Adjusting your bankroll while betting to reduce variance

Automatically

In ValueBetting, we now calculate the correct Kelly stake size even with multiple open bets. Just go to options and make sure Adjust for open bets is enabled. With this feature, there is no need to update your bankroll several times every day. It is however still recommended to update your bankroll daily.

Manually

Sometimes it can be sensible to update your bankroll more than once per day to reduce variance. If you turn over a significant percentage of your bankroll each day, you need to update your bankroll more often. You can adjust your current bankroll under Options.

This is because the Kelly stake sizing is calculated using your bankroll. If you have half your bankroll in unsettled bets, and still calculate stake sizing based on your full bankroll, you might be taking more risk than you want.

A reasonable way to do this could be to remove half of the total amount of open bets from your bankroll. Example: You have a total bankroll of 1000 units. If you have 500 units in open bets, you could subtract 250 (50% of 500) from your total bankroll. Enter your bankroll as 750 (1000-250).

This is also dependent on the average odds you place value bets on. For instance, if you only bet on value bets with odds 3.00, you will see way more variance than if your average odds is closer to 2.00. If you know that this applies to you, a more conservative approach could be to deduct the full amount of open bets from your bankroll.

No need if your bankroll is large

If you just turn over just a small percentage of your bankroll every day, there is little need to update your bankroll more frequently than once per day.

Also, you might have a large bankroll but chose to just use a small part of it. In this scenario there is also little need to frequently update your bankroll.

Expected Value, Closing Line and Variance

Profit (green) and the closing line value (CLV, in grey). CLV is your expected value, over time.

Terminology

First, here are some words you need to understand to really know why value betting works.

Value is the percentage you see beside every value bet in RebelBetting. This is the value (also called edge, ROI or yield) of this particular odds right now compared to the “true odds”. Note that a value might decrease or increase closer to match start, as the bookmakers converge closer to the true probability. This is called the closing line.

Closing Line Value (CLV) is based on the sharp bookmakers odds just before match start. We call this the true odds. This is proven to be the best predictor of the outcome of a match.

We use CLV as the predictor of your expected value (EV). Both these terms can be used, and they mean the same thing in RebelBetting.

If you regularly bet on odds higher than the closing line, you will be profitable. This is called beating the closing line. ValueBetting customers beat the closing line over 80% of the time. Detailed explanation of the closing line.

Note that even though the sharp bookmakers make extremely accurate predictions, this does not mean you will win every bet. You often bet on value bets with odds over 2.0 (lower than 50% chance of winning), and often the underdog wins. This means your actual profit will at times differ a lot from the profit predicted by the CLV. This is called variance.

Variance measures the difference between your profit and the CLV. Or how far a set of numbers are spread out from their average value.

Profit, ROI and Yield measures your actual results, which depends on the outcome of the matches. Read more about the difference between ROI and Yield.

Flat profit or unit profit is used when comparing users, betting systems or tipsters against each other, without taking bankroll size and betting strategy into account. It’s the profit you would have achieved if you used a flat staking strategy (also called fixed staking). This means betting one “unit” (1% of your bankroll) at each bet. A unit is different for every user, it can be €10 or €100 – since it’s a relative number you can easily compare the results. Note that betting using the Kelly criterion (a proportional staking strategy) will improve your profits compared to flat staking.

To view your ValueBetting profit and CLV, they are shown at the top of the BetTracker, and also in your detailed reports.

Coin toss example

The probability of a coin to land on Heads is 50%. But assume you get the odds 2.10 on Heads and bet €10.

• If you win you profit €11
• If you lose you lose €10

To calculate the expected value of the bet you can use this formula:
(profit per bet * probability of winning in decimals) – (loss per bet * probability of losing in decimals).
In this case: (€11 * 0.5) – (€10 * 0.5) = €0.5
Therefore you would expect to make an average profit of €0.5 (or 5%) for each €10 bet, because the odds offered are better than the implied odds of the coin toss.

However, after only one toss you would have either lost €10 or earned €11, not won €0.5. So if you only place 1 bet, the variance will be huge.

