A statistical analysis of bankroll management. Two year old thread.

[timotinbowen]

How can you possibly know what percentage of bets you will hit in the future?

Past performance is never a guarantee of future performance...especially in sports wagering.

I'm not trying to bust balls...but I must still be missing something.

How can you say it doesn't matter if you lose 55 bets in a row? You will lose your bankroll.

Arg, I'm frustrated that I'm not communicating this effectively. If anyone else can make it easier to understand, feel free to chime in. But I'll try again...

We base our mathematical model on the fact that we know (approximately) what percentage of games we are going to hit. This takes lots of work and much observation. Suppose you have been tracking your plays for 8 years, and you hit 56% winners over a sample of thousands of games. You can assume that you are a 56% capper. Of course, there will be natural variance. You might even see some 25-75 runs, which hurt. But in the long run, you are a 56% capper. Obviously, if you think you are a 56% capper and bet accordingly, and then hit 51% for the rest of your life, the system is going to fail. But any betting scheme would, because every bet a 51% bettor makes is -EV.

Now, to make the most money possible, and keep a 0% Risk of Ruin (assuming we do average 56% over our next large span of games), the chart shows that we should bet about 6.9% of our bankroll on each game. That means 6.9% of our current bankroll, not starting bankroll. So if you start with $1,000 your first bet would be about $69. If you lose, your bankroll is now $931. 6.9% of 931 is 64.24, so that is our next bet. And so on... If we lose 20 games in a row, our BR will sit at $239.32. If we lose 55 games in a row, our bankroll will be $19.60. That's ok, as long as we hit 56% of our games over time (which, again, we should do according to the law of averages and regression to the mean). This system tolerates short term fluctuation and produces identical results no matter the order of wins and losses.


All that I'm trying to indicate is that if you know approximately what % of bets you hit, this is the best betting strategy. Any deviation will ultimately cost you money (and the amount it costs you rises exponentially with the number of plays you pick). There is no risk of ruin because you never bet more than X% of your bankroll. It can handle all variance that binomial distribution provides. As long as we truly are winning cappers (and we track our statistics so we know what to expect in the long term) this is the best method. Obviously past performance is not a perfect guarantee of future outcomes. To achieve that we would need a sample space of infinite games. However, we can achieve a confidence interval of less than .01% with a certainty of 99% with under 1,000 games. So really a large enough past sample can predict what you will do over a large future sample. And this post was only meant for the experienced bettors that would have such a sample anyway.

 

[Mistermj]

Don't get frustrated...you just explained it well.

The problem is still knowing what your percentage of winning is...most people do not have 1000 games of record keeping to fall back on...or a system that is repeatable for that matter.

I'm a systems guy...I like to try to build repeatable ATS winning systems

I have experimented with volume approaches to wagering..because I think in theory it should be easier to win with a small known advantage and volume.

Wagering on every single NFL game is a lot of work however...but I did do it for two seasons.

Some people don't understand...but a volume approach can be very profitable.

 

[MrJ]

Tim, I'm wasn't disagreeing with the maths, I'm just pointing out why suggesting to bet 1% is generally good advice. If you know you're a 55% capper, betting just 1% is a far from optimal, but the people who know that are already aware about sizing your bet relative to the edge and the success rate.

Something you need to remember though is that mathematics is not 'real world'. While a 55% capper should be betting 5%, betting limits, capital preservation, emotions etc all play a role. It's not as simple as a 55% bettor making 5% bets.

2. I think you're forgetting that this is a dynamic model. If you are a 55% capper, it is OK to have 20 game losing streaks. You are only betting a certain percentage of your current roll, which takes away the ROR.

No, losing streaks have nothing to do with what I'm saying. I'm talking about people overestimating their edge, so betting optimally can actually lead to overbetting (i.e. they weren't really betting optimally in the first place). It takes a very large sample to have a good idea you're at least a 54% bettor, and as MR_MJ says, past results will not necessarily reflect future results. Sportsbetting is not a static market, so what may have worked in the past may not work in the future.

3. I agree that discipline is important. This is only aimed at people who can hit enough winners to beat the juice. Then they simply need to plug in numbers to determine what is optimal.

It's not about dicipline, it's about emotional tolerance. Very, very few professionals could live with 5% bets and regular 40%+ swings. You have to bet within your comfort zone.

Again, I'm not disagreeing about the maths, just about the practical application.

 

[Railbird]

I guess this is the line of thinking I was trying to discourage. What is "gambling math"? By keeping a fluid model, you eliminate ROR. So if you think you are a 57% bettor over time, bet accordingly. I've heard the 1% and I used to think that way, but it is not maximizing value. You're correct that the laws of math don't lie. And that same math shows us exactly what to bet if we know our percentages...

