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Sensible Betting Staking


A perennial topic for bettors of all kind is the staking plan one should be using when playing selections given by a proven method or system, or provided by a profitable service (assuming there is such a thing). Opinions on this topic are abound, and sometimes it is difficult to see the wood from the many trees trying to reach the sky.

Points

The staking method I use takes several factors into account when arriving at the suggested bet size. All bets are proportional to my current bankroll since anything else would be sheer lunacy. It works with any system or method, and can even be used for system testing. First of all…

–        Pardon me, but could we get back to that bit about ‘sheer lunacy’?

 –        Hello there! What sheer lunacy?

 –        Well, you said ‘anything else would be sheer lunacy’. Could you explain that? For example, I use a point system, and a friend of mine uses level stakes. We are both making lots of money. Are we lunatics?

 –        Well, no, you are not lunatics. I didn’t say that. Everybody has the right to use whatever staking plan they feel comfortable with. But that doesn’t sanctify those staking plans even if the players employ their methods successfully. What I mean is that any staking plan that doesn’t take into account the size of your bankroll is plain crazy.

 –        Sure, but that’s stating the obvious! Everyone will bet more if they have more money in their pockets.

 –        Perhaps, perhaps not. If we could proceed now, we’ll get to those points in due time…

 –        Don’t let me stop you…

 –        Thanks. So I was saying…

First of all, one needs a profitable system or method (or tipping service), i.e. one that is showing level-stakes profit for the period…

–        There you go!

–        Where?

–        There! You just said ‘level stakes’! So you’re suggesting we should use level stakes. You sound like my friend.

 –        No, not at all. I was saying that we needed a method which showed level-stakes profit. I am not advocating level staking, I simply use it as a yardstick for system performance. If a method is not profitable at level stakes, no staking plan will turn the method around.

 –        How is that? Surely we can double up, wait for the favourite when it’s due, or stop at a winner and stuff. Haven’t you heard about these proven plans?

 –        Yes, I have, although I wouldn’t say they are ‘proven’. I will explain another time why what I said is so. Just accept it as fact for now, and forget about your loss recovery schemes and other magic. There is a place for those, too, but not here and now.

 –        Alright then, I’ll shut up…

Bankroll, Growth, Risk and System Parameters

So… we need a method that is showing level-stakes profit for the period for which reasonably detailed records of the system exist. We will shortly examine the exact pieces of information to be recorded, but first let us have a discussion on what I mean by ‘sensible staking’.

–        OK, I’m here to discuss…

 

–        I had in mind rather a monologue than a dialogue, but if you’re already here anyway…

 

–        Sure, fire away!

 

–        Thanks, you’re so generous with your time…

–        Don’t even mention it!

–        Well then… by ‘sensible staking’ I mean a method by which an optimum staking level can be calculated for each individual bet that maximises profit and minimises risk while keeping in mind that system parameters used for this calculation may not be entirely reliable. This would be it in a nutshell. How does that sound?

–        Sounds great, but could you break this down into chewable pieces?

–        I’ll try. You understand ‘maximising profit’ and ‘minimising risk’, right?

–        Sure do, that’s what my betting is all about!

–        Really!? I thought you used a point system.

–        Right. When I feel more confident about a horse, I use 2, 3 or 4 points. A banker would be 5 points. Surely I am maximising my profit on bankers and minimising my risk with the one-pointers?

–        Maybe. And how many points is your bank?

–        Silly question! Twenty points, how many. Isn’t that what everybody uses?

–        Don’t think so. People using a point system may start with a 10, 20, 40, 50 or 100 point bank, or whatever they feel is right. To become ‘sensible’ in their staking, they need a twofold change in strategy: first, they would need to bet a proportion of their current bankroll, and second, they would need to calculate what that proportion is.

–        And why is that?

–        Because, by sticking to points, you are ignoring your current wealth.

–        My current wealth, if you want to be so fancy with words, has always been the same. My pay check is indexed to inflation, and we’ve always lived in this place. Sure we change cars every 10 years, so perhaps you could take this into account, but…

–        No, I mean your current betting wealth, your betting bankroll. The money you have set aside for betting.

