Round Robins Combinations based on Parlay Size

Many people size the parlays in their round robins using the number of teams in the round robin minus 1. For instance, 5 teams in the round robin, they would play it on 4-team parlays. This method can be written with the formula P = N-1 where P is the number of teams in each parlay and N is the number of teams in the round robin. This is not a good idea for most round robin sizes, as we will discuss further down this page. Using P = N-1 the number of wagers in each round robin will be equal to the number of teams in that round robin. This is demonstrated in the following table:

N =		P =
# teams in		Parlay	# of
round robin	Teams	Size (N-1)	Wagers	Combinations
3	A,B,C	2-team	3	AB AC BC
4	A,B,C,D	3-team	4	ABC ABD ACD BCD
5	A,B,C,D,E	4-team	5	ABCD ABCE ABCE ACDE BCDE
6	A,B,C,D,E,F	5-team	6	ABCDE ABCDF ABCEF ABDEF ACDEF BCDEF

Playing smaller parlays in a box results in many more combinations. This table summarizes the number of parlays in each round robin:

N =	number of wagers are in blue
# of teams in	P = Parlay Size
round robin	2-Team	3-Team	4-Team	5-Team	6-Team	7-Team	8-Team
3	3	1	n/a	n/a	n/a	n/a	n/a
4	6	4	1	n/a	n/a	n/a	n/a
5	10	10	5	1	n/a	n/a	n/a
6	15	20	15	6	1	n/a	n/a
7	21	35	35	21	7	1	n/a
8	28	56	70	56	28	8	1

How do we choose the best parlay size? We start by calculating the probability of each number of possible wins in each round robin. We do this calcuation for several handicapping strengths: a) 45% ATS weak handicapper, b) 50% ATS average, c) 53% ATS good, d) 56% ATS very good, e) 60% ATS pro. Note: Beginners usually think they can do better than this. Believe me, hitting 60% ATS over a long period of time is much tougher than it sounds! Then we feed these probabilities into tables which calculate the return for each round robin combination.

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Probability of ATS wins in each Round Robin

First, let's understand how many result combinations there are for 4 teams (we will call them teams A, B, C, and D). There are 16 possible ATS results not counting pushes (2^n where n is number of teams in parlay). There is only one way to go 4-0 ATS (A,B,C,D all win), and one way to go 0-4 ATS (A,B,C,D all lose). There are four ways to go 3-1 ATS (A wins, BCD lose, or B wins ACD lose, or C wins ABD lose, or D wins ABC lose.). Correspondingly there are four ways to go 1-3 ATS. There are six ways to go 2-2 ATS.

This table enables us the win/loss possibilities for each round robin size calculated according to a person's average ATS. to see the odds of hitting if we are average (50% picks correct). The middle column shows how many picks out of the 4 teams win. If we play this round robin on 2-teamers, we would hit exactly one parlay 37.5% of the time. Having 3 picks ATS would give us three 2-teamers (25% chance) while a sweep 4 of 4 gives us six 2-teamers (6.3%). Playing this on 3-teamers means than we would hit only on 3 picks or 4 picks (2 of 4 results in a loss).

# teams in round robin = 4		Possible # of ways to come up with this number of wins ...	if you hit 50% ATS, your probabily for each # of wins is ...
	ATS
	(win/loss)	# of combinations	Probability
	0/4	1	6.3%
	1/4	4	25.0%
	2/4	6	37.5%
	3/4	4	25.0%
	4/4	1	6.3%
		16	100.0%

If you are good enough to hit 56% against the spread, the probablilites change to:

# teams in round robin = 4		Possible # of ways to come up with this number of wins ...	if you hit 56% ATS, your probabily for each # of wins is ...
	ATS
	(win/loss)	# of combinations	Probability
	0/4	1	3.7%
	1/4	4	19.1%
	2/4	6	36.4%
	3/4	4	30.9%
	4/4	1	9.8%
		16	100.0%

You now have higher probabilities of hitting 3 of 4 (25% increases to 30.9%) and getting a 4 of 4 sweep (6.3% increases to 9.8%). An average player (50% ATS) playing this 4 team round robin on 3-team parlay would hit 31.3% (probability of hitting 3/4 plus 4/4) of the time. A very good player (56% ATS) would hit 40.7 % of the time. This difference is extremely important, as we will see when we start calculating the ROI tables...

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Return on Investment by ATS & Round Robin Type

A word about the calculations ... Amount invested is static regardless of the number of combinations. Example:

$100 is wagered on a 5 team round robin:
5 teams played on 3-team parlays =10 combinations = $10 wager size ($100/10).
5 teams played on 4-team parlays = 5 combinations = $20 wager size ($100/5).

These tables show the chances of win/loss for each round robin size depending on the player's average ATS. More importantly, the ROI's are displayed for each round robin/parlay size possibility. The calculations are a bit too convoluted to go into here. If you would like more details on how these numbers were calculated, you may download this spreadsheet parlay_calculations.xls. This is in Microsoft Excel format. Right-click and "Save As" will download from most browsers.

