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Introduction

The purpose of this project is to show a simple way to take advantage of BetMGM’s One Game Parlay (OGP) insurance promotion. An OGP is a parlay where all the legs come from only one game. The sportsbook currently offers the promotion for the NBA, NFL, and NHL. A bettor can take advantage of this promotion once per day, per league. Using the NBA as an example, the promotion is defined as follows:

Place an NBA One Game Parlay with at least four legs. If all legs hit but one, you’ll get up to $25 back in free bets.

This means if a bettor places a 4 leg OGP, but only 3 legs win, they will be rewarded a $25 free bet. A free bet differs from a normal bet because the stake is not returned as part of the winnings. If a $10 bet wins with +100 odds, the payout is $20 (the $10 of winnings and the original stake of $10). If a $10 free bet wins with +100 odds, the payout is only $10. This is a very important distinction, as a good free bet conversion rate is very important in sustaining success in sports betting.

Expected Value and Free Bet Conversion

In order to evaluate whether the methodology is profitable, the expected value (EV) of each league’s OGP will be calculated. EV is just how much money a bet is expected to make on average over the course of many bets. A free bet conversion rate of 70% is a common goal among bettors, meaning they expect to win $7 for every $10 in free bets they receive. You can learn much more on free bet conversion and +EV betting here. I highly recommend this article as a starting point if you are interested is +EV betting.

A quick explanation of EV is just the amount each bet would be expected to make over the course of many bets. For example a $25 bet with an EV of +10% would be expected to on average make a profit of $2.50, which can add up much faster than it sounds.

A quick explanation of a wager’s free bet conversion is just the free bet amount multiplied by the probability of the bet hitting and the odds given. For example, a $25 free bet with a probability of hitting of 25% with odds of +240 would have an EV of $25 * 0.25 * 2.4 = $15, which would give us a free bet conversion rate of 15/25 = 0.6 or 60%.

Methodology

The idea behind this strategy stems from the idea that sportsbooks do an incredible job at setting the spread and total for games. When games end close to how the sportsbooks predicted, the bets win.

The strategy used is the same for all 3 leagues, although the odds differ. The 4 legs follow the pattern below:

This methodology takes advantage of the fact at least 2 of the legs are guaranteed to hit, as at least one team has to cover the spread and the over or the under has to hit. It only takes the spread or the total to be relatively accurate for the free bet insurance to kick in.

For the NFL and NBA, the bets will look the same. The point spreads added together will be 20, and the total points scored will have to fall in a range of 20, as you can only tease the spread and the point total 10 points in either direction. See the example screenshots below for a visual explanation.

NBA

NFL

NHL

Assumptions

Historical Analysis

The historical odds of NFL, NBA, and NHL games were used to evaluate the methodoology. The data consists of 833 games from the 2020 season through the 2022 season. The NBA odds consist off 668 games in the 2022-2023 season. The NHL data consists of 776 games in the 2022-2023 season.

NFL

As shown below, the NFL OGP hits roughly 31.2% of the time, a free bet is given 59.6% of the time, and the OGP misses 9.2% of the time.

There was not much variance when accounting for spread and total either. Some of the totals and spreads on the lower and upper ends were grouped together because of low sample size, but there is no clear pattern. The only argument that could be made is low game totals are a better strategy. This does conceptually make sense, as a low scoring game would make it more difficult for the winning team to cover 10 points more than the original spread, but again the sample size of games with totals below 40 is small enough where that assumption comes with some risk. Spreads over 11 also had a low sample size, but do not provide any advantage for this methodology.

Expected Value

Without accounting for this free bet, the EV calculations can be seen below.

nfl_results <- read.csv('nfl_results.csv')
ogp_hit <- nfl_results$sgp_hit #Probability parlay hits
payout = 25*(175/100 + 1) #Payout if parlay hits
ev = round(ogp_hit*payout/25,3)*100 - 100 #Expected Value
paste0('Expected Value: ',ev,'%')
## [1] "Expected Value: -14.2%"

