%), risking a total of $15,400 ($1,100 per game) you will profit $4,600. If you instead make three team parlays every way, you would profit $9,400 while risking the same amount.
I just need to walk through your 3rd point, Tom, for my own understanding:
During byes, 14 games a week, you wager $1,100 on each for -110 ($15400 wagered). Get 9 correct, no pushes, win $18,900. Total gain: $3,500 or +22.7%
If you parlayed all 14 games in sets of 3, you'd place 364 bets for +600, which is $42.31 per parlay for the same BR. You get 9 games right, so 84 wins of your 364 parlay bets. Wins payout $296.17, so 84 wins nets $24,878.30. Total gain is $9,478.28 or +61.5%
Wow, I never would have guessed that it was so much more profitable to parlay, if you could be assured such a high accuracy as 65% correct. Though quite a bit of legwork, laying 26 times as many bets. Curious as well that 3-team parlays at +600 are 50% more profitable than 2- or 4-team parlays at that win rate.
Quote: studmuffnCurious as well that 3-team parlays at +600 are 50% more profitable than 2- or 4-team parlays at that win rate.
In the 9-5 example, four team parlays do even better, with a $10,350 profit on $15,400 risked, before dropping off at five. It isn't a matter of the win rate so much as the sample size. One three-team parlay loses even if you pick 66% winners.
If you include sides and totals, you would go 21-11 on NFL games in a given week. If you include college sides and totals, you could go 65-35. Now compare the millions (or would it be in the billions?) you could win on all the possible 20-team parlays (each paying out 417,500 to one) with the mere $26,500 you would win if you just put $1,100 on each game
I think that the difference in our result above came from my use of +1000 for a 4-team parlay, rather than +1228.
I'm having difficulty comparing the benefits of parlaying, as we did above, for non-integer win totals, such as 7.5/14. I think I need to weight each number of wins using a distribution with a mean of 7.5/14, but I'm not sure if the distribution is normal, nor what the variance in wins would be. The Wizard's page on NFL bets FAQ mentions a SD of 1.0333 for each point spread bet, so I think I will start with that times sqrt(14) = 3.866 and a normal distribution.
Quote: TomGIn the 9-5 example, four team parlays do even better, with a $10,350 profit on $15,400 risked, before dropping off at five. It isn't a matter of the win rate so much as the sample size. One three-team parlay loses even if you pick 66% winners.
Does this take into account the change in odds when you go from a 3 team parlay to a 4? Here are the possible combinations and odds i'm working with:
28 Parlays of 2 Teams: 2.6/1
56 Parlays of 3 Teams: 6/1
70 Parlays of 4 Teams: 10/1
56 Parlays of 5 Teams: 20/1
28 Parlays of 6 Teams: 40/1
8 Parlays of 7 Teams: 75/1
1 Parlay of 8 Teams: 10/1
So, Tom is correct in that a four team parlay produces the most chances to spread out your total risk, but of course, less parlays means more possible return... Except for an eight team parlay, I think it's because it exceeds the limits like Tom mentions. I really don't know what the best option is. You guys have my head spinning.
Quote: studmuffnI'm having difficulty comparing the benefits of parlaying, as we did above, for non-integer win totals, such as 7.5/14.
for two team parlays your chance of winning will be (7.5/14)^2
for three teams (7.5/14)^3
Another way you can try it is to randomize 536 wins and 464 losses and see the results of those 500 or 333 parlays. Because you should win very close to 28.7% for the two-teams and 15.4% for the three-teams, it will almost certainly earn more money than if you bet those 1000 games as single wagers.
Quote: Chodempole56 Parlays of 3 Teams: 6/1
70 Parlays of 4 Teams: 10/1
Just look at it this way: normally four teams at 10-1 would be a very poor bet, because you are essentially risking $700 to win $1100. But in this scenario, you have a 65% chance of winning the fourth bet after winning the first three, so in that case risking $700 to win $1100 is good.
The farther you get above picking 53% winners, the better and better the parlays become compared to single game bets. The farther you get above picking 53% winners the better and better it gets adding more teams to each of your parlays
(the inverse is also true, picking fewer than 52% winners means parlays will lose more money than betting only on single games)
Quote: AyecarumbaIt should be noted that if the 65% "chance of winning" is actually the win percentage over the whole season, your bankroll may have to be significant to withstand the weeks you go 2-10, especially if they happen to be the first three of the season.
Nope. If you have a 65% chance of winning each game, the chance of losing 10 of the first 12 is extremely low. Yet, starting with just $1000 and somehow losing the very first 10 games and then going on to win 13 out of every 20 afterwards (for a reduced winning percentage of 62.5%), you will still earn over $300,000 if you bet every game according to Kelly Criterion.
Also, for the sake of realism, let's not use 65% as a probability of winning. Nobody is going to maintain a percentage like that long-term.