Variance will be higher in the beginning

Variance is particularly high when the sample size is small, for instance at the start of your value betting career.

The more bets you place, the variance will have far less effect and your results will over time move closer and align with your expected value. Note that we’re not talking about a few hundred bets, it may require a couple of thousand bets. Read more about statistical significance in sports betting.

The importance of thinking long-term

It’s important to see value betting as a long-term way to profit. The number of bets, as well as using a staking and max bet strategy, play an important role to reduce variance. Here are some tips on how to reduce variance when value betting.

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How much money can I make with ValueBetting?

Play around with the ValueBetting profit calculator and see for yourself.

Calculations based on actual statistics from our users since 2019 (over 1 million bets).

Sound too good to be true? That’s actually the average result of our members. Below you can see updated results from our users.

Curious to see more real results from ValueBetting users? Join the RebelBetting community. This is a place for you to share and discuss results, betting strategies and much more.

Kelly criterion for stake sizing

The Kelly criterion is a staking strategy that calculates the optimal stake for maximum growth of your bankroll, based on the perceived value of the bet.

We use the Kelly criterion when recommending the optimal stake when you’re betting on value bets.

Fractional Kelly

You can also choose what Kelly stake sizing you want (also called fractional Kelly). This is a balance between expected profit and money risked. Decreasing the Kelly percentage will make you risk a lot less money, while only decreasing your profits very slightly.

30% Kelly is the default setting in ValueBetting and is a good balance between profit and risk.

You can change this by going to Options in ValueBetting. But before you do, please make sure you have understood how your Kelly stake sizing affects variance.

Using a Kelly above 50% is not recommended and will lead to very high variance and steeper draw-downs, with very little increase in profits.

Fractional Kelly stake sizing can also be combined with a max bet size.

Kelly and multiple simultaneous bets

The original Kelly criterion is proven to be mathematically optimal when placing a single bet, an infinite number of times. In reality, your goal is to maximize your expected bankroll growth over a finite number of bets, often having many simultaneous bets open.

Automatically adjust bankroll for open bets

When you have many open bets, they must be subtracted from your effective bankroll used when calculating the Kelly stake size for the next bet, to maintain the same risk level.

This is especially important if you often bet a majority of your bankroll each day. If you have 50 open bets and bet the same amount on every bet, you are effectively ignoring the Kelly criterion, resulting in high variance.

On the other hand, if you only bet 10% of your bankroll every day, you will not notice much difference. The feature can be turned off in Options, just disable “Adjust for open bets”.

In ValueBetting (web version), we calculate this adjusted bankroll automatically for you. Just keep the checkbox “Adjust for open bets” enabled in Options (it’s enabled by default). This will slowly decrease the recommended stake as the number of open bets increase, helping you manage your risk while optimizing your profits.

Comparison charts

Here you can see how your bet size and bankroll will change when adjusting for open bets or not. In the example we’re having multiple 5% value bets open simultaneously.

Without adjusting for open bets

Here you bet the full “single bet Kelly” percentage of 1,4% on every bet. You can place 70 bets before your bankroll is fully turned over. You notice there is no decrease of bet size (and risk) even though your effective bankroll decreases.

When adjusting your bankroll for open bets

Here the bet size is decreasing together with the bankroll. Note that maintaining a proper Kelly criterion means lower risk, lower variance and smaller drawdowns, but also slightly less average profit. Your bankroll will never run out, since the strict Kelly criterion will never suggest you bet your entire remaining bankroll.

Max stake relative to bankroll

We recommend using a maximum stake on your bets. The max stake is set in percent relative to your bankroll.

Example: You have a total bankroll of €1,000 and you set your max stake to 2%. ValueBetting will then limit your stake to €20, even if the Kelly stake sizing suggests a higher stake.

Setting a max stake is done to reduce variance. Also remember to update your bankroll often.

Generally, the fractional Kelly criterion is a better method to get maximum long-term profit. However, you might also want to reduce variance, especially when starting out. This is best done with setting a safe max stake of around 1%. If you’re all about maximizing your profits, and can handle downswings, you might want to increase max stake to 2% and let the Kelly criterion work more effectively.

