NFL math

Say you're a handicapper and you are able to achieve a very high winning percentage (65% or better). To achieve a percentage that high you obviously have to hit a few great streaks here and there throughout the season. Well, my question is this: would it be better for the handicapper to just make straight bets throughout the season or to do 3 game parlays, for instance, to try and win less, but increase earnings per win. And let's say the parlay pays 6 to 1. Any math that supports this kind of problem?

Quote: Chodempole

Any 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.

Trying to get past the name Chodempole long enough to look at this problem, but it is killing me haha.

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: studmuffn

Curious 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

This has certainly opened my eyes to the potential of parlaying, which I had previously dismissed as a sucker bet. I will bring this to a friend who does a lot of point spread bets (once I make sure his accuracy is greater than 50%).

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: TomG

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.

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: studmuffn

I'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: Chodempole

56 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)

It 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.

Quote: Ayecarumba

It 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.