Agree, saw you posted 12%, which is fine, especially of you are football only.

 

[ensign_lee]

This is *really* good stuff. Thank you very much for your hard work. I'd never looked at bankroll management this way before.

Would you mind running it with laying -107 and -105 as normal vig paid? I want to make sure that the numbers I'm coming out with are correct as well.

Thanks!

 

[CoolBreeze22]

I would say maybe 1 person out of 100,000 could hit 56% over the span of 2000-5000 plays laying -105 thru -110.

 

[PatsFan1283]

Better yet, what is it at -102 or -103, which is about the price we all get on matchbook....

By the way, if you aren't on matchbook yet, get on matchbook!

 

[VegasRandy]

There is a psychological component to betting that is under estimated by most gamblers because they don't understand it.

Here is a passage that will explain it better than I.

From the book, "Influence, The Psychology of Persuasion"

A study done by a pair of Canadian psychologists uncovered something fascinating about people at the racetrack: Just after placing a bet, they are much more confident of their horse’s chances of winning than they are immediately before laying down that bet. Of course, nothing about the horse’s chances actually shifts; it’s the same horse, on the same track, in the same field; but in the minds of those bettors, its prospects improve significantly once that ticket is purchased. Although a bit puzzling at first glance, the reason for the dramatic change has to do with a common weapon of social influence. Like other weapons of influence, this on lies deep within us, directing our actions with quiet power. It is, quite simply, our nearly obsessive desire to be (and to appear) consistent with what we have already done. Once we have made a choice or taken a stand, we will encounter personal and interpersonal pressures to behave consistently with that commitment. Those pressures will cause us to respond in ways that justify our earlier decision.

Take the bettors in the racetrack experiment. Thirty seconds before putting down their money, they had been tentative and uncertain; thirty seconds after the deed, they were significantly more optimistic and self-assured. The act of making a final decision-in this case, of buying a ticket-had been the critical factor. Once a stand had been taken, the need for consistency pressured these people to bring what they felt and believed into line with what they had already done. They simply convinced themselves that they had made the right choice and, no doubt, felt better about it all.

Expected win rates are flawed.

 

[timotinbowen]

Expected win rates are flawed.

Unless you've tracked your winrate.

 

[timotinbowen]

Better yet, what is it at -102 or -103, which is about the price we all get on matchbook....

By the way, if you aren't on matchbook yet, get on matchbook!

I'll get on this soon... Gotta go out-of-state to a relative's funeral. Back on Monday.

 

[artiesliver]

Great discussion guys.

One thing to consider is a minimum bet. Assuming you lose 1-x # of bets in a row until you are down to say $0.19. Yes, you may now win x in a row to bring you to your expected win % rate, but you are now faced with finding a book that will take a bet on a % of $0.19. Theoretically you will get to your expected payout, realistically you may never have the opportunity.

The psychology of the bettor will also play a tremedous part (as described by several above), but by following a bankroll mgmt system such as this is to eliminate the psychology side of it (again, theoretically).

 

[NorthernStar]

timotinbowen I did many studies about the kelly criterion and if all gamblers used it they would be much better off because the goal is to optimize the bankroll and never lose more than the bankroll (which too many lose more than they can afford). I have a couple practical things you probably don't know. If you think you can hit 57%. Still run a kelly like you only think you can hit 54 or 55%. Reason being if you play a bankroll based on 57% and hit say 54% you may actually lose money (I didn't check this mathematically), but if you are hitting a lower % your profits go down. On the flip side if you hit a higher % your profits go down but you should be willing to have less profits and less chances of loses. Below is a post of mine earlier about how to handle multiple games going off simultaneously. I have other ideas on how to manage a bankroll. Which are more sophisticated version of Kelly.


Ganchrow some info on the Kelly Criterion. Kelly was an engineer for Bell Labs and he used what is now known as the Kelly Criterion to describe the "nodes in the phone system". Kelly criterion has nothing to do with picking winners. You pick losers you are going to lose money and your bankroll is heading to zero maybe just not as fast as with other ways of betting on games. Kelly uses an optimization.

When you win or lose has no outcome in your performance of your bankroll using the kelly criterion.

To calculate where your bankroll would be at at given point with Kelly the equation is:

Bankroll Now = Starting Bankroll * ( 1 + (ave payout * % of banroll wagered)) W ((1- % bankroll wagered )L).

Note I am in a hurry.

