A Primer On NFL Parlay Betting

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Parlay bets are enticing. It is the sports betting world equivalent of the lottery. If you follow any of the books on Twitter, you will see that they commonly tweet out massive parlays that hit. Here is WynnBet jumping the gun in case the bettor lost the last leg:

After he won, the book double-dipped on the advertising by posting it again:

Notice the tag line, “We Win Together.” Isn’t that nice? Your book is on your side. You two are in it together. (Written with a heavy feeling of sarcasm). I have never seen a book tweet out every parlay from that same day that lost. I wonder why that is? Books want you to bet parlays. When you do, their profits rise. 

For these reasons, parlays have historically been described in two words, sucker bets. I have a tough time believing that anything in this world is so binary. Moreover, the rapid expansion of the sports betting market since the Supreme Court’s decision in PASPA has radically expanded the options. Before the ruling, our choices were the brick-and-mortar boos in Vegas, off-shore books, and bookies. Now, new players are entering the market, FanDuel, and DraftKings for example, and forcing the old guard to adapt.

Let us separate parlay wagers into two groups. First, the longshot flyer bets for minimal risk. The true lottery tickets. Where those are concerned, my response is, fine, have fun. Though try not to take every moneyline favorite. I am impressed that the person above took all “unders.” I am more concerned with the parlay that involves two to five sides and typically involves significantly more significant risk.  

To make these second types of parlay wagers successful, you need to know a few numbers and the principle of correlation. 

The Anatomy of a Parlay Wager:

I will use standard spread bets to explain the basic math behind a parlay wager, but you can substitute the relevant percentages for any other type of wager. 

After the book sets a line, its goal is to make the wager a 50/50 proposition. To determine the expected win percentage of a three-team parlay, we need to multiply the expected probability by the power of the number of sides in the parlay (trials). In a three-team parlay that equation equated to.50^3 = ..125, or 12.5%. 

We simply divide 100% by 12.5% to determine the correct odds, and we get eight. Since we get our bet returned in addition to our winnings, the correct payout on a three-team parlay is 7 to 1. In the chart below, I lay out the correct odds for specific sides in a parlay.

Number of LegsPercent to HitCorrect Odds
225.00%3 to 1
312.50%7 to 1
46.25%15 to 1
53.13%31 to 1
61.56%63 to 1
70.78%127 to 1
80.39%255 to 1
90.20%511 to 1
100.10%1023 to 1

If you wanted to do the same math with different probabilities for each leg, simply multiply the probabilities together, ex. .5 x .25 x .73, etc

Of course, books do not pay those odds. On a three-team parlay, most books pay 6 to 1, although it is possible to find some 6.5 to 1’s out there. However, they have been deceptive about it. I walked into a book recently and saw advertising everywhere that indicated their three-team parlays paid the best odds, “7 for 1.” I am not sure who they were trying to fool. Odds of 7 for 1 are identical to odds of 6 to 1. In the former, the book gives you seven but keeps your initial wager. In the latter, the book gives six and your initial wager back. It is truly a six or half-dozen argument. 

Below, I have recreated the chart above with the required success (Win % Needed) rate on each leg to make the book’s odds a break-even proposition:

Number of LegsPercent to HitCorrect OddsTyp. Book PaysPercent to HitWin % Needed
225.00%3 to 12.6 to 138.46%62.20%
312.50%7 to 16 to 116.67%55.10%
46.25%15 to 111 to 19.09%54.92%
53.13%31 to 122 to 14.55%53.91%
61.56%63 to 145 to 12.22%53.05%
70.78%127 to 190 to 11.11%52.60%
80.39%255 to 1180 to 10.56%52.35%
90.20%511 to 1360 to 10.28%52.20%
100.10%1023 to 1720 to 10.14%52.00%

Since books pay out less than the correct odds, the only way to make a parlay wager have a positive expectation is to possess a success rate on the parlay legs, which exceeds the percentage indicated in the final column of the chart. If you have a success rate on the games you wager that is more than the rate needed, then, you may think it is a good bet, it is not. At least not yet. 

You will run into the same problem discussed in the primer on moneyline bets. Specifically, suppose the following is true: you have a win percentage of 55.3% on your top three sides each week. Looking at the chart, you may conclude that you should parlay those teams each week. In an 18 week season, that would mean your necessary win total is 9.954 (18*.553) weeks a year. Since you cannot win fractions of a week, you would need ten winning weeks out of 18.

If we move this over to a binomial distribution calculator, we will get the following expectation. 

As you will recall from the primer on moneylines, this means that you would expect to have a profitable season 5.87 times out of ten (Cumulative probability that wins are equal to or greater than 10). In turn, this means that you would lose four or five years in a ten-year window. So to make the parlay a valuable proposition, a successful season in seven out of ten years, you will need the following winning percentage. 

If your win percentage on your top three sides each week is greater than 59%, by all means, bet the three-team parlay.

If your success rate is not naturally high enough to make the parlay a positive expectation wager, which is the case for most bettors, then the only other option is to find a correlated parlay.  

Correlated Parlays

A correlated parlay involves legs that are more likely to happen in concert. Before the relatively new advent of same-game parlays, this usually involved a weather-related phenomenon. For example, suppose a late-breaking snowstorm that would hit Chicago and Green Bay during their respective home games, and you were aware of the weather before the book could adapt its lines, you could parlay the unders in both games. There are other ways as well. The point is, success on one leg of the parlay needs to make the success rate on the other leg more probable. 

With the advent of same-game parlays, the ability to find correlation became significantly more straightforward. Of course, the odds are altered as well. However, an individual’s rushing yards could be correlated with the opposing teams’ defense. You could fade one back in favor of another based on the matchup and your analysis in a back by committee approach. The list is endless. Just ensure that your correlation advantage exceeds the percent the book’s implied percentage. 

A Word of Caution

Many people have been vocal about the idea of putting “anchor” sides into parlay legs. The idea is, bet X is my favorite bet of the week, so I will parlay it with team Y, and team Z, and teams Y and Z. Other people advocate taking your three best legs of a parlay and then combining them with both sides of a fourth game. I strongly advise you to avoid this strategy. If you see validity in it, I would ask you to do the math. Chart your favorite, or three favorite legs, over the course of a month, and then play out the parlay wagers you would have made. See, if, at the end of four weeks it looks profitable. Most likely, it will not. Variance is too high in the NFL.

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