Help calculating expected earn

[DOTTT]

Suppose you have a $10,000 bankroll and will be flat betting 5% on each game or $500. You long term win rate is at 56% how much do you expect to make a year if you think you can find 250 games to play? If someone can show me the math I'd really appreciate it.

Thanks.

[MasterShakes]

$9,500 and I did the math in my head. I'm awesome. Don't bet more than 2% of your bankroll on any one game though.

[DOTTT]

Sorry didn't really post what I wanted to ask. What I really want to know is supoose you know your long term win rate is a 56% and you start of with $10000 and flat bet 5% how can you calculate your total win amount after 250 games if you will increase your bet size to adjust to your wins and losses after those 250 games. I'm not sure this can even be answered, can it?

[jmillerdls]

Yes, it is very easy to figure out. Unless you have a tremendous streak of luck right from the get-go, you will have an extremely high chance of going broke with such an enormous percentage flat bet.
Next, you shouldn't be increasing your bets after a standard number of plays, but instead after your bankroll has increased a certain percentage (i.e. when you have 15k, having increased 50%).

[Mr_J]

"Don't bet more than 2% of your bankroll on any one game though."

Unless you understand and respect the maths /images/graemlins/smirk.gif

[Mr_J]

Guys, if he was certain he will go 56% longterm and can doesn't have many simultaneous wagers, then 5% is fine. OP, what makes you think your bets will be 56% longterm?

BTW I'm not saying he should bet 5%, just that if he IS a 56% bettor then it'd be fine. This is assuming he resizes very reguarly, and doesn't just bet $500 a game.

[raccon]

It's $8,630, assuming that you're making bets with odds -110 and that you flat bet with $500.

Here's how it goes:

You bet 250 times $500, total $125,000.
You win 140 times out of 250 (140/250 = 0.56).
Your winnings are 140*1.909*$500=$133,630
(-110 is 1.909 in decimal format)

Your net profit is $133,630-$125,00=$8,630.

I would recommend smaller bet size though since 20 bet losing streaks DO happen. 2-3% would be MUCH better. Cheers.

[DOTTT]

Thanks, but again this is not what I'm asking. I'm really intrested in knowing how much I will make if my win rate stands at 56% and if I will increase the amount I bet as my bankroll grows over 250 games.

[DOTTT]

Well the thing is I've been working on a football system for the past 4 months. I've backtested it over the past 6 seasons and it has a win rate of 56.7% over that span. However, if I take the past 10 seasons then it only shows a win rate of 52.8%. With the biggest lossing year at 46% and longest losing streak at 11 games , so I feel comftable enough to bet 5% of my bankroll on every game.

[whipsaw]

Adjusting your bet size in between each bet, I put your final bankroll at 23667.14. The math isn't easily explained, I had to do it in excel. Also, my calculations are based on expected return with each wager, not based on whether you actually won or lost the wager, which would more wildly vary your bet size, and thus your final bankroll. If you PM me I can email you the excel file.

[Mr_J]

"'ve backtested it over the past 6 seasons and it has a win rate of 56.7% over that span. However, if I take the past 10 seasons then it only shows a win rate of 52.8%."

Don't assume you'll hit 56% going forward, you probally won't. What data did you use to form your hypothesis (system)? If you backtested over seperate data that's ok, but if you used the same data then your results are obviously biased.

You can't assume it'll hit 56% going forward.

You're probally fine betting 5% though if you heavily hit bonuses, line shop, low vig and free points. If you don't do these then definately lower the % you're betting.

I don't think you have any idea what you are getting into though. 5% units create huge variance, you have to be a real cool customer. If the money means anything to you then lower your %.

[DOTTT]

Well it basiaclly contians the following.

1. Public Opinion
2. Line Moves
3. Trend analysis


In all three I have anywhere from 1-10 stats (or data) inputs that I use. I'll be betting at Hollywood which offers -107 on all their bets, and I think I can handle the variance. Playing poker for the past 3 years helps a lot there.

I'm not sure what you mean though when you say

[ QUOTE ]
What data did you use to form your hypothesis (system)? If you backtested over seperate data that's ok, but if you used the same data then your results are obviously biased.


