In this post we are focusing on the square root staking plan, but the question still remains if staking plans are the root of evil, or the branch to success and increased profits?
Our series looking into individual staking plans uncovers the history behind each staking plan, why it was created, how it works, if it increases your profit and how much extra risk of losing your bankroll it creates.
You can see every article in this series here.
THE SQUARE ROOT STAKING PLAN HISTORY
The square root staking plan is credited to being created by James N. Selvidge.
He called it the Base Bet Plus Square Root staking plan, also known as BB+SR, and it first appeared in his book Money Management published by Jacada Publications.
It was a method of staking that was also recognised by James Quinn, a well known US handicapper, as offering…
…the best return on money invested by the small bettor. That is, the risk factor associated with the method is as low as can be found anywhere.
The square root method of staking is commonly considered to be the best alternative to the Kelly Criterion, a method of staking which can be extremely volatile.
James N. Selvidge was also the author of a book called Hold Your Horses and used to teach a class in Advanced Thoroughbred Handicapping in Washington.
THE SQUARE ROOT STAKING PLAN TYPE
The square root staking plan is not a loss recovery staking plan. Instead it increases the stakes you are betting based on how much profit you’ve made over a set timeframe.
One if the big decisions to make is what that timeframe is. It could be daily, weekly, monthly, quarterly, yearly or all time.
Usually the only staking plans we suggest you use are based on the odds of the selections, such as this staking plan, or flat stakes.
However, there is a possibility that this may become part of our recommendations for a low risk way of increasing your stakes.
HOW THE SQUARE ROOT STAKING PLAN WORKS
The rules for the square root staking plan are nice and simple. It all begins with a base bet.
Your base bet is a fixed amount that you bet on every horse.
If you are in profit over your chosen timeframe, then you take the square root of this profit and add it to your base bet.
The two major questions are:
- Deciding what your base bet will be
- Deciding what timeframe your profit will be based on
Let’s look at how we do this in practcie.
STEP #1: Deciding Your Base Bet
To decide your base bet you can simply choose a one unit from your bankroll, or alternatively you could use the Kelly Criterion to determine the size of your bet based on your edge.
Using the Kelly Criterion to determine your base bet you would follow this sum:
((Winning Percentage x Average Odds) – Losing Percentage) ÷ Avg. Winning Odds
If you had a 33% strike rate and your average winning odds were 3.60 and average odds were 5.00, this would mean:
((33 x 5.00) – 67) ÷ 3.60 = 27.20
This would indicate a 27.20% of bankroll as the base bet. However, I’d recommend you only do a half or even quarter kelly, which means dividing this by two to get 13.61% or four to get 6.80% of your bankroll.
You calculate the base bet once, so if you had a bankroll of £100 then your base bet would be £6.80 or rounded down to £6, and then it doesn’t change.
STEP #2: What Timeframe Is Your Profit Based On
I recommend that you do this over the lifetime of your selections.
However, every day, week or month, you should be taking out some of your profit to pay yourself for the work you’ve been doing.
Whenever you take some of the profit out, you then should restart your calculations using the same base bet amount but the square root will be left on the profit in your betting account, excluding the amount you’ve removed.
As you can see, if you were taking the profits out every day then the staking plan won’t have any time to take effect. So I’d recommend if you’re using this staking plan you only take a percentage of your profits out weekly, or ideally each month.
Every six months or year you should reset entirely, remove all the profit you want to, re-calculate your base bet and start fresh.
STEP #3: When To Use The Square Root
To calculate your stake size you always use your base bet. This only changes when you have made a profit.
If there is a profit, then you take the square root of the profit and add it to your base bet stake.
For example, if you had a £6 base bet and you had made £30 profit, you would calculate the square root of the £30 profit to give you £5.48.
You add £5.48 to your £6 base bet for a total stake of £11.48.
To calculate the square root use the square root button on any standard calculator, or use the =SQRT(30) in Excel, replacing the 30 with your profit.
