Fair Moneyline Odds

Here's an excerpt from an earlier post describing what I call "Fair Moneyline Odds" (FMO):

Use week 3's DEN at OAK -125/+105 game as an example. I strictly use decimal odds* in all of my calculations, it's much easier to use in calculations. The decimal odds are DEN 1.80, OAK 2.05.

NFLSim determined the probability of DEN winning to be 77%. To determine the Fair Moneyline Odds, divide 1 by the probability (as a decimal). 1/0.77 = 1.30. Assuming the NFLSim has assigned the correct probability - and this only works if it does - then out of 100 games, DEN will win 77 of them. Starting with $100 and making 100 $1 bets, you will win 77 of bets. At a payout of 1.30, 77 winning bets gets you back to $100, you break even. Any payout larger than 1.30 will produce a profit after 77 wins.

In the case of the DEN game, DEN offers a 1.80 payout. At NFLSim's probability, 77%, you are expected to win 77 bets at 1.80. 77*1.80 = $138.6. There is an expected profit of $39. A payout of 1.80 is greater than the break even odds of 1.30 (the Fair Moneyline Odds), so it is a good bet.

On the other side of the matchup is OAK 2.05. The probability of OAK winning is 23%. The FMO would be 1/0.23 = 4.35. If you win 23 bets at a payout of 4.35, you break even at $100. Currently, Vegas pays 2.05 for an OAK win. If you win 23 bets at a payout of 2.05, you end up with $47.15 for an expected loss of $52.85. A payout of 2.05 is less then the FMO of 4.35, this is a bad bet.

In the spreadsheet, I list the break even moneyline odds for the specified team. If your sportsbook has odds greater than what is listed for that team, it is good to place that moneyline bet. However, if the odds are less than break even, it is a good idea to bet on the opposing team (even if they're picked to lose). With this system, it is irrelevant who you think will win the game. This is all about exploiting the inefficiency in the line.

*To convert American odds to decimal odds:
For the underdog, add 100 then divide by 100. OAK +105 =>  (105 + 100)/100 = 2.05
For the favorite, divide -100 by the odds, add 1. NYJ -125 => -100/-125 + 1 = 1.80

2008 Season Results

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These results from last year, excluding weeks 1 and 2, which there wasn't enough data for. It's broken into 3 sections: Straight up Winner, Against the Spread, and Over/Under. I broke down the approximately 200 games into 5 intervals, each interval representing a confidence spread of 10%. When you see 96 games in the 50-59% interval, that means of the 200+- games NFLSim picked, 96 games fell in the confidence interval of 50-59%. Likewise, 70 games had winners predicted as 60-69% favorites (in the straight-up category). To the left of the 'Games' column is the 'Correct' column. That is simply the number of NFLSim's correct picks in that interval. Accuracy is the percentage of time that NFLSim correctly picked a game in that interval.

1. Straight up Winner
NFLSim was absolutely phenomenal when it came to picking the winner. At first glance, you see the season record at 139-70 (66.5%). That's nothing special until you take a deeper look at the statistics.

Straight-up	% Interval	Wins	Games	Win %
	50-59%	61	96	63.5%
	60-69	45	70	64.3
	70-79	27	36	75
	80-89	4	5	8
	90-100	2	2	1
	Total	139	209	66.5

First, lets take a look at the 'expected number of wins' for each interval. In the 50-59% interval, it can be expected that after a large number of games, 55% of those games should be picked correctly(the mid-point of the 50's). In the 60-69% interval, 65% should be picked correctly, and so on. The closer NFLSim's number of correct picks is to the expected number of correct picks, the better NFLSim approximates reality. This is very important, because if you know the exact probability of a team winning, you automatically know if Vegas' payout makes for a good bet or a bad bet. The closer that the predicted probability is to the actual probability, the smarter your bets are. The smarter your bets, the more $ you make! (This is the basis for the Bet Optimization Algorithm.... which is new and much improved this year.)

If we take a look at the first interval, 50-59%, 96 games took place. In theory, you should expect that 55% of those teams predicted to win should actually win. 55% of 96 games, 55% * 96, equals an expected number of wins of 53. NFLSim actually picked 61 winners, so it beat the expected number of wins by 8. This is great because it picked more winners than it was supposed to, but it was pretty far from the expected number of wins. From 60% on is where it gets very, very interesting. NFLSim reaches near theoretical perfection - the probability given by NFLSim is the actual probability that the team will win!!! If anyone has seen this feat achieved by anyone else please let me know.