W = wins (and it is raised to that power)
L= Losers (and it is raised to that power)

If you had made 100 wagers and your record was 57-43

if you had wager 9% on the plays your bankroll would be 1.53
10% of bankroll it would be 1.54
11% of bankroll it would be 1.52

You could have lost the first 43 and won the next 57 it would be at the exact same spot. 10% shows is very close to the optimal wager when you hit 57%.

I will assume you know how to calculate the optimal wager amount:
= % winners- (%losers/average payoff).

Ideally with the kelly criterion you would place one bet determine the outcome and adjust your bankroll up or down and place your next wager.

The problem arises when on sunday afternoon you want to place 3 wagers on games going at noon. For simplicity (and by no means any recommendation) lets say you are wagering 10% of $1,000 bankroll. If you wager $100 on three games and go 0-3 your bankroll is $700 it should have been $729. On the other hand if you went 3-0 it is $1,300 and it should have been $1,331.

I am just glancing at my paper and it was back before offshore joints and parlays only played 12/5 so you might need to tweek it a bit.

Staight wager

Team A $1,000 X 0.1 x .6 = $60
Team B same $60
Team C same $60

Then a round robin on two team parlays:
A and B $1000 x 0.1 x 0.2 = $20
A and C the same $20
C and B same $20

when you go 0-3 you lose $240 and have a bankroll of $760,
when you go 3-0 you win $163 on the straight plays, $52 x 3 on the parlays to bring your bankroll $1,319.

Never going to get the bankroll to exactly mimic all of the outcomes 0-3, 1-2,2-1 and 3-0. I shade my parlay percentages so I do a little better on a bad night like 0-3 rather than on a good night like 3-0. You can get closer to mimicking the actual results by changing even more and adding 3 team parlays into the mix but it isn't worth the added pain.

On two teamers you woul go $66 straight plays and onparlay for $33.

One last thing about Kelly, try to remain selective in which games you choose to play and hit a higher percentage. If you statrted with a bankroll of $1,000 and played 6% of your bankroll each selection. Lets just say you made one play a day and you hit 58%, which isn't out of the question. After 1500 plays your record would be 870-630. Your bankroll would be $1,372,000.

Good Luck on your handicapping and I hope this information on money management helps you in your endevors. Money management is probably the bigest down fall of most players.

As Always Good Luck

Northern Star

 

[terpkeg]

after about 5 years of basically losing my mind with the emotional swings of gambling, i have been on a strict money management system since about april 1 and while i inderstand the math formulated above, practically, i think it would be impossible for me to implement.

first, i place the majority of my wagers far in advance. mma is my best sport and i typically have wagers in place 1-2 months ahead of time to get the best numbers (which are may times weak when the first come out). i expect to put my football wagers in by monday/tuesday as well. therefore, i will never know what my bankroll is going to be at the time the bet starts.

so in meek one i might place 5 wagers, have 4 fights pending and maybe a future or two. i can go 0-11 and my bankroll is gone.

the only way to avoid this would be once the bet is placed to place my next wager of the amount of my available funds which i wouldnt want to do.

second, even if i go over the first hang-up, i dont think that i could handle placing bets if my roll was down 70%, or even 30% for that matter. It would be too much work and time to be putting in wagers for $2.67 or something like that.

i found one unit = 1% of my roll and adjusting upward to a 5% max and very rare to be that high to be my gambling savior.

but in all this was a good analysis and if it works for you more power to to you because in my opinion you must be aware of money management if you want to keep this up over time and not damage your life.

 

[VegasRandy]

The psychology of the bettor will also play a tremedous part (as described by several above), but by following a bankroll mgmt system such as this is to eliminate the psychology side of it (again, theoretically).

I would bet a game early in the week and grow confident in the bet as the week went along and then bet the game again. This would be the poison pill of money management for me. That's why I posted the passage above.

Now that I understand the common weapon of social influence, I have a rule to never bet a game twice.

My money management has improved since.

 

[PatsFan1283]

54-55% is the absolute high end of what a good handicapper can do in my opinion. 58% is nearly impossible to me, although, I'm guessing some of you dabble in softer markets than the major sports, however, if anyone on this board has actually hit 57-58% over 800+ plays, please let me know so I can just tail you and save myself a ton of time...

 

[PatsFan1283]

This is a really good post. Anyone know whatever happened to timo? Just wondering....

 

[ensign_lee]

epic bump. Love this thread

 

[copacabana]

Use Kelly Criteria, enter your bankroll.......your avercity & bet strength, then the odds you can bet vs the true price (to 100%)........

 

[PatsFan1283]

Yeah I like it a lot too, its helped me tremendously. However, where did the dude go?

 

[goblue12]

In Kelly, aren't you suppose to adjust your risk / win amount based on the size of your current bankroll to avoid the whole "I hit a rough patch and lost it all" stage?