Flat or Fixed % Bets??

[farbror]

I did a smallish simulation to figure out the differences between strict flat bets and betting a fixed % of your bankroll assuming different odds and Hit rate.

The results look interesting. Flat Betting is often better but only with the tiniest of margins. Often less than 1 unit. Fixed% might beat Flat bets with up to 10+ units when you find the Motherload. Also, during cold streaks Fixed% will lead to smaller bets and less damage to the bankroll.

<TABLE width="90%" border=2><TBODY><TR><TD align=middle>Hit Rate</TD><TD align=middle>Odds</TD><TD align=middle>Diff < -1u</TD><TD align=middle>-1u < Diff < 1u</TD><TD align=middle>Diff > 1u</TD></TR><TR><TD align=middle>0.45</TD><TD align=middle>1.91 (-110)</TD><TD align=middle>0.08%</TD><TD align=middle>60.72%</TD><TD align=middle>39.20%</TD></TR><TR><TD align=middle>0.53</TD><TD align=middle>1.91 (-110)</TD><TD align=middle>0.10%</TD><TD align=middle>88.16%</TD><TD align=middle>11.74%</TD></TR><TR><TD align=middle>0.55</TD><TD align=middle>1.91 (-110)</TD><TD align=middle>0.12%</TD><TD align=middle>85.20%</TD><TD align=middle>14.68%</TD></TR><TR><TD align=middle>0.45</TD><TD align=middle>1.95 (-105)</TD><TD align=middle>0.02%</TD><TD align=middle>66.70%</TD><TD align=middle>33.28%</TD></TR><TR><TD align=middle>0.53</TD><TD align=middle>1.95 (-105)</TD><TD align=middle>0.12%</TD><TD align=middle>85.54%</TD><TD align=middle>14.34%</TD></TR><TR><TD align=middle>0.55</TD><TD align=middle>1.95 (-105)</TD><TD align=middle>0.16%</TD><TD align=middle>79.82%</TD><TD align=middle>20.02%</TD></TR></TBODY></TABLE>
Diff = Fixed Bankroll – Flat Bankroll

Example: Assuming 55% hit rate an -110 the difference between Flat and fixed is less than 1unit about 85% of the time. Fixed% wins more in 14.68% and sometimes 10+ units more than flat betting.

The simulations are based on 75 bets per season and all cells in the table is based on 5000 iterations. The flat bet size was 2% of the starting bankroll. The fixed% was also 2%.

Comments?


Cheers, Farbror

 

[mgmhatesme]

Re: Flat or Fixed % Bets??

farbror, glad to see someone interested in money mgmt

Personally I think you go with either 1-2% of your bankroll as your flat bets and never adjust downward. Check to see if you need to re-adjust upward every 2 months.

Flat bet everything

more often than not I get burned by thinking some of my wagers are higher percentage wins than others. You either make the wager or you do not. If its not a high enough percentage win in your estimation, just dont bet it. Many people overestimate their perceived percentage advantage ("Its a lock"). Respect the oddsmakers and the lines, truth is if there is a mistake that has been made it is probably the bettor's mistake and not the oddsmakers.

That's my take, thanks for all your research-

 

[farbror]

Re: Flat or Fixed % Bets??

Money Management is KEY! I do not mind adjusting the bet size downwards when things turn cold. In theory I agree with your idea not to fiddle too much with bet sizes. However, in real life I do different. I might bet another 0.5% on games I really like.

I did some other number crunching trying to figure out how much cappers tend to over estimate their Hit Rate>

Assuming that the line and the capper has the same magnitudes of error and assuming that the capper only bets on games he/she thinks are 55%+ then the true hit rate on those games might be as low as 53%. A die hard Kelly fan will therefore often severely overbet!

 

[buffettgambler]

Re: Flat or Fixed % Bets??

Fabor,
Glad you made this post, as Money Management is a vital and often overlooked part of handicapping. I would love to comment on it now, but I am heading out to lunch, and will comment fully on it in a couple of hours. Too make a long story short though, there is no difinitive answer, as there are times in which flat betting is better and times in which % of bankroll betting is better. MGM is right regarding having high disparity of nominal bets, as it is NOT sound form of betting for someone who has a long term proven track record of postive post vig returns.

There have been 100's of Monte Carlo simulations and run tests that have come to a conclusion on these issues. For now, I will say that your quantitative test (like you said) is too small of a sample, and does not factor in a key variable of "timing" or the path in which takes you to your %. This is the main variable that defines what is a better approach to money management.
I will comment on it more later.
Good luck.

 

[farbror]

Re: Flat or Fixed % Bets??

sirs,

Thank you for your interest in my pet projects.

I am not sure what you mean by "timing". My simulations are quite simple and assumes independency between bets and a fixed true hit rate for the bettor. Things might turn out different if you instead used some random fluctuation on the Hit Rate (i.e different winning chances on all bets).

There area few minor write-ups on stuff like this on my blog. Unfortunately almost all of it is written in swedish.

 

[buffettgambler]

Re: Flat or Fixed % Bets??

Farbror,

As mentioned earlier, there has been a lot of test simulations regarding what the best money management technique is used. What has been concluded is that it is dependent on three unknown variables that have to be estimated- timing, variance, and volume. I am not going to go into too much detail on the results, but will rather some up the conclusions.