Set your max stake, and more settings, under Options.

If you throw a coin ten times and gets ten heads in a row, it’s just an unlikely random event.

If you throw a coin ten thousand times and gets 55% heads, you know the coin is unbalanced.

Why? Because of statistical significance. Ten coin flips are just not enough data to draw any conclusions from.

It’s the same in sports betting.

If you place 100 bets with an average odds of 2.0 and get a 5% yield (profit per dollar invested), there’s still a one-in-three chance you got that result just out of pure luck. The p-value is below 0.3.

The number of bets required to reach statistical significance is much higher than what most people think intuitively.

For example, if you after 1100 bets still have 5% yield – you’re most likely on to something. The risk of these results being pure chance is now just 5% (p <0.05). So there is a 95% chance that there is something else going on. Like skill, or a profitable value betting product.

A p-value below 0.05 is generally accepted as “statistically significant” – but that is a highly arbitrary limit. There is nothing stopping you from requiring stricter proof, like a p-value below 0.01.

If you want to dive deeper into the math behind this, I recommend reading about statistical significance, the t-test and the p-value.

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Is it possible to do value betting on sharp bookmakers? Yes. But when it comes to betting against the sharp bookmakers and exchanges, it’s a different ball game. 

Before we dive deeper into this, first you might want to read about the difference between soft and sharp bookmakers to understand the difference between these two types of bookmakers. Many Asian bookmakers are considered sharp. 

Making a profit value betting on sharp bookmakers and exchanges is more difficult than using only soft bookmakers. If you’re a beginner, you might consider betting on soft bookmakers, to begin with. Or only bet on the sharp bookmakers with proven profitable results.

The reason for this is that a sharp bookmaker generally has odds that are closer to the true probability, compared to a soft bookmaker. This means you have to consider more parameters than just the value percentage:

• We calculate the value by using a combination of sharp bookmaker odds, algorithms and market bias. But sometimes the sharps don’t agree with each other and have quite different odds. In a case like this, you need to determine the reliability of the value. This requires knowledge and experience.
• You need to consider the time until the match start. Bookmakers have the least amount of confidence in odds when they are first published, growing increasingly confident as the market adjusts. So there might be a lot of value in early markets, but also a lot of unreliable odds.
• Sport and leagues. Some sharps have excellent odds (with little value) on a particular sport or league, but less so on others.

In short: It’s more difficult to value bet on sharps. If you’re a beginner you might want to start with soft bookmakers until you’re more experienced. The upside is: there still exist a lot of value on sharps, and you can bet large amounts.

Why yield and CLV is lower than the value

If you place 1000 value bets with our ValueBetting service, all with a 4.4% value — your closing line value will on average be 2.6%.

So why is it that average CLV and yield is always lower than your average value at bet placement in the long run?

The major reason is that the sharp bookmaker margin typically shrinks over time. As we get closer to match start, the sharp bookmakers get more confident in their odds, thus lowering the margin. As margins shrink, sharp odds will increase slightly, bringing down the value of the bet.

As explained by Joseph Buchdahl: “where net market movement is zero between opening and closure, a closing price will still be a little longer [higher, less likely] than it’s opening one”.

So, while it’s frustrating to see the value decreasing, it’s a completely expected movement in the betting market. And an average yield of 2.6% per bet will still give you a pretty amazing profit over time.

Statistics from ValueBetting (5 million bets placed)

• 60% of all sharp odds will increase between bet placement and match start (closing odds).
• Value shrinks by 40% on average from bet placement.
• 84% of all our value bets still beat the closing line. This is the most important metric in sports betting.
• 69% of all our value bets beat the closing line and still has a positive value (adjusting for margin).

You should always bet on the highest value while still turning over your bankroll as often as possible. But knowing your yield will end up around 40% lower than the average value, try to set your minimum value filter accordingly. For example, if you want a 2.6% average yield, your average value at bet placement should be 4.4%.