Here is a table of expected numbers of wins:

	Expected Correct	Actual Correct
50-59%	53	61
60-69	46	45
70-79	27	27
80-89	4	4
90-100	2	2
Total	132	139

In the graph: Red is what should have happened, Blue is what did happen.



Now that I've gone through the whole explanation of the stats, I'll skip straight to the numbers.

2. ATS
ATS didn't do as well as straight-up. Looks like it was pretty close to a flip of a coin. The right team would win by the wrong score. I would hate to tamper with the program when the straight-up accuracy is so reliable after 209 games. I'll probably just stop posting ATS until I can fix it up.

ATS	% Interval	Wins	Games	Win %
	50-59	37	86	43
	60-69	46	78	59
	70-79	18	33	54.5
	80-89	0	3	0
	90-100	1	1	100
	Total	102	201	50.7

	Exp. Correct	Actual Correct
50-59%	47	37
60-69	51	46
70-79	25	18
80-89	3	0
90-100	1	1
Total	127	102

Interestingly, the slope of the trend line is almost what it should be. Had 1 of the 80% games won, it would be almost perfect (albeit far lower than it should be). That suggests that all I may need to do is to add/subtract from the calculated probability to arrive at the true probability... interesting. There is back testing to be done!

3. Over/Under
Finally, if you haven't gone to sleep yet, here are the O/U stats. O/U actually did much better than I expected. It performed much better than the ATS and its accuracy approached the expected accuracy.

Over/Under	% Interval	Wins	Games	O/U Win %
	50-59	77	145	53.1
	60-69	30	48	62.5
	70-79	3	6	50
	80-89	2	3	66.7
	90-100	2	2	100
	Total	114	204	55.9

	Exp. Correct	Actual Correct
50-59%	80	77
60-69	31	30
70-79	5	3
80-89	3	2
90-100	2	2
Total	121	114

O/U actually performed very well compared to what was expected. And hell, at 56% accuracy, you'll be making money anyway.












You've seen the performance, you've seen the stats, you know what to expect. What it comes down to:

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Week 8: Results

This past week was an amazing week. Perhaps the best week yet. NFLSim knocked 'em out of the park, going 2 for 3 with underdogs (missed TB), 10-4 (71.4%) picking the winner, 8-4 (66.7%) against the spread, and 7-6 (53.8%) against the O/U. The spread and O/U combined for 15-10 (60%). Even BOA, which I've been tracking, but not posting, returned a solid 19%.

Straight	%	Wins	Games	Win %
	50-59	3	4	75.0%
	60-69	3	6	50.0%
	70-79	4	4	100.0%
	80-89	0	0	---
	90-100	0	0	---
	Total	10	14	71.4%
Spread	%	Wins	Games	Win %
	50-59	4	7	57.1%
	60-69	4	4	100.0%
	70-79	0	1	0.0%
	80-89	0	0	---
	90-100	0	0	---
	Total	8	12	66.7%
Total		Wins	Games	Win %
	50-59	6	11	54.5%
	60-69	0	1	0.0%
	70-79	1	1	100.0%
	80-89	0	0	---
	90-100	0	0	---
	Total	7	13	53.8%