% of bankroll method is my personal favorite, and the method I use for baseball. What it does account for which the fixed system does not account for is essentially the power of compounding, which is a much underestimated tool in any realm of investing. Essentially you are using the compound returns, which allow you to bet more when you are doing well and less when you are doing poor. This strategy is best used for baseball, basketball, and ?grinder? handicappers, as compounding returns has an exponential type reaction. Therefore, the better effects happen later in the season after a few 100 bets, which football doesn?t allow you to make. Variance is also a key variable in distinguishing what approach is better. Simply put, the lower standard deviation of returns one has, the better effects and results one would get with the % of bankroll method. For instance, a low volume, highly volatile capper would be exposed to the negative aspects of such a money management technique, as the see-saw type results will make your lower nominal bets result in wins while the bigger bets will be losers (example 2-0,0-2,2-0, 0-2). So the smoother the results, the better the compounding would work in your favor. Timing is correlated to a bit to variance, but it accounts for more of the course of the season. A profitable season, as far as positive post vig returns, could result into a season in the red using the % of compounding method if your cold streak is hit at the beginning or end of the season. If it hits at the beginning, you are forced to bet a nominal amount below the base amount, which will make it take longer to get back up to par. ( i.e. it may take going 4-0 the second day of the season to make up going 0-3 the first day) If you hit a cold streak that the tails end of a profitable season, you would hit it at your peak betting amounts.

There have been a lot of tools by these types of handicappers use to offset the negative aspects of this strategy. A couple would be to never bet an amount lower than the starting base amount. A more powerful tool is to lower the negative effect of a high standard deviation, by using a 3- to 7 day % of bankroll system (depending on the sport, variance, and volume of bets per day). This allows for much smoother returns that are better suited for compounding.

Over the course of a good (i.e 55%) baseball or basketball season of over 500 to 1000 bets with not too much variance, the disparity between a % system compared to a fix system could be ASTRONOMICAL. Probably a lot more than you are thinking. From a standard distribution model, the % of bankroll returns are positively skewed with a positive kurtosis. I noticed that you used a 75 bet football season model, which would assume you bet about 4 games a week with playoffs. This is not a likely model in which would result in a % of bankroll approach being the optimal approach for any capper hitting below 60 percent a year (almost all cappers). This is when it would be prudent to use a fixed bet system, which is the system that I use for football as well (and then update the fixed bet amount at the end of the season).

If you bet and have done well in a sport in which you bet over 500 bets a season, I strongly advise you to look into establishing some type of hybrid % of bankroll system, in which I could help you develop different techniques to help you offset the negatives in which it may produce.

On the topic of money management, two often misconstrued techniques that cappers that have had a long term success rate in handicapping is that they use different size bet amounts dependent on how strongly they ?feel? on a particular game. If they are confident in their capping and that they could earn a positive post vig return, a % of bankroll method would earn them superior results about 98% of the time. Also, a lot of people think betting too many games always leads to negative results. They claim that if they bet 100 games they could hit 58% but if they bet 500 games they would only hit 55%. Remember, simple economics would tell you that the expected marginal wining % of adding x amount of bets is the true determinant how many games you should bet, not your winning %.

 

[farbror]

Re: Flat or Fixed % Bets??

Buffettgambler,

Thank you for an excellent post on Money Management strategies. I am however still confused by ?timing issues? and I fail to see why timing matters. This is how my slow mind works:

Suppose I bet eight games on a season and that I use Fix % as my betting strategy. My pre-coffee morning brain cannot see how the sequence of Wins and Losses (for a given number of wins) will influence the final bankroll size. A win followed by a loss will have the same net result as a loss followed by a win since a*b = b*a. Or?

Doing the algebra it is fairly easy (but quite boring) to see that Flat Betting does better than Fixed % for outcomes ?close? to 50% ATS. The differences is however fairly small. Fixed % does better for extreme results. The fact that Fixed % does better for extreme results is very-very important. Standard results from Random Walk Models tells us for example that the difference in number of Heads and Tails in a long series fair coin flips tend to be far away from zero (you start off with a zero difference but the Expected number of ?flips? needed to get back to a zero difference is Infinite despite the fact that you will be back in two flips with probability ?!!!). What do Random Walks have to do with Money Management? Well, the sequence of Wins/Losses can be viewed as a Random Walk.

I noticed in my simple simulations that the Median difference between Flat and Fixed% tended to favour Flat Betting (with a small margin) but the Mean difference favoured Fixed Betting due to the skewness of the results.

Optimality sounds great but is hard to define and somewhat subjective. From my perspective Fixed% sounds appealing (or optimal, if you like) even for a ?short? 50-75 bets NFL Season. The price you pay for betting Fixed % seems to be a fraction of a unit in the worst cases and the benefits might be 5-10 units even during a Football Season with modest expected Win Rate.

Again, thank you very much for responding to my post and for sharing your wealth of knowledge. All the questions/comments from me is just an expression of my eagerness to learn and please do not read them as criticism.

 

[mgmhatesme]

Re: Flat or Fixed % Bets??

good stuff here guys

I tend to do 2 things in money mgmt that I do not consider optimal. One, I tend to have a double unit wager on some weekends on a particular game I feel better about. Two, I do not risk the same per wager. Flat betting should really mean that you risk the same amount per wager, yet on favorites it is the "to win" amount and on dogs it is the "risk" amount for me.

Regardless, I do not think either of those strategies are sound long-term strategies. Sometimes easier to say what is the right thing to do, then to do it. I am starting a sports investment with a business partner of mine and I will follow strictly the 1% and having the same risk amount per wager in this account, as we are more interested in conservative returns for this investment.

On the fixed percentage for every wager, I do not like like lowering my wagers because I am comfortable with my expectation that I can have a long-term winning percentage around 55%. If I encounter a losing streak and start lowering my bets, it will take me that much longer to get my money back. Simple as that. I do not chase, raising my bets during a losing streak, but nor will I have "scared money" and underbet my perceived advantage. At the same time, I do not think it is wise to always press and overbet when you are on a winning streak. I dont think you can anticipate streaks and really can only see them in hindsight.