A WORKING EXAMPLE OF THE SQUARE ROOT STAKING PLAN
Now that you’ve got the rules you need to implement the square root staking plan, this is a working example to show you how to put it in practice, and it is based on a base bet of £6.
| Horse | Pos. | BSP | Stake | Profit | Total Profit |
| Al Ozzdi | 2 | 6.44 | £6 | -£6.00 | -£6.00 |
| Global Spirit | 4 | 20 | £6 | -£6.00 | -£12.00 |
| Fountain Rose | 11 | 213.33 | £6 | -£6.00 | -£18.00 |
| Heath Charnock | 1 | 4.7 | £6 | £21.76 | £3.76 |
| Alix James | 3 | 9.2 | £7.94 | -£7.94 | -£4.18 |
| Bhangra | 7 | 17.05 | £6 | -£6.00 | -£10.18 |
| Financial Conduct | 505 | 52.96 | £6 | -£6.00 | -£16.18 |
| Frankly Darling | 1 | 2.07 | £6 | £6.29 | -£9.89 |
| Mister Blue | 1 | 36 | £6 | £205.80 | £195.91 |
| Breanski | 7 | 10.66 | £20.00 | -£20.00 | £175.91 |
| Hold Fast | 1 | 9.69 | £19.26 | £164.05 | £339.96 |
| Dark Vision | 2 | 3.85 | £24.44 | -£24.44 | £315.52 |
THE TRUTH BEHIND THE NUMBERS
Now we know how the square root staking plan works, and we’ve gone through an example, what we really want to know is whether this is something you should be using or not.
THE RISK vs REWARD
Starting with a £100 bankroll, the reward in the above sequence of bets was £315.52, a big portion of which came from a winner at odds of 36.
But how would the results have looked flat staking £6 bets or using stakes based on the odds of each horse.
Flat staking profit would be £236.94
Kelly style staking, as outlined here, and based on a 1% edge and £100 bankroll would be £3.02.
But that’s not really fair because the £6 stakes indicate a far higher edge than 1%. To get a similar stake size we’d need to push the edge up to about 25%, which in practice we’d never do. Doing this the profit would still only be £75.52.
The big issue with Kelly style staking is that it’s very hard to determine. your edge. With this in mind we tend to always go lower than higher, because if we set the edge too high we are almost guaranteed to lose our bankroll because Kelly staking aims to maximise bankroll growth.
Interestingly, the square root staking plan out-performed both of the others, and also solves the primary issue with Kelly type staking
CONCLUSION
This investigation into the square root staking plan has surprised me. Generally I don’t like staking plans because the majority tend to work by increasing your stakes during winning streaks to a point where you end up betting more on the losers during. the losing streaks than you do on the winners.
They tend to give an increased profit, but at a massively decreased return on investment and significantly increased risk.
Which is why I don’t like them.
However, the square root staking plan does not do this.
What’s clever about it is that as the profit increases you will be betting a smaller percentage of that profit. And, as an added bonus, if get a big priced winner the benefit will be significant.
In conclusion, I really like this staking plan, to the point where I will consider using it instead of the Kelly style staking for a simpler method, which reduces volatility and keeps bankroll growth as a premium.
Leave me a comment if your already a fan of this staking plan, or if this is a new one to you that you’re going to try.
Being new to betting and wanting to increase my bankroll before taking a profit this seems ideal for me. Therefore I will look to implement it shortly
Great. You should always take out 30% of every new high point in your bankroll and re-invest 70%, this means that if your approach stops working you will have taken some profit and payment for your time spent and it will give you the motivation to keep learning, practicing and moving forwards as you’re getting a tangible result. You should do this even if it’s only a couple of pennies to get into the practice of doing it.
Do you have a formula I can use in a spreadsheet to calculate the required stakes relative to my betting results?
I think this staking plan has potential I should like to compare it with the De L’ambert one I use
Thanks
Chris
Absolutely, in Excel you can use the formula:
=base bet+(sqrt(profit))
If your base bet was 10 and your profit was 100 it would look like this:
=10+(sqrt(100))
And the result would be 20.
So if your strike rate is 56%-44% , how do you work out the next part of the equation the average winning odds
I have 228 total races
I have 129 winning races.
The sum of my odds is 118
Okay, if we assume a 50 unit bankroll and your base bet is 1 unit. Let’s say your bankroll is £1000, that makes your base bet £20 (divide the bankroll by 50 units).