–        Oh, that! Well, it’s 20 points, I’ve told you that already. It has always been 20 points.

–        So you win some and lose some? Not really making any money then, are you?

–        I have my good days, but when I lose the whole bit, I just top it up. So it’s always 20 points.

–        I see. So you don’t really have a bankroll set aside for betting, do you?

–        Well, no, but that would defeat the purpose of my betting. Should I just stop after a bad day?

–        If you lost your bankroll, yes, you should stop. Then take a deep breath and read some of the staking articles in SMARTsig magazine. They may actually help you appreciate the importance of correct staking and prudent money management. And to do that it is imperative that you should know your system parameters, which…

–        OK man, thanks for your advice, but I gotta go now. First race is starting soon! Wish me luck!

–        Good luck, then! And thanks for your time!

Alright, where were we? Oh yes, betting bankroll, maximising profit, minimising risk and system parameters… To avoid getting back to the discussion above, I will bravely assume that SMARTies have a separate bankroll for betting and they know what their current betting wealth is. They also appreciate the importance of minimising risk and maximising growth. Furthermore, they might actually know their system parameters, and how much they can be relied upon…

Proportional and Level Staking – The Kelly Criterion

Now you may ask why we always need to bet a proportion of our bank? The short answer is that a fixed proportion will ensure the same level of growth and risk for each bet provided that conditions for individual bets are identical. By conditions I primarily mean perceived edge and actual odds. But they never are the same, are they? That is correct. This is why we need to calculate what this proportion should be for each individual bet. To keep growth and risk at the same level for each bet.

–        Sure thing, you are driving at the Kelly criterion, aren’t you?

–        Oh, hi! I certainly am in a sense, but with ‘sensible staking’ we cannot take Kelly at face value.

–        I know all about that! That’s why I’m sticking to level stakes now.

–        I see, so you’re the friend of our ‘pointer man’, then?

–        Sure am! Tried his point system and Kelly, too. They were both disastrous. I’m happy to bet at level stakes. Serves me right.

–        We’ve talked about using points with your friend, but what about Kelly? How come it didn’t work for you?

–        Basically I hit a couple of nasty losing runs with high stakes and was totally wiped out. Those odds-on favourites did me in, you know? But that was a long time ago.

–        I see. So you were lumping on because Kelly told you to divide your edge by the odds, right, and you had a string of low-priced losers?

–        Exactly. The man is crazy, I tell you! Maybe his system works on paper, but it didn’t work for me/

–        And you have abandoned Kelly and are now with level stakes. Is this correct?

–        Damn right! Now my fingers are not shaking when typing my bet in and I can sleep at night. Beats that roller coaster any day!

–        So you are happy with level stakes.

–        Sure am! So I’m not buying your Kelly argument.

–        You don’t have to because I’m not making a case for Kelly. At least not in its original form.

–        What do you mean?

–        I mean that the Kelly criterion is sound, but only when the system parameters are known.

–        Sure thing. There is only one parameter you need for Kelly, and that’s your edge. Is this what you refer to as ‘system parameters’?

–        Not quite. Your perceived edge is a result of a calculation based on system parameters. For example, if you pull out your records for last year, what do you find?

–        I find that I made 837 bets, of which 264 were winners, producing a nice profit of 187.30 points at level stakes.

–        Nice going! Your strike rate was 32% and profit on turnover 22%. Now we could simply assume that your edge is 22%. But herein lies the danger. Two dangers, actually.

–        I know about one for sure. When those dog-gone ‘bankers’ come along at odds of 1/2, I would need to plunk on 44% of my bankroll. A couple of those losing in a row reduces my bank to less than a third of its original value. Just two bets!

–        Yes, that’s one of them alright, which actually hides both issues. Let’s look at what kind of assumptions are made when we bet 44% of our bank in this situation. One of them is that our edge is 22% across the board, regardless of odds. The other one is that our edge this year will be the same as the one realised last year. Two huge assumptions that will lead to disaster in the battle field.