ARI at CAR -4, 43.5
Winner: CAR, 57%
Spread: ARI +4, 59%
O/U: OVER, 51%

ATL at PHI -9, 45
Winner: PHI, 75%
Spread: ATL +9, 51%
O/U: OVER, 58%

BUF -1.5 at MIA, 42
Winner: MIA, 54%
Spread: MIA +1.5, 54%
O/U: OVER, 60%

KC at NYJ -13.5, 39
Winner: NYJ, 72%
Spread: KC +13.5, 64%
O/U: OVER, 71%

OAK at BAL -7.5, 36
Winner: BAL, 65%
Spread: OAK +7.5, 59%
O/U: OVER, 55%

SD -3 at NO, 46
Winner: NO, 54%
Spread: NO +3, 64%
O/U: UNDER, 55%

STL at NE -7, 43.5
Winner: NE, 67%
Spread: STL +7, 59%
O/U: OVER, 56%

TB at DAL -1.5, 40.5
Winner: TB, 68%
Spread: TB +1.5, 70%
O/U: UNDER, 52%

WAS -7.5 at DET, 42
Winner: WAS, 69%
Spread: DET +7.5, 52%
O/U: OVER, 62%

CIN at HOU -9, 44.5
Winner: HOU, 78%
Spread: HOU -9, 56%
O/U: OVER, 57%

CLE at JAX -7, 42
Winner: JAX, 60%
Spread: CLE +7, 66%
O/U: UNDER, 52%

NYG at PIT -3, 42
Winner: PIT, 56%
Spread: NYG +3, 55%
O/U: OVER, 57%

SEA at SF -5, 41
Winner: SF, 60%
Spread: SEA +5, 56%
O/U: OVER, 52%

IND at TEN -4, 41
Winner: TEN, 79%
Spread: TEN -4, 69%
O/U: OVER, 51%

Week 7: Results

I'm happy with this week's straight pick results. Hit 2 out of 4 upsets. Hit 10 out of 14 total (71.4%). The picks that lost had confidences of 51, 52, 53, and 67%. I can live with that. I'm very happy with the result of the Dallas - St. Louis game. My injury adjuster worked very well. In fact, the average simulated scores actually had STL outscoring DAL 21.79 to 21.02. That was one of the rare times that the average scores disagree with the win %.
These occurrences include: Week 7, MIN 52% (Correct), CHI 20.29 to MIN 20.13; Week 6, GB 54% (Correct), GB 24.95 to SEA 25.05. So when confidence and average point differentials disagree, confidence is 2-1.

It's also encouraging that as confidence % increases, accuracy increases. The progressive results are looking good. After the half-way point of the season, I'll write up a detailed report.

BOA had a great week, up 91%, further proving the volatility which I'm not comfortable with.

By the way, if I ever make any mistakes, let me know so I can fix it.

BAL at MIA -3, 36.5
Winner: MIA, 67%
Spread: MIA -3, 56%
O/U: OVER, 60%

DAL -7 at STL, 43.5
Winner: DAL, 51%
Spread: STL +7, 74%
O/U: UNDER, 52%

MIN at CHI -3, 38
Winner: MIN, 52%
Spread: MIN +3, 59%
O/U: OVER, 54%

NO at CAR -3, 44.5
Winner: CAR, 53%
Spread: NO +3, 59%
O/U: UNDER, 62%

PIT -9.5 at CIN, 35
Winner: PIT, 60%
Spread: CIN +9.5, 63%
O/U: OVER, 62%

SD at BUF EVEN, 44.5
Winner: BUF, 64%
Spread: BUF, 64%
O/U: OVER, 55%

SF at NYG -10.5, 46
Winner: NYG, 67%
Spread: SF +10.5, 68%
O/U: UNDER, 53%

TEN -9 at KC, 35.5
Winner: TEN, 69%
Spread: KC +9, 61%
O/U: OVER, 66%

DET at HOU -9.5, 46.5
Winner: HOU, 82%
Spread: HOU -9.5, 59%
O/U: OVER, 58%

CLE at WAS -7, 42
Winner: WAS, 77%
Spread: WAS -7, 55%
O/U: OVER, 53%

IND -2 at GB, 47
Winner: GB, 60%
Spread: GB +2, 65%
O/U: UNDER, 53%

NYJ -3 at OAK, 41
Winner: OAK, 55%
Spread: OAK +3, 65%
O/U: OVER, 63%

SEA at TB -10.5, 38
Winner: TB, 69%
Spread: SEA +10.5, 59%
O/U: OVER, 63%

DEN at NE -3, 48
Winner: DEN, 53%
Spread: DEN +3, 63%
O/U: OVER, 53%

Straight	%	Wins	Games	Win %
	50-59	2	5	40.0%
	60-69	6	7	85.7%
	70-79	1	1	100.0%
	80-89	1	1	100.0%
	90-100	0	0
	Total	10	14	71.4%
Spread	%	Wins	Games	Win %
	50-59	1	6	16.7%
	60-69	4	7	57.1%
	70-79	1	1	100.0%
	80-89	0	0
	90-100	0	0
	Total	6	14	42.9%
Total		Wins	Games	Win %
	50-59	2	6	33.3%
	60-69	4	6	66.7%
	70-79	0	0
	80-89	0	0
	90-100	0	0
	Total	6	12	50.0%

Week 3: BOA Results

I'm going to be brief with the results this week. I've had a ton of work this week and I'm a little short on time. BOA was down 78% this week. The probability of all of those teams losing was 0.2%, nice. Watching this go up 65% week 2, down 78% week 4, it tells me that there's too much huge swings. This isn't good for a long term strategy. I'm going to work on it to figure out better risk management. Until then, I'm going to stop posting it.