[/ QUOTE ]

One of the first things I set out to look for is a system that has been working for the past 3-5 years. I don't think historical data pre lets say 1990 is all that important, espcially not for my system since it uses a lot of variables that only recently have come about.

[Mr_J]

"Playing poker for the past 3 years helps a lot there."

The swings in sportsbetting are much, much bigger.

"I'll be betting at Hollywood which offers -107 on all their bets"

Very silly. In the longrun bonuses, low vig, free points, line shopping etc will probally be worth just as much as what your picks. You're leaving ALOT of money on the table by using just 1 book. The extra EV you make from the other stuff also acts as a buffer against overbetting.

"One of the first things I set out to look for is a system that has been working for the past 3-5 years."

Sounds like you used the same data, and if you did then your system isn't worth anything. When you test your system, you can't use the same data as you used to develop it. If you develop a system off the '03-'04 season, you can't include that data in your tests. So, what seasons did you use to develop your systems, and what seasons did you test over to see if the system worked?

[raccon]

Yes, $23,667 is the correct answer assuming that your every bet wins what's expected (impossible situation) and the expected profit is always added to the bankroll before making the next bet.

It's a bit difficult for me to explain this since english isn't my main language. But I'm sure me and whipsaw got the right answer.

This is how it goes:
1st bet
-------
Bet size: $10,000 * 5% = $500
Expected return: $500 * 1.909 * 0.56 = $534.52
Expected net profit: $34.52
(You EXPECT to win this bet 56 times out of 100, but with particular bet you can obviously lose the whole $500 or net $454.5 profit. What matters is that on average you net $34.52 with every bet)
Expected growth of the bankroll: $10,034.52 / $10,000.00 = 0,3452%

2nd bet
-------
Bet size: $10,034.52 * 5% = $501.73
Expected return: $501.73 * 1.909 * 0.56 = $536.37
Expected net profit: $34.64
Expected growth of the bankroll: $10,069.16 / $10,034.52 = 0.3452%

As you can see, on average your bankroll grows 0,3452% with every bet. Now it's easy to calculate how big the bankroll will be after 250 bets:
1.003452^250 = 2.366741
With your $10,000 bank, this will be $23,667.

Hope this clears things a bit.

[raccon]

With 46% win rate season (this happens even if you average 57% over long haul [thousands of bets]) your $10,000 bankroll is expected to drop to $2,200. If you can stand those kind of fluctuations, then it's ok.

[rvg72]

[ QUOTE ]

Sounds like you used the same data, and if you did then your system isn't worth anything. When you test your system, you can't use the same data as you used to develop it. If you develop a system off the '03-'04 season, you can't include that data in your tests. So, what seasons did you use to develop your systems, and what seasons did you test over to see if the system worked?

[/ QUOTE ]

That is a really good point... If you averaged 56.7% over 6 seasons and a 52.8% over 10 then assuming about the same number of bet games each year:

((52.8*10)-(56.7*6))/4 = 46.95% over the previous 4 seasons.

If you remove the season(s) that you built the system from the data then overall it is probably much closer to 50%...

This could be wrong and you may have found a great system but betting 5% per game would be a mistake IMO. Even a "real" 56% system stands about a 30% chance of dipping $10K over 250 games at $500/game.

rvg

[DOTTT]

I tested this over 6 seasons starting from 1999. The thing I love the most about is it's win rate has actually gotten better with every passing year. Even when I tested it for the past ten seasons it showed a some what similar trend. With only 1997 showing a decline from the year before.

[DOTTT]

.

[Mr_J]

But what seasons did you use to come up with the system?

With all due respect, I don't believe the 23k figure is correct. Since you're bet size is changing with bankroll, I belive this will change you're EV. However, this is grad school level stats. You can try simulating this in MATLAB or Excel to make it a bit easier.

[whipsaw]

[ QUOTE ]
With all due respect, I don't believe the 23k figure is correct. Since you're bet size is changing with bankroll, I belive this will change you're EV. However, this is grad school level stats. You can try simulating this in MATLAB or Excel to make it a bit easier.