You now always bet £20, but when you’re in a profit you add to it the square root of the profit.
If your first bet won at 5/1, then you’re profit is £100 and your bankroll is now £1100. The next bet is your base bet if £20, plus the square root of the £100 profit. The square root of £100 is £10, so your stake is now £100 + £10 = £110. If you’re in a loss position, then you just use your base bet.
Should that be the next bet is your base bet of £20 plus the sq root of £100 which is £10, so the next stake is the base bet of £20 plus £10 = £30 rather than £110?
Yes Chris, it should be 🙂
This looks like a very small sample size to draw a conclusion from.
This was just an example to show how it worked, not a sample size for testing 🙂
The formula is wrong. I think it is meant to read ((win% x avg odds)-lose%)/avg odds.
This is a mis-application of the Kelly formula ((win odds x probability of winning)-probability of losing)/win odds. In other words edge/odds.
It takes the probability of (the bet) winning to be the strike rate and the odds to be the average odds. This is correct for things like coin tosses or dice rolling where the winning probability of every bet is known as are the odds. However in sports betting the winning probability is not known and the odds vary.
Using this formula you would never have an edge on bets with odds less than those represented by your strike rate (e.g. 3/1 for a 25% strike rate) as the top line of the equation would be less than or equal to zero. This is clearly wrong as a strike rate of say 25% would be made up of selections greater than and less than 3/1. Indeed, the majority of winners would be less than 3/1.
Thank you for the spot on the formula, you’re right it was supposed to be that and I’ve updated it and adjusted it to suit. The issue of not knowing the edge on every single bet in horse racing is the problem with using Kelly on horse racing, however this can be a quick way to calculate a base bet for this staking plan if you want to use it. Not sure I’m understanding what you’re saying about the edge in bets with odds less than those represented by your strike rate, although it is a bit early for me to be doing maths. If you had average odds of 3/1 and had a 25% strike rate, then if your average winning odds were only 2.00 you’d still have a 12.50% edge based on 25 x 4 = 100, 100 – 75 = 25, 25 / 2.00 = 12.5.
It’s ‘odds’ not decimal price, So for a 25% strike rate and average odds of 3/1 it would be,
25 x 3 = 75, 75 – 75 = 0. You have no edge if your average odds are the same or less than your strike rate.
My comment referred to methods that use strike rate as the ‘probability of winning’ along with the odds of the selection. They would say 25% x odds of 2/1 = 50, 50 -75 = -25. So no edge therefore no bet. Using this logic you would only bet at 3/1+ which is crazy as your profitable system with a strike rate of 25% would have been made up of bets at all sorts of odds and edges including some below 3/1.
Using average odds in the formula to calculate edge at least reflects the fact that you have an edge OVERALL but it implies this is fixed across all bets. E.g. you have a strike rate of 25% and avg odds of 3.25/1. Then you would have an edge ACROSS ALL YOUR BETS of 25 x 3.25 =81.25, 81.25 – 75 = 6.25%
Kelly would say bet 6.25/3 = 2.08% on a 3/1 shot IF THE EDGE ON THAT BET IS 6.25% not because that is your overall edge.
Applying this overall edge (based on strike rate and average odds) to all bets and then scaling every bet to ‘average win odds’ rather than the ‘actual odds of the selection’ defeats the underlying principle of Kelly which is to scale your bets to the odds/chance/edge ‘of the selection’ so as not to go broke and to optimise returns in the long-term.
I know you’re just setting a base bet but staking systems that calculate your edge using strike rate as the probability of EVERY BET winning are flawed.
Incidentally, in every simulation I’ve seen, the square root system is outperformed by level stakes when using the same level of base bet for both. If you take a sequence of bets that show say an 8% ROI at level stakes, then ramdomise these through thousands of permutations the result is always 8%.
If you take the same bets and do the same thing for the square root system, you will get times when it delivers high returns but it will also deliver losses and go broke depending on the sequence of bets. Taking average returns, level stakes always comes out ahead. Properly structured Kelly also delivers huge returns and some losses but never goes broke. On average it outperforms level stakes and all other systems.