–        Aha! I think I’m starting to get your drift. So you’re saying on one hand that just because we made 22% profit last year, it could be different this year. Yeah, I’ll buy that. My profit rate has fluctuated between 12% and 33% for the past 4 years.

–        Sure. And we all know that assuming a higher perceived edge than what it is in reality will unnecessarily increase risk and reduce growth. It is always better to underestimate your edge with Kelly because in this case the most you can lose is a potentially higher growth rate. Overestimating your edge, however, not only has the same affect but it also unduly increases risk.

–        And you’re also saying that my edge may vary depending on the actual odds? You mean I may only be able to squeeze out 5% from odds-on bets but my edge could be 45% on 5/1 shots? Yes, now that I think about it, that’s entirely possible.

–        Exactly. See, if the average odds of your ‘bankers’ are 8/13 and your perceived edge is only 5%, the Kelly criterion calls for a maximum bet size of roughly 8% of your current bankroll. And if you look at your 5/1 shots and find that they are returning 45% on the average, you would want to bet no more than 9% on them. Assuming a blanket 22% edge is not simply misleading but suicidal because on one hand it would tempt you to bet 35% on odds-on selections but only allow 4% on those going off at 5/1. The reality, however, is that in both cases the advised maximum should be 8-9% of your bank. Ignoring this information would increase your risk considerably on your ‘bankers’, and wouldn’t let you take full advantage of your most profitable bets. So you are losing on two counts: significantly increased risk and much reduced growth, which could eventually get you busted despite having a highly sophisticated staking plan and a well established and profitable method.

–        Yes, I see what you mean, and now I also understand why level staking works for me so well. I think I will have a closer look at my records to find out what my real edge may be at different odds. This might take time, but sounds like it’ll be worth it.

–        For sure.

–        I’ll do that some time this week. Sorry, I have to go to work right now.

–        Work? Oh, I see… Well then, thanks for talking to me!

–        My pleasure. Actually… will you be here tomorrow? I wouldn’t mind going over my numbers with you along these lines.

–        Certainly, I’ll be happy to talk some more.

–        See you tomorrow, then!

–        Yeah, see ya!

Well, interesting fellow that ‘level-staker’, don’t you think? We’d better get to work here so we’ll have something to offer him tomorrow!

Calculations

From the foregoing discussion it is apparent that we need to do some kind of record keeping with respect to actual bets or selections. How are we to know how much to bet if we cannot even analyse our past bets? Given this, the only question remaining is what kind of information to record. We need information that will readily produce the kind of parameters that will facilitate the calculation of stakes. This at a minimum should include the date, time, course, horse, starting price (SP) and result (whether the selection was a winning bet; if not betting to win – e.g., place or lay betting –, then one must also record the amount of level-stakes profit/loss for each individual bet; to keep the discussion simple, we will assume win bets in what follows). It is also useful to record many other pieces of information (e.g., distance, racing code, handicap or not, trainer, jockey, weight, draw, form figures, interval times, etc.) so you can analyse your performance with respect to the different variables. It is best if you have records for at least a full year, but this is not a necessity.

We will use an Excel sheet to calculate ‘sensible stakes’. As we have seen, this will involve estimating our perceived minimum edge for various odds ranges. A useful simplification of the process will be taken advantage of in order to keep complexity to a minimum.  System parameters required to do the simplified calculation are as follows (parameter names in the worksheet are noted in parentheses):

·        length of period or total number of elapsed days ('TDays')

·        total number of selections or bets ('TBets')

·        total number of winning bets ('TWins')

·        total amount of level-stakes profit at SP ('TProfit')

In addition, two further parameters are used to provide as much safety (bankroll protection) as desired:

  • safety margin ('Margin')
  • maximum stake ('MaxStk').

The process consists of calculating the following in order:

1. Strike rate and profitability

2. Periodic (weekly, monthly, annual) figures

3. Average odds

4. Minimum number of wins

5. Minimum profit

6. Minimum strike rate and profitability

7. Suggested stake

8. Periodic profit

With the exception of number 4, these are pretty basic calculations.