These tables cover 3-team, 4-team, 5-team and 6-team round robins.

45% ATS (weak) Table
50% ATS (average) Table
53% ATS (good) Table
56% ATS (very good) Table
60% ATS (pro) Table

This table is a summary of the only really important stat, the ROI's for each type of play broken down by player ability (ATS win%).

		Return on Investments
	ATS Win %--->	40	45	50	53	57	60	62
# teams in Round Robin	Parlay size	Return on Investments
4	2-team	-42.5%	-27.1%	-10.0%	1.1%	17.0%	29.6%	38.4%
4	3-team	-55.2%	-36.2%	-12.5%	4.2%	29.6%	51.2%	66.8%
5	2-team	-42.4%	-27.1%	-10.0%	1.1%	17.0%	29.6%	38.4%
5	3-team	-55.2%	-36.2%	-12.5%	4.2%	29.6%	51.2%	66.8%
5	4-team	-69.3%	-50.8%	-25.0%	-5.3%	26.7%	55.5%	77.3%
	straight wagers	-23.6%	-14.1%	-4.5%	1.2%	8.9%	14.6%	18.4%

If you hit 53% of your picks, your most profitable strategy is to use 3-teamers regardless of whether your round robin contains 4 or 5 teams. This follows for 57% players as well, even though the 5 team round robin/4-team parlays starts to pay well by then. Star handicappers (60% ATS and up) can do well on 4-teamers.

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Greencapper's Advice

> Use round robins only on your stronger picks!
The preceding summary table shows that if you hit below 53% of your picks you will lose your money quicker playing round robins than if you were playing straight wagers. Round robins really start paying off once you get to 56%+ ATS. Therefore, round robin wagers are not for casual plays (game is on TV, your alma mater is playing, etc.).

> Choose the 3-team parlay option, regardless of the number of teams in your round robin.
The preceding summary table shows that 4-team parlays do not start paying off until you approach hitting 60% ATS. You should not assume you can hit 60% over the long run, even though this does not sound that hard (it really is). If you can manage 53% to 60% ATS, your 3-teamers will pay a nice return. The following section on parlays- house edge helps to explain why it is so much harder to profit on 4-teamers.

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Parlays - House Edge

The house percentage differs depending on the size of a parlay. It is fairly low for 2-teamers and not too bad for 3-teamers. Once you get up to 4-teamers and higher, the house take will climb significantly. Look at it this way ... if there were absolutely no house edge, you would get paid 1:1 on a football play. In a 2-teamer your chances of hitting are 1 in 4 (25%) so if there were no house edge, it would pay 3:1, instead of the more common 13:5. The following table shows the size of the parlay, the payout in units if there were no house edge, the actual payout with the house edge, and the percentage of true odds the house is paying back (this may vary from one sportsbook to another, odds taken from BetJamaica):

1 unit bet		Paid if no edge	Actual payout	% that house pays
1 team	1 in 2	1	0.91	91%
2-teamer	1 in 4	3	2.6	87%
3-teamer	1 in 8	7	6	86%
4-teamer	1 in 16	15	11	73%
5-teamer	1 in 32	31	22	71%
6-teamer	1 in 64	63	40	63%
7-teamer	1 in 128	127	75	59%
8-teamer	1 in 256	255	100	39%

The bottom really falls out once you get into larger parlays! Straight bets (1-teamer) have the lowest takeout, but most gamblers want to have a little fun and go for the larger payoffs. The takeout really drops between 3-teamers and 4-teamers, and it only gets worst as the number of teams increase.

The increased house edge is why round robins are only for those who can hit a good ATS %. Weak players will lose their money faster, while stronger players can use the accumulation of parlays to increase their winnings. See tables at the top of this page for breakdowns. Tables were calculated using this Microsoft Excel worksheet: calculating round robins.xls.

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Other Ideas

2-Team Parlay Side with Total This is where you play a 2-team parlay on a single game using both the team and the game total. This is often used when you think a team's chances depend on their offense (or defense) having a banner day. Also if you think the play is against a team because their offense (or defense) is due for a bad game. Example: Peyton Manning is ripping teams and Jacksonville is their next opponent. If you believe the Jaguars have an excellent secondary that will slow Peyton down, you might consider a parlay on Jacksonville +points and the Under.	Money Line favorites parlayWhen playing a favorite on the money line you are often risking a lot to win a little. One strategy is to put two or three favorites together on a parlay. Example: You like Yankees at -250 and Mets at -200. You could bet $100 on each game and win $40 on the Yankees and $50 on the Mets for +$90. Take the same $200 and put them on a 2-team parlay and the payout is $220, a $130 improvement. How did I get $220? See my parlay calculator page for instructions on how to calculate payoffs.
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