At -14.2%, it is clearly a bad idea to make this bet without the promotion. However, since over half of the bets will return a $25 free bet, that has to be added to the EV of the bet. Two EVs will be calculated. The first will be an assumed 60% free bet conversion, which in this case would give every free bet received a value of $15. (25 * .6 = 15). The second will assume all of the free bets received will be used on another NFL OGP.

ogp_free_bet <- nfl_results$sgp_ins #Probability of receinving free bet
ev_60 <- round((ogp_hit*payout + ogp_free_bet*25*.6)/25,3)*100 - 100 #EV with 60% free bet conversion
ev_rerun <- round((ogp_hit*payout + ogp_free_bet*25*ogp_hit*1.75)/25,3)*100 - 100 #EV of re-betting the OGP
ev_60_string <- paste0('Expected Value w/60% Free Bet Conversion: ',ev_60,'%')
ev_rerun_string <- paste0('Expected Value of Using Free Bet on OGP: ',ev_rerun,'%')
cat(c(ev_60_string,ev_rerun_string),sep = '\n')
## Expected Value w/60% Free Bet Conversion: 21.5%
## Expected Value of Using Free Bet on OGP: 18.3%

The results clearly show using this methodology with the MGM NFL promotion has historically been profitable. The 60% free bet conversion rate is better, but even by just using the free bet to bet another NFL OGP, the EV is significantly positive. At 18.3%, each bet would be expected to return $4.575. In the 2022 NFL season, there were 61 game days. Remember, the promotion can only be used once per day. Over the course of an NFL season, the expected return would be $4.575 * 61 = $279.08. This is a fairly conservative number considering the assumed odds are only +175 and most games are higher than that. Additionally, there are better ways to use the free bets than placing the NFL OGP again, but this was a simple way to show the profitability of the method without having to search for good bets to use the free bets on. Refer to the article linked at the top of this page to learn more about better free bet conversion strategies.

NBA

The bar plot below shows the NBA OGP hits roughly 24.3% of the time, a free bet is given 50.3% of the time, and the OGP misses 25.4% of the time.

The NBA results, similar to the NFL results, do not show a clear advantage to choosing an OGP based on the spread or total. I did group the games into bins for the totals since there was such a wide range of spreads and each individual number did not have a high sample size. No matter how the data was analyzed, no pattern was shown to have any significant difference in probability in hitting compared to the dataset’s mean of 24.3%.

Expected Value

Without accounting for this free bet, the EV calculations can be seen below.

nba_results <- read.csv('nba_results.csv')
ogp_hit <- nba_results$sgp_hit #Probability parlay hits
payout = 25*(230/100 + 1) #Payout if parlay hits
ev = round(ogp_hit*payout/25,3)*100 - 100 #Expected Value
paste0('Expected Value: ',ev,'%')
## [1] "Expected Value: -20%"

At -20%, the NBA OGP is also a bad bet without the promotion. Again, after accounting for the free bets received, the two EVs will be calculated.

ogp_free_bet <- nba_results$sgp_ins #Probability of receinving free bet
ev_60 <- round((ogp_hit*payout + ogp_free_bet*25*.6)/25,3)*100 - 100 #EV with 60% free bet conversion
ev_rerun <- round((ogp_hit*payout + ogp_free_bet*25*ogp_hit*2.3)/25,3)*100 - 100 #EV of re-betting the OGP
ev_rerun <- round(ev_rerun,3)
ev_60_string <- paste0('Expected Value w/60% Free Bet Conversion: ',ev_60,'%')
ev_rerun_string <- paste0('Expected Value of Using Free Bet on OGP: ',ev_rerun,'%')
cat(c(ev_60_string,ev_rerun_string),sep = '\n')
## Expected Value w/60% Free Bet Conversion: 10.2%
## Expected Value of Using Free Bet on OGP: 8.1%

The results clearly show using this methodology with the MGM NBA promotion has historically been profitable. Again, the 60% free bet conversion rate is better, but even by just using the free bet to bet another NBA OGP, the EV is still +8.1%, meaning each bet would be expected to return $2.025. In the 2022-2023 NBA season, there are 168 game days scheduled, not including the playoffs. Over the course of an NBA season, the expected return would be $2.025 * 168 = $340.20. The assumed odds are only +230 and most games are higher than that, and again this calculation just assumes the free bet is used to re-bet an NBA OGP.