1. Strike rate and profitability

Strike rate ('SR') = TWins/TBets

Profitability ('POT') = TProfit/TBets

2. Periodic (weekly, monthly, annual) figures

Number of selections per period ('PBets') = TBets/TDays*PDays

Number of winning bets per period ('PWins') = TWins/TDays*PDays

Level-stakes profit per period ('PProfit') = TProfit/TDays*PDays

where 'PDays' is the number of days in the period in question, i.e. 7 for weekly, 30 for monthly and 365 for annual figures.

3. Average odds

Average odds (starting prices) of all selections ('AvOdds') = (TProfit+(TBets-TWins))/TWins

4. Minimum number of wins

The crux of all calculations is estimating how well your system will perform in the future. For this, we will assume that profitable past results were just a happy deviation from some hypothetical 'mean'. Statistically speaking, we’ll be calculating a confidence interval for a population mean. This is where the safety margin comes into the picture, which is essentially the number of standard deviations past results are supposed to be out from this assumed 'mean'. I am using the term 'minimum' for the hypothetical 'mean' as this is much easier to picture than the other way around. So we basically say that the number of wins (or strike rate) will not fall below this level with a certain confidence. This is an important step as it is my experience that the straight figures from past results may overestimate the system's performance, especially if they are obtained from system development (optimising) and not actual bets.

The calculation is as follows:

Minimum number of wins ('MinWins') =

(TBets*(2*TWins+Margin^2)/(TBets+Margin^2)-SQRT((TBets*(2*TWins+Margin^2)/(TBets+Margin^2))^2-4*TBets*TWins^2/(TBets+Margin^2)))/2

where SQRT() stands for square root.

I know this is a bit involved, but you can simply copy and paste this equation into Excel, which will perform the calculation with ease. For the safety margin, I typically use 2.0 if actual past results are involved, and anything between 3.0 and 6.0 for system development. The former is equivalent to a 97.7% level of confidence, while the latter will give us assurances in the range of 99.9% to virtually 100% (statisticians please note that we are looking at only one side of the bell curve). Once we have successfully tackled this hurdle, we'll be cruising to the finish line.

5. Minimum profit

Minimum profit ('MinProfit') = MinWins*AvOdds-(TBets-MinWins)

6. Minimum strike rate and profitability

Minimum strike rate ('MinSR') = MinWins/TBets

Minimum profitability ('MinPOT') = MinProfit/TBets

7. Suggested stake

Suggested stake ('SugStk') = IF(MinPOT<0,"",MIN(MaxStk,MinPOT/AvOdds))

This is calculating the Kelly criterion using the minimum figures and capping at the maximum stake (for which I typically use 5%). At this point it is quite safe to use the full Kelly limit. Naturally, if minimum profitability is negative, we cannot make any bets.

8. Periodic profit

Periodic profit ('PProfit') = IF(SugStk="",0,SugStk*MinProfit*PBets/TBets)

I use the periodic profit figure to assess the promise or importance of systems I am working on. Obviously I will be investing more time in a system that is expected to make more money.

Examples

To give you a couple of examples for checking the formulas, here are some real systems I am testing live at present (3 standard deviations and 5% maximum stakes are used for the calculations below):

1. System CV: 65 days, 228 bets, 76 wins, 119.16 profit

Average odds: 3.58

Minimum wins: 56 (25%)

Minimum profit 29.69 (13%)

Suggested stake: 3.6%

Weekly profit: 12%

Very excited about this one!

2. System CFB: 130 days, 155 bets, 76 wins, 80.40 profit

Average odds: 2.10

Minimum wins: 58 (37%)

Minimum profit 24.43 (16%)

Suggested stake: 5.0% (the maximum)

Weekly profit: 7%

Another nice one with a high strike rate.

3. System PP: 2187 days, 464 bets, 136 wins, 154.65 profit

Average odds: 3.55

Minimum wins: 109 (23%)

Minimum profit 30.17 (7%)

Suggested stake: 1.8%

Weekly profit: 0.2%

Nice long record, but not very exciting in terms of gross profit.

