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

Week 3: BOA

Originally, I decided to put up a simplified version of BOA's results. Bad idea. I'll need to mention a few things first. I chose to leave out bets against the spread and just include moneyline bets, for now. The fundamental reason BOA works is because of inefficiencies in Vegas' line making. After simulating last season, and after extensive backtesting, NFLSim showed a remarkable tendency to assign accurate probability values for games. BOA exploits this. The only way BOA can be successful is if it assigns the correct probabilites to games, enabling for an optimal allocation of funds to different bets with different payouts. The second important point is that every bet is a different amount, based on the difference in those probabilities. Again, I don't feel that the spread predictions have reached that point yet, though I am comfortable with just striaght picking.

At some point I'd like to write up a rigorous mathematical proof showing why this works, but I'll need to meet up with my statistics professor for that.

Before using this table, consider that the season is just beginning; this is only week 3, so the simulations aren't as accurate as they will be. I can't tell you not to bet, but just keep that in mind.

Since Baltimore's win % against Cleveland is so ridiculously high (97%), I decided to run BOA using a more conservative 80%. At 97%, BAL showed up in pretty much every bet. If BAL loses, lots of bets would lose. Better safe than sorry. If you can't tell by now, I like to err on the side of conservatism.

Once more, this is what each heading means:
~"BOA ODDS" are BOA's calculated probability that the particular bet will win.
~"VEGAS PAYOUT" is the payout for that bet according to Vegas, in decimal form.
~"% OF BANKROLL" is the amount bankroll that should be devoted to that bet.
~"POSSIBLE PAYOUT" is the amount won if the bet is won. (BANKROLL * % OF BANKROLL * VEGAS PAYOUT)

Here is the team key, each number corresponds to a particular bet. 1-ATL means that when you see the number 1, it means bet on ATL to win. If you see 5,7, it means parlay NE and TEN.

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

Alright, let's look at this. That table is based on a bankroll of $100. One of the other reasons BOA works is because it spreads risk over numerous bets in a way such that if one bet fails, other bets can still keep you afloat. If you don't feel like making 19 bets, my advice would be to scale the bets that you do make. If you only want to make the top 5 bets, for example, add the top 5 "% BANKROLLs" together. To find the new percentage to bet, divide that bet's "% BANKROLL" by the sum of the 5 "% BANKROLLs". So... 7.21+6.94+6.2+6.12+5.79 = 32.25. Bet 1 will be 7.21/32.25 = 22.36%. Bet 2 will be 6.94/32.35 = 21.51%, and so on. All 5 percentages should add up to 100%.

As you decrease the number of bets, you increase the amount of risk. For example, if you bet all 19 bets and and all teams win except 5-NE, which has a 90% confidence, you will lose 7.91% of your bankroll. If you decide to only bet the top 5 bets, you'll lose 22.36%. It's about all about your tolerance for risk, which is yours to figure out.

I hope this makes everyone happy. If not, send me some angry emails.

Bet Optimization Algorithm

The results for week 2 were none too impressive, but this makes my Bet Optimization Algorithm ("BOA") look much better. Simply put, BOA takes up to 21 individual bets, i.e. NYG win, MIA win, DAL win, MIN +3, etc., the payouts on those bets that Vegas offers, and the confidence NFLSim generates. Using the algorithms, BOA generates the optimal bets as well as what percentage of your bankroll you should wager on each bet. It spits out single bets and parlays of up to 6 teams. I didn't post the BOA's suggestions last week because I didn't want anyone relying on it, but I'll put them up for week 3. Keep in mind, it's still early in the season so things aren't as accurate as they could be, so be careful. Use at your own risk. Anyway, here's what it said to bet on last week. It generated a return on investment of 64% on the bets (all 31 of them). I'd say that's pretty successful.

To make it easier for me, I assign a number to each bet. All bets are on straight up winners on the moneyline, NO SPREAD. If there are numbers separated by a commas, those are parlays. All calculations are based on a total bankroll of $100. Makes calculations easier.

~"BOA ODDS" are BOA's calculated probability that the bet will win.
~"VEGAS PAYOUT" is the payout for that bet according to Vegas, in decimal form.
~"% OF BANKROLL" is the amount bankroll devoted to that bet.
~"POSSIBLE PAYOUT" is the amount won if the bet is won. (BANKROLL * % OF BANKROLL * VEGAS PAYOUT)
~"ACTUAL PAYOUT" is 0.00 if the bet loses or POSSIBLE PAYOUT if it wins.