Week 4: BOA

Now, the increasingly popular Bet Optimization Algorithm (BOA). Things should be more exciting this week since there are 3 underdog picks. That means greater risk and greater rewards (or greater losses). Remember, these are all MONEYLINE bets, they are NOT ATS.

I've noticed that as the number of bets increases, the success of BOA increases, so I'll put up 30 bets this time.

1-TEN, 2-DEN, 3-SF, 4-NYJ, 5-TB, 6-ATL, 7-JAX, 8-CIN, 9-SD, 10-BUF, 11-DAL, 12-PHI, 13-BAL

BET	BOA ODDS	VEGAS PAYOUT	% of BANKROLL	PAYOUT
10	82.00%	1.25	5.73%	7.16
8	78.00%	1.53	5.39%	8.25
1	74.00%	1.61	4.90%	7.90
6	65.00%	3.70	4.71%	17.42
3	65.00%	3.00	4.52%	13.56
8,10	63.96%	1.91	3.82%	7.31
6,10	53.30%	4.63	3.66%	16.94
6,8	50.70%	5.66	3.56%	20.15
1,10	60.68%	2.01	3.49%	7.02
3,10	53.30%	3.75	3.46%	12.98
1,8	57.72%	2.46	3.44%	8.47
3,8	50.70%	4.59	3.39%	15.55
2	67.00%	1.21	3.37%	4.07
13	55.00%	2.90	3.35%	9.71
1,6	48.10%	5.96	3.34%	19.89
1,3	48.10%	4.83	3.17%	15.29
3,6	42.25%	11.10	3.14%	34.86
6,8,10	41.57%	7.08	2.82%	19.98
3,8,10	41.57%	5.74	2.66%	15.27
1,6,10	39.44%	7.45	2.65%	19.76
2,6	43.55%	4.48	2.62%	11.74
1,6,8	37.52%	9.11	2.60%	23.69
1,8,10	47.33%	3.08	2.56%	7.89
8,13	42.90%	4.44	2.55%	11.29
12	57.00%	1.59	2.54%	4.04
10,13	45.10%	3.63	2.54%	9.20
3,6,10	34.65%	13.88	2.54%	35.21
6,13	35.75%	10.73	2.52%	27.07
1,3,10	39.44%	6.04	2.49%	15.05
1,3,8	37.52%	7.39	2.46%	18.21

Week 3: BOA Results

Wow. Things almost couldn't have gone any better. I say this because I'm extremely pleased with how BOA performed this week. It spread out the risk while still offering a high level of reward. 7 of the 9 teams were correct. 10 of the 19 bets were correct. If only Vegas' 12.5 point favorite, my 90% favorite had beaten one of the worst teams in the league, I'd be much, much happier. So for week 3, if you started with a bankroll of $100, you would have lost $14.38, or -14.38%. I hate to play the 'what if' game, but I can't help myself this week. What if the 12.5 pt favorite, NE, had decided to beat MIA? $100 would have turned into $157.79. Fine. There's always next week.

Tracking BOA: Week 2, started with $100. Up 64.62% week 2, down 14.38% week 3.
Initial Investment: $100
Current Investment: $140.95
ROI: 40.95%

1-ATL, 2-BUF, 3-CHI, 4-MIN, 5-NE, 6-NYG, 7-TEN, 8-WAS, 9-SF, 10-SEA, 11-DEN, 12-PHI, 13-IND, 14-BAL, 15-DAL, 16-SD

BET	BOA ODDS	VEGAS PAYOUT	% of BANKROLL	PAYOUT
5	90.00%	1.11	7.21%	8.01
7	87.00%	1.43	6.94%	9.92
6	84.00%	1.11	6.20%	6.88
14	80.00%	1.77	6.12%	10.83
9	79.00%	1.50	5.79%	8.68
5,7	78.30%	1.59	5.76%	9.14
2	79.00%	1.19	5.46%	6.50
5,14	72.00%	1.96	5.14%	10.10
7,14	69.60%	2.53	5.13%	12.98
6,7	73.08%	1.59	5.00%	7.93
5,6	75.60%	1.23	4.97%	6.12
7,9	68.73%	2.15	4.82%	10.35
5,9	71.10%	1.67	4.79%	7.97
13	71.00%	1.43	4.52%	6.46
5,7,14	62.64%	2.81	4.50%	12.64
11	70.00%	1.40	4.48%	6.28
10	71.00%	1.20	4.39%	5.27
5,6,7	65.77%	1.76	4.39%	7.74
5,7,9	61.86%	2.38	4.38%	10.44