4. System TR: 24 days, 245 bets, 93 wins, 66.47 profit

Average odds: 2.35

Minimum wins: 72 (29%)

Minimum profit -5.07 (-2%)

Suggested stake: (none)

Weekly profit: (none)

A promising system, but too early for action.

Sensible Staking

There are many nice properties of sensible staking, among which is the simplicity of real-time staking (i.e., it is not dependent on actual odds), the built-in safety, and the ability to tailor the two basic parameters (safety margin, maximum stake) to one's risk-taking appetite. By using average edge and odds for the staking calculations, one also avoids the huge bets typically called for with Kelly at low odds. This works well for prices lower than average because edge for that range is usually smaller than average. Higher than average prices, however, don't use reduced stakes, so if one's price range for betting is wide, this could use some further refinement. It's not a problem for me since I don't typically bet over 6/1.

–        Me neither, but I know that my friend does.

 

–        Ah, you’re back! How was your day?

–        Alright. I took some of your observations on board yesterday.

–        Good. How did it go?

–        I decided to put 3% on all my selections. It was a bit unusual for me because I needed to change my actual stakes within the day. Not by much, mind you, but it was an interesting exercise.

–        So you switched from level stakes to a fixed 3% proportion of your bank yesterday?

–        Right.

–        How did you get at this figure?

–        Simple. I know I’ve been betting ₤130 lately. That’s roughly 3% of my ₤4,200 betting bank.

–        Good work. Let’s see if your assumption is reasonable based on the work we did while you were away. You said you had 837 bets, 264 winners and made 187.30 points last year, right?

–        Exactly! But how did you remember these figures so well?

–        Well… I’m writing this article for a magazine, you know, and I have it in front of me…

–        I see. Can I have a look?

–        Sure. I’ll let you have a look after we’re finished talking… Getting back to your figures, your average odds last year were 2.88/1. Let’s calculate your minimum number of wins now.

–        What do you mean?

–        I explain this in the article, but it simply means that you are fairly confident that your strike rate will not fall below a certain limit.

–        Sure. Mine was 29% the lowest so far. A pretty lean year that was.

–        I bet. Let’s see, if we go with 2 standard deviations, the figure that comes out of the calculation is 238. That is equivalent to a 28% strike rate. Assuming that conditions remain essentially the same, you will have strike rates above that figure 98 times out of 100 years.

–        You think I will live that long?

–        No, I was just speaking statistically.

–        I see.

–        Your minimum profit will be 10%... hmmm… 49 times out of 50 years.

–        Makes sense. My lowest was 12% so far. Just 4 years, mind you.

–        Right. Based on all this, your suggested stakes are 3.6% of current bankroll. So actually you weren’t far off with your gut feel.

–        That’s good to hear. So I’m doing all right?

–        You certainly are. If you keep to 3-4% stakes with your method, you should be more than alright. You are expected to make just over three times your bankroll as a minimum every year. 3.07 times to be exact.

–        I usually make between ₤15,000 and ₤40,000 each year. It’s just a hobby, you know. I keep my bankroll around ₤4,000, that’s about the level I feel comfortable with. So what are you saying?

–        I’m saying you are likely to make over ₤12,000 each year. Well, except for one year in the next fifty years.

–        Oh, yes? Which one?

–        I can’t tell you that, nobody can. It’s just what the numbers indicate. Statistically speaking, you know?

–        OK, understand. Well, nice to have chatted with you. Thanks for your stats, I feel much better now.

–        Glad to hear that. Perhaps we can take a look at your performance at various odds ranges next time, and refine your staking even further?

–        Sure, sounds good. Bye now!

–        OK, see you!

Smart chap. Just doing it as a hobby? My goodness, most people would make a comfortable living on those incomes! Interesting, though, that his intuitive staking was so close to calculated figures. Perhaps that’s one of the reasons he is successful…

What’s that you say? That I just made those numbers up for the sake of the article? Not real people? Not a real story?

Well now, and what’s your confidence level for this unutterable insinuation?

 








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