Update: I did find one NBA OGP that went down to +210. The EV will drop down slightly if those are the assumed odds used in the analysis.

NHL

The bar plot below shows the NHL OGP hits roughly 41.2% of the time, a free bet is given 50% of the time, and the OGP misses 8.8% of the time.

The NHL spread is almost always 1.5 goals, and since we are using the assumption all games will have a spread of 1.5 goals, the results will only need to be evaluated by the total goals scored line. For the NHL OGP, there may be something to betting on the higher total goals line. Now, over 90% of the games had a total set at either 6 or 6.5 goals, but there were 46 set at 5.5 goals, and those hit about half as often. And while there were only 15 games with a line of 7, they did hit at the highest rate of the group. As the chart shows, the hit rate did go up as the total goals line increased. Further analysis would need to be done to identify if there is a real trend here.

Expected Value

Without accounting for this free bet, the EV calculations can be seen below.

nhl_results <- read.csv('nhl_results.csv')
ogp_hit <- nhl_results$sgp_hit #Probability parlay hits
payout = 25*(100/110 + 1) #Payout if parlay hits
ev = round(ogp_hit*payout/25,3)*100 - 100 #Expected Value
paste0('Expected Value: ',ev,'%')
## [1] "Expected Value: -21.3%"

At -21.3%, the NHL OGP is also a bad bet without the promotion. Again, after accounting for the free bets received, the two EVs will be calculated.

ogp_free_bet <- nhl_results$sgp_ins #Probability of receinving free bet
ev_60 <- round((ogp_hit*payout + ogp_free_bet*25*.6)/25,3)*100 - 100 #EV with 60% free bet conversion
ev_rerun <- round((ogp_hit*payout + ogp_free_bet*25*ogp_hit*100/111)/25,3)*100 - 100 #EV of re-betting the OGP
ev_rerun <- round(ev_rerun,3)
ev_60_string <- paste0('Expected Value w/60% Free Bet Conversion: ',ev_60,'%')
ev_rerun_string <- paste0('Expected Value of Using Free Bet on OGP: ',ev_rerun,'%')
cat(c(ev_60_string,ev_rerun_string),sep = '\n')
## Expected Value w/60% Free Bet Conversion: 8.7%
## Expected Value of Using Free Bet on OGP: -2.7%

The results show using this methodology with the MGM NHL promotion has historically been profitable, but not if the free bet is used on another OGP. The free bet conversion rate of a given bet is just the probability of the bet hitting multiplied by the payout. So using the NBA OGP as an example, the free bet conversion would be 24.3% * (+230/100) to get 55.89%. If we re-run the calculation using this number as the free bet conversion rate, the NHL OGP’s EV is about 6.7%, or $1.675 per $25 bet. There are 178 different game days in the 2022-2023 NHL season, not including playoffs. Over the course of an NHL season, the expected return would be $1.675 * 178 = $298.15. While the assumed odds are -110, most games give better odds than this. Also, a free bet conversion of 55.89% can easily be topped. Even still, the data shows this methodology does work for the NHL OGP. The one caveat when compared to the other two leagues is the free bet should not be used on another NHL OGP.

UPDATE: As I was creating this report, MGM decided to add a required minimum odds 0f +400 for the NHL OGP only. This removes the opportunity to follow this methodology. Hopefully they remove the minimum odds again one day.

Summary

The final results of the 3 different OGPs can be seen below.

While the NHL OGP hits the most often, since the odds are so much lower, it has the lowest EV of the group. The NFL OGP has the highest EV of the bunch, but since there are so many more NBA games in one season compared to the NFL, the NBA OGP is the most profitable over the course of the season. The table below summarizes the expected value of each OGP over the course of the season. The NHL and NBA totals do not include the playoffs.

Even using extremely conservative odds, it’s clear this methodology is a very simple, quick way to consistently turn a profit on MGM’s OGP promotion. Hopefully they drop the minimum required odds for the NHL OGP. It’s unknown if they will include the MLB once their season is underway, or if they will bring back the promotion next fall for the NFL. As for now, the second half of the NBA season is a good opportunity to take advantage of this promotion while it lasts.

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