Low limits. Try betting just a few dimes at a Las Vegas sportsbook on a line that's better than market price. It is much less likely to be rejected if it's in a parlay
Small markets. It only takes a few hundred to move the line on most WNBA games. Put them into parlays and you can bet a lot more at a better price
Correlated parlays. Even if the correlation is small, if it exists and both sides are profitable, it is obviously definitely better to make a parlay
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Also, it doesn't take that long for the variance in a 16.67% bet to even out. For someone who can do better than 54% you can randomize 540 wins against 459 loses and see how 999 straight bets would have compared against 333 parlays (obviously risking the same amount in both scenarios). That represents only a very small fraction (like 1 to 2%) of an entire career of a professional sports bettor (we can also try 5400 wins against 4599 losses)
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Kelly Criterion calculator I use says expected profit on a single game bet with a 54% chance at -110 is 0.1051% expected profit. A 15.75% chance at +600 is 0.1751%.
Quote: TomGLow limits. Try betting just a few dimes at a Las Vegas sportsbook on a line that's better than market price. It is much less likely to be rejected if it's in a parlay
Small markets. It only takes a few hundred to move the line on most WNBA games. Put them into parlays and you can bet a lot more at a better price
Good points. I agree that parlays generally don't move lines. A good strategy if limits are an issue is to mix them into parlays first. Then, before you leave, pop 'em with some straight bets and let them move the lines.
Quote:Also, it doesn't take that long for the variance in a 16.67% bet to even out. For someone who can do better than 54% you can randomize 540 wins against 459 loses and see how 999 straight bets would have compared against 333 parlays (obviously risking the same amount in both scenarios). That represents only a very small fraction (like 1 to 2%) of an entire career of a professional sports bettor (we can also try 5400 wins against 4599 losses)
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Kelly Criterion calculator I use says expected profit on a single game bet with a 54% chance at -110 is 0.1051% expected profit. A 15.75% chance at +600 is 0.1751%.
Here is my analysis given a 54% chance of winning each side:
Straight bets:
Advantage = 0.030909091
variance = 0.90532562
Kelly bet = 0.034141408
Bankroll gain per bet =0.00105528
3-team parlay (paying 6 to 1)
Advantage = 0.102248
variance = 6.500785346
Kelly bet = 0.015728561
Bankroll gain per bet = 0.001608214
However, you get to bet the straight bet three times. Expected gain over the three bets = 3*0.00105528 = 0.00316584. That is 97% more profit compared to the optimal Kelly bet on the parlay.
Quote: Wizard
Also, for the sake of realism, let's not use 65% as a probability of winning. Nobody is going to maintain a percentage like that long-term.
Thank you. I definitely believe people can make occasional spot bets with a 65% result. But I don't believe anyone can make weekly 4 team parlays with a 65% success on each bet. 58% would be a tremendous result over the course of a season and I doubt anyone can do that over multiple seasons.
Quote: WizardHowever, you get to bet the straight bet three times. That is 97% more profit compared to the optimal Kelly bet on the parlay.
That is big issue and enlightening to see it that way. I guess it ends up being all those other "real-world" conditions that make three-team parlays better and not merely the -109 and higher EV that comes with it.
(I get 0.03400 and 0.01704 as the correct Kelly bet using the formula here: https://en.wikipedia.org/wiki/Kelly_criterion)
Quote: ChodempoleWizard, i'm having a difficult time deciding which way of betting will satisfy specific goals. One goal may be to increase earnings as fast as possible, one may be to minimize bankroll loss, another may be a mixture of both or anything in between. But you would know better than most which strategy fulfills each goal. For me, I would put more focus on the speed of increased earnings because of how positive I feel about my handicapping strategies. Obviously not the fantasized 65%, but absolutely a winning rate of some kind. But I'd like to hear what you, or anyone else has to say about what you believe to be the best betting strategies for different goals and their drawbacks. I appreciate the help in advance and apologize for any headaches this may cause you guys for thinking too much.
If speed is your goal, than the multi team parlay is the way to go. High variance is the price for lottery type odds. You could lose alot on one weekend, but you could also win a wheelbarrow full of cash.
Quote: TomGIn the 9-5 example, four team parlays do even better, with a $10,350 profit on $15,400 risked, before dropping off at five. It isn't a matter of the win rate so much as the sample size. One three-team parlay loses even if you pick 66% winners.
Tom may have been the most accurate though, use a four team parlay and bet every possible combination. I do have the time and means of making that bet. So it's not out of the question with regards to the extra legwork that would need to be done to make all 70 bet combinations
Quote: Chodempole...with regards to the extra legwork that would need to be done to make all 70 bet combinations
I should probably let this thread rest peacefully, but I'd hate for you to go to the bookie with 70 units, when there are 1001 possible 4-way parlays from 14 events. Also, much thanks to the Wiz for tempering our wild dreams with some realism and br management.
Quote: studmuffnAlso, much thanks to the Wiz for tempering our wild dreams with some realism and br management.
You're welcome. Just doing my duty.
Quote: WizardYou're welcome. Just doing my duty.
Hello. Will you be posting the 1/2 point cards and picks again this season? Hope so....
Quote: NokTangHello. Will you be posting the 1/2 point cards and picks again this season? Hope so....
I shall!