[/ QUOTE ]

Well golly gee, mister, thanks for coming off your throne to explain this to us idiots here. We surely a-per-see-ate it. Why don't you post the math and give us a final number rather than just trolling for threads relating to math and critiquing them.

Not trying to offend anybody here. I don't know how to do this using a formula. If anybody does, please let me know. Using MATLAB, i got $19,900 as the expected return. The only assumptions i used were that each bet paid off even money and there was a 56% chance of a good outcome.

Here's the code:
>> home
>> clear
>> TotalBets=500;

p=.56; %chance of winning
PercentBet=.05;

for trial=1:10000

Bankroll=10000;
for i =1:TotalBets;
betsize=Bankroll*PercentBet;
temp=rand(1);
if temp < .56
Bankroll=Bankroll+betsize;
else
Bankroll=Bankroll-betsize;
end
end
finalBank(trial)=Bankroll;
mean(finalBank)
end

[whipsaw]

[ QUOTE ]
Not trying to offend anybody here. I don't know how to do this using a formula. If anybody does, please let me know. Using MATLAB, i got $19,900 as the expected return. The only assumptions i used were that each bet paid off even money and there was a 56% chance of a good outcome.

Here's the code:
>> home
>> clear
>> TotalBets=500;

p=.56; %chance of winning
PercentBet=.05;

for trial=1:10000

Bankroll=10000;
for i =1:TotalBets;
betsize=Bankroll*PercentBet;
temp=rand(1);
if temp < .56
Bankroll=Bankroll+betsize;
else
Bankroll=Bankroll-betsize;
end
end
finalBank(trial)=Bankroll;
mean(finalBank)
end

[/ QUOTE ]

That looks more like high school level computer programming rather than "grad school economics" to me, but whatever. Raccoon explained the math pretty well in an earlier post, but I'll try and explain it again so that your elite brain can handle it.

First of all, you made two errors. First, it looks like you ran your recursive function 500 times, not 250 as DOTTT originally posted. Second, and more importantly, you assumed that bets pay out even money--they definitely don't.

In a usual football spread bet, the bettor is laying $110 to win $100, meaning if he wins he gets $210 back, which is approximately 1.909 (210/110) times the original bet. Therefore, for his original $500 bet, if he wins he will get back $954.50.

If his expected win percentage is 56%, then on his first individual bet his expectation is to receive $534.52 (.56*$954.50), or a profit of $34.52, which is 6.904% of the original bet.

Recursively adding the expected return of 6.904% and then adding it to the bankroll for the next bet (which gets resized to stay at 5% of the bankroll) over 250 bets yields a total bankroll of $23667.41.

Of course, as raccoon noted, there are downfalls to this calculation, because with each bet you really don't get your expected return, but instead win or lose.

First of all, I said the formula was grad school stats. Simulating this type of thing isn't so hard, but it is very effective. Second, the 2 things you just mentioned should only lower the EV. Third, getting the EV on each game is probably not a solid assumption. The changes to the simulation will be made soon and results posted.

[jmillerdls]

Well, you seem confident that someone with a 56% rate will not go broke betting 5%. I really hope this guy keeps us updated because I think there an extremely large chance he will go broke betting this much. 56% is not such a large advantage that you will not have pretty large swings in both directions. Hope I am wrong, but this seems like suicide.

[bradha]

Actually, I think the math is fairly simple - it reminds me of a math problem I had back in college. Assuming that you always bet 5% of your total bankroll and that you are betting at the standard bet 110 to win 100 rake, then: after each win new BR = BR * (1.04545) and
after each loss new BR = BR * (0.95).
After a series consisting of M wins and N losses, you have
new BR = BR * (1.04545)^M * (0.95)^N . This is true regardless of the order of the wins and losses. If over 250 trials you average exactly 56% winners, then you have M = 140 and N = 110. This is about 1.788 times your original bankroll, making $7,888 in the first year.

If you get a better rate, e.g. betting $107 to win $100, then you get new BR = BR * (1.04672895)^M * (0.95)^N, which is about 2.12 BR for M = 140 and N = 110, making $11,202 in first year.

Note: I have a lot more confidence in these numbers than I have that your system will actually yield 56% winners...

Brad