Parlays and Round Robins Can Be Good Bets - Bankroll Management

Conventional wisdom stipulates that parlays are bad bets for the typical sports bettor. Most people are sucked in by the large payouts for small investment, but if you miss 1 pick, you lose your bet.

But what if you're extremely concerned about bet limits, for example? Parlays aren't actually a bad idea, as suggested by Ed Miller, author of The Logic of Sports Betting, on Ed Feng's Football Analytics Show. But there are some major caveats that have to hold true:

1. Your win rate is profitable, obviously (> 52.38%)
2. You have extremely diligent bankroll management
3. You have very high volume - this won't work over a small number of bets
4. Your book is not adding juice on parlays - this is extremely important

Take, for example, a series of three -110 bets with a win rate of 55%. And say we try three strategies, with a base risk of $100 on each straight bet ($300 total), $100 on the parlay, or $50 on each round robin parlay ($150 total).

The math works out: you're expected to make varying degrees of gross profit, but a better ROI by using either non-straight bet strategy.

		Straight			Parlay			Round Robin
Result	Prob	Risk	Profit	ROI	Risk	Profit	ROI	Risk	Profit	ROI
WWW	16.64%	300	273	90.9%	100	600	600.0%	150	390	260.0%
WWL	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
WLL	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
WLW	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
LWL	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
LWW	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
LLW	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
LLL	9.11%	300	-300	-100.0%	100	-100	-100.0%	150	-150	-100.0%
	100.00%	E[X]	15	5.0%	E[X]	16	16.5%	E[X]	13	8.9%
		Min	-300		Min	-100		Min	-150
		Max	273		Max	600		Max	390
		Min W	82		Min W	600		Min W	30
		Min L	-109		Min L	-100		Min L	-150
		% Win	57.48%		% Win	16.64%		% Win	57.48%

To test this theory further, and to determine the added level of variance (the biggest concern), I ran a couple of scenarios through 100,000 simulated bets. I used 1 unit per straight bet, 1 unit per parlay, and 0.5 unit per round robin parlay.

Here are the results with a 55% assumed win rate:

Straight		Parlay		Round Robin
Risk	300,000	Risk	50,000	Risk	150,000
Result	15,524	Result	8,461	Result	13,535
ROI	5.20%	ROI	16.90%	ROI	9.00%
Min	-2.66	Min	-14.5	Min	-3
Max	15,546.89	Max	8,461.00	Max	13,545.00
MaxStreak	-18.54	MaxStreak	-25	MaxStreak	-16.5

The ROIs line up with the above math example (so the model is calibrated), and reaches the following conclusions:

1. You can do WAY more with your money using parlays - in this example, ~3x the ROI on 1/6th the bankroll usage
2. Your volatility, predictably, is way up - the largest streak of losses was 25%, which would be a quarter of your bankroll if you're sizing units to percent of bankroll

Obviously the win rate is hugely important, so here's how it would look with a 54% win rate:

Straight		Parlay		Round Robin
Risk	300,000	Risk	50,000	Risk	150,000
Result	9,890	Result	4,824	Result	7,948
ROI	3.30%	ROI	9.65%	ROI	5.30%
Min	-19.82	Min	-18.5	Min	-1.5
Max	9,892.29	Max	4,863.00	Max	7,950.60
MaxStreak	-21.54	MaxStreak	-26	MaxStreak	-15

And a 53% win rate (some thin margins here, probably shouldn't be betting this kind of volume if your win rate is 53%):

Straight		Parlay		Round Robin
Risk	300,000	Risk	50,000	Risk	150,000
Result	4,488	Result	2,392	Result	1,601
ROI	1.50%	ROI	4.78%	ROI	1.07%
Min	-5.05	Min	-20	Min	-6.6
Max	4,515.93	Max	2,524.50	Max	1,633.20
MaxStreak	-20.45	MaxStreak	-31	MaxStreak	-18

And finally, here's how it would look with only 2 team parlays:

Straight		Parlay
Risk	200,000	Risk	50,000
Result	10,486	Result	4,709
ROI	5.24%	ROI	9.42%
Min	1.73	Min	0.8
Max	10,490.18	Max	4,710.40
MaxStreak	-25.44	MaxStreak	-18