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This section is very important for all of you who are still on your way of becoming  a semi-pro/pro bettor. Some of you who are already winning bettors can still learn something new about expected goals and money management. Many of you have probably heard of expected goals as even some big UK newspapers have these statistics available for their readers.

1. Expected goals

2. Kelly's criterion

3. Power ratings on soccer & ice-hockey ( available later this week)

 

1.What is expected goals?

Bottom line: To be a winning soccer bettor  you have to understand

and be able to calculate expected goals (xG)

  •  (xG) is a statistic used to work out how many goals should be scored in a match.

  • Every single shot is awarded an xG value based on the difficulty of the attempt, with factors including distance from goal, the scoring potential of the attacking player, type of shot and number of defenders present affecting the value.

  • The higher the xG of a particular shot, the more likely a goal should be scored from that shot.

  • The xG value of every shot in a game is then used to calculate the expected goals in a particular match.

Here is an example from an epic World cup match Croatia vs England  to show our readers how (xG) is calculated. This text was written right after the match. We recommend you read it carefully and watch the match at the same time of possible.

As many of you probably remember Croatia knocked England out of the World Cup thanks to a 2-1 win in extra-time, booking a place in their first ever World Cup final.

THE BEST TEAM DID WIN

Croatia, with a population of just some 4 million people, become the lowest populated nation to reach a World Cup final since 1930, and deservedly so.

Over 120 minutes, the Croats created by far the better chances, racking up 2.19 xGF( expected goals for (F) Croatia) compared to England's 0.75 xGF.

On the left England's attacking map

On the right Croatia's attacking map

The size of the circle illustrates the likelihood of a goal being scored.

 

 

 

 

 

 

 

 

 

 

 

 

Croatia dominated the second half and all of extra-time, with Luka Modrić running the game and man of the match Ivan Perišić proving to be a constant threat.

Zlatko Dalić’s side were superior on the night, and while many thought they may tire as the game went on, it was a bit surprisingly the opposite, as they were the stronger team later in the match.

As for England this was a match of disappointment despite a good first half showing. 

They played very well in the first half, taking the lead through a great free-kick from Trippier some 10% chance of scoring.

Many bettors and soccer fans came out after the game saying that England should have been 2-0 or even 3-0 up at half-time given the chances they created, but expected goals shows that wasn't really the case, and it's worth noting that Harry Kane's golden opportunity and close-range effort which hit the post were both ruled offside!

While England were the better team in the first half, Gareth Southgate’s side generated just 0.35 xGF - this equates to a 30% chance of scoring one goal, and just 5% chance of scoring two goals from the opportunities they created.

So while England may have been on top in the first half, over 120 minutes they could only muster 0.73 xG, indeed their worst attacking display of the tournament.

2.Kelly's criterion 

HOW TO USE KELLY’S CRITERION?

The formula and idea of Kelly’s Criterion is in principle very simple, it is about your bet being as large as the probability of a win minus the likelihood of a loss. This is to say, if you have a 55% chance of winning and a 45% chance of losing, you should bet 10% of your betting account (55-45+10). As mentioned earlier, the formula discourages you from betting on a game if the value of it is zero or minus. The system reduces the chances of becoming bankrupt because it assumes you always play a certain percentage of your bankroll.

The Kelly Criterion - Formula and example

(likelihood of a win x odds – 1) / (odds – 1) =Bet

Here's an example to explain it:

You have thought about betting on Arsenal to win at home against Tottenham Hotspur. According to your evaluation, Arsenal has a 50% chance of winning. This also means that there is a 50% chance that the match will end in a draw or a Tottenham win, which would lead to a loss in total. The betting company offers odds of 2.10 on an Arsenal win. If we put all this in a formula, it looks like this:

(0.50 x 2.10 – 1) / (2.10 – 1) = 0.045

This means that according to Kelly’s Criterion, you should use 4.5% of your betting account on this match as this is the advantage you have against the betting company that is offering the odds.

 DISADVANTAGES WITH THE KELLY CRITERION

Kelly’s Criterion is the best known formula to determine the optimal stake. However there is a problem of betting on several matches at the same time. Say you have 20 bets pending with 1.5% of the bankroll invested in each bet. This means you have risked 30% of your bankroll. We deduct the amount of money invested on each bet from our bankroll as if it was lost before placing the next bet. This strategy cuts bankroll growth a bit in the long-run but it is a safe and responsible way to do money (bankroll) management.
Kelly's criterion requites you can estimate a likelihood of an outcome as an exact percentage. This is  of course impossible even for the best pro bettor who in the long run is able to estimate probabilities correcly on average. A good example of a sports event where "everybody" meaning the betting market and every serious bettor on the planet was wrong is The Ausralian Open last January. It was a match between Djokovic and Nadal that was expected to be more or less 50/50. Perhaps 55-45 in favor of Djokovic or Nadal. However Djokoviv was totally dominant and won in 3 sets. Nadal, a superstar had no chance at all. So, what can you do to fix this problem.. Let's take a look..

THE FRACTIONAL KELLY METHOD


Due to the disadvantages and risks associated with the system, many variants have been created. The most well-known variant is known as the fractional Kelly. This is what we at Valuebetting also use. This variant entails that you must reduce your bet at a certain percentage of the core system. It could be that you reduce the percentage by 75% or more. We at Valuebetting think the percentage should be at least 75%. Many pro sport bettors agree, some apply even a higher percentage. We change the percentage from sport to sport and event to event depending and how accurate we believe our probability estimation is. We always attach a probability estimation for every pick to help you understand how much value we believe the bet has. Let's assume from now on that you are a beginner in betting and have a bankroll of 1000$

An example of a fractional Kelly

Let's take a look at soccer match between Arsenal vs Tottenham again. You think Arsenal has to high odds. According to your estimation, Arsenal has a 50% chance of winning. This also means that there is a 50% chance that the match will end in a draw or a Tottenham win, which would lead to a loss. A bookmaker offers odds of 2.10 on an Arsenal win. If we put all this in a formula, it looks like this:
(0.50 x 2.10 – 1) / (2.10 – 1) = 0.045

This means that according to Kelly’s Criterion, you should invest 4.5% of your betting account on this match as this is the advantage you have against the betting company that is offering the odds.You have found an expected value of 1.05  compared to the odds on a match. This According to the Kelly Criterion, you should invest 4.5% on your betting account. However, instead, you use the system kelly/4, a common strategy for many pro sports bettor which means that you divide the original recommended stake 4.5% by 4  (4.5%/4= 1.25%). If your bankroll is $1000 you invest $1000x0.0125= $12.50


This means that your winnings will be less, your bankroll will grow slower but also that the risk of losing large percentage of the bankroll during a short period of time will be reduced. This gives you time to enchance your analysis and perhaps find some systematic errors in you make. But as we already wrote he main reason to use a divider is the fact that you can't EVER know the exact probability for each outcome in any sports event! Through using the divider the possibility of long-term stable profitability increases. If you know that you indeed have a long-term edge on the betting market/ bookies, there is no point in striving for the quick and big wins. After all, betting is a marathon, an endless "war against the bookies" not a sprint.