1-BUF, 2-CHI, 3-DET, 4-MIN, 5-NO, 6-NYG, 7-KC, 8-TEN, 9-ATL, 10-SF, 11-BAL, 12-ARI, 13-NYJ, 14-DEN, 15-PIT, 16-PHI

BET	BOA ODDS	VEGAS PAYOUT	% OF BANKROLL	POSSIBLE PAYOUT			ACTUAL PAYOUT
15	91.00%	1.36	4.72%	6.41			6.41
9	80.00%	3.50	4.15%	14.53			0.00
10	79.00%	3.50	4.08%	14.28			14.28
7	81.00%	1.51	3.82%	5.77			0.00
8	79.00%	1.95	3.81%	7.44			7.44
9,15	72.80%	4.76	3.75%	17.85			0.00
10,15	71.89%	4.76	3.69%	17.55			17.55
8,15	71.89%	2.65	3.43%	9.08			9.08
14	74.00%	2.00	3.41%	6.82			6.82
7,15	73.71%	2.05	3.40%	6.99			0.00
9,10	63.20%	12.25	3.36%	41.21			0.00
7,9	64.80%	5.29	3.25%	17.17			0.00
8,9	63.20%	6.83	3.23%	22.05			0.00
7,10	63.99%	5.29	3.20%	16.89			0.00
8,10	62.41%	6.83	3.18%	21.70			21.70
6	76.00%	1.20	3.13%	3.76			3.76
14,15	67.34%	2.72	3.09%	8.41			8.41
16	65.00%	3.50	3.07%	10.76			0.00
9,10,15	57.51%	16.66	3.07%	51.17			0.00
9,14	59.20%	7.00	2.98%	20.88			0.00
7,9,15	58.97%	7.19	2.98%	21.39			0.00
8,9,15	57.51%	9.28	2.96%	27.46			0.00
10,14	58.46%	7.00	2.94%	20.55			20.55
7,10,15	58.23%	7.19	2.93%	21.06			0.00
8,10,15	56.79%	9.28	2.91%	27.05			27.05
7,8	63.99%	2.94	2.89%	8.52			0.00
1	64.00%	2.90	2.88%	8.36			8.36
6,9	60.80%	4.20	2.88%	12.08			0.00
7,8,9,10,15	36.80%	49.06	1.98%	97.36			0.00
7,9,10,15	46.58%	25.16	2.48%	62.51			0.00
1,8	50.56%	5.66	2.34%	13.22			13.22

Total Bankroll: $100
Total Winnings: $164.62
Total Profit: $64.62
Return on Investment: 64.62%

So even when the predictions aren't terribly accurate (53.3%), BOA is able to perform well based on the idea that the probabilities generated by NFLSim are equivalent to the probabilities in reality. Hopefully, for everyone, this will continue.

2007 Results, Analysis, and Betting Applications

Well, since starting back in week 12, I'd say I've gotten some pretty good results. Now before everyone starts yelling at me, I'll preempt it by saying that yes, I know it was only a quarter of the season, and yes, I know that for the spread and o/u it was only a few games. At this point the results may be statistically inconclusive, but it's a start. I worked with what was available- the program was 'completed' in time for week 12. Up until the playoffs, changes were being made to achieve a greater degree of realism. Those changes in no way affected either team exclusively, they affected both teams in exactly the same way.

The results for the playoffs and Super Bowl:

Wins: 4-7 36.4%
Spread: 5-2 71.4%
O/U: 6-1 85.7%

The Law of Any Given Sunday proved too much for me. Though you can't argue with a spread/ o/u combined win percentage of 78.6%


The results for the 2007 regular season, weeks 12 through 16:

Straight-up Wins	% Range	Games	Wins	Win %
	50-59	34	21	61.8%
	60-69	29	19	65.5%
	70-79	14	11	78.6%
	80-89	3	3	100.0%
	90-100	0	0	0.0%
	Total	80	54	67.5%

This is a graph of the above table. It shows the astonishing correlation between the predicted percentages and the real win percentages. The x-axis shows the different % Ranges- like in the tables. The y-axis is the win percentage. So the predicted range 50-59% has a real win percentage of 61.8%. The straight, dark line shows what would happen if all of the teams won exactly as they were supposed to, according to my predicted percentage. Lets say I pick 100 teams to win, and they all fall in 50-59. If my system was perfect, about 55% of those teams would actually win. Since the green line (what actually happened) is so similar to the black line, we're able to conservatively assume that the predicted percentage to win is the same as the real percentage of a straight up win.


Now that we know the probability of a team winning, all of a sudden the moneyline completely opens up. Now we can look at what Vegas is offering and immediately know if it's a statistically favorable or unfavorable bet.

If you have $100 and you make 100 bets at 50% each, and each bets pays out 2:1, then after your 100 bets, you've won 50 of them. Since they pay out 2:1, you've made it back to $100, breaking even. Likewise, if you have $100 and you make 100 bets with a probability of 20%, to break even, each bet must pay 5:1. If each bet pays 4:1, you've won 20 bets, but at 4:1, you only make it back to $80, so you've lost money. At 6:1 you get up to $120. Break-even odds are neutral- in the long run you don't make money, and you don't lose money. We only make bets that are above break-even.

Let's look at the Super Bowl. The Giants were 11.5 dogs. Vegas was offering to pay out 4.25 to 1. The probability that the Giants would win- as calculated by me- was 33%. If you win 33% of your bets, each bet must pay out 3.03:1 (Break-even payout = 1/percentage in decimal form; 1/.33 = 3.03). So, since you need at least 3.03:1 odds to make an intelligent bet, you note that Vegas wants to give you 4.25. 4.25 is bigger than 3.03 so you bet on the Giants to win. And if you had bet on the Giants to win, you'd be one happy camper right now.

Note: If you bet in this manner using a reliable source of percentages, sensible money management, and patience, you'll be successful in the long run...with the moneyline! And it doesn't hurt when you're picking 68% of the games correctly... Of course this also works with the spread and o/u.