Demystifying Betting Myths
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How to Calculate Average Odds in Football Betting

Example of Harmonic Mean

Understanding formulas and calculations is always best done using a tactile example…

Here you can download a free Excel spreadsheet with Arsenal’s 2011-2012 data and associated sample calculations of arithmetic and harmonic mean for their respective home, draw and away odds for the whole of that season:


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Note: The calculations provided in this download include more data and sample calculations than shown in this article.

Breaking down the Arsenal example into an easier workable chunk, we will now compare the harmonic and arithmetic mean of just 5 of their recent home matches:

Harmonic Mean-example Excel

The calculation of the harmonic mean:

harmonic mean - example 1
harmonic mean - example 2

For comparison, the calculation of the arithmetic mean:

Arithmetic Mean - example

You can clearly see that the two methods produce different results and therefore, basing long complicated analyses and studies on the wrong intermediate result (i.e. using the arithmetic mean rather than the harmonic mean), will ultimately leave you just as far from consistently positive betting results than you were before beginning your odyssey!

Should this be a new topic for you then Soccerwidow recommends playing around with computing average odds and, for example, practising the harmonic mean calculation (using the highest betting odds you can find for the market) for the whole of a league’s season.

It may come as a surprise to some and perhaps enlighten others to discover that the harmonic mean of a season’s odds reflects the observed average distribution of results pretty closely, far closer than the arithmetic mean (which is commonly, but wrongly used for calculating ‘the average odds’).

How do those sly bookmakers achieve this? 😉

Last Update: 30 January 2014

Categories:Odds Calculation Value Betting Academy

14 Responses to “How to Calculate Average Odds in Football Betting”

  1. 4 December 2018 at 7:59 pm #

    Came across the article here whilst browsing – informative, even for a maths person like myself. My question is: what does harmonic mean GIVE us? Is it the ‘average’ odds per match, whose common value would give us the same returns as the originals? I have been playing with a spreadsheet, using only 3 values (3/1, 2/5 and 9/4 (aka 4.00, 1.4 and 3.25)) which gives a HM of 2.3585, but I can’t make the formulae work to give me the same returns as the calcs using the original values individually as an accumulator. Any possibility of a worked example? Regards A

  2. 30 September 2016 at 3:54 pm #

    Hello Soccerwidow!

    Can you tell me please, how are the Asian Handicap markets calculated?


    • 1 October 2016 at 2:09 pm #

      Hi sarkec, ASH calculation is going to be a whole course, much more massive than the OU course. It’s a very tricky calculation. Cannot be explained in few words. Sorry.

  3. 26 April 2013 at 5:36 am #


    When averaging the two zero odds for a home and away team in your over/under course, you use the arithmetic mean rather than the harmonic mean. In your example of U4.5 in the Wolfsburg v Bayern match the numbers are 1.16 & 1.24 so both averages come out quite close to 1.2

    However, looking at U 2.5 in the same tables, using odds of 2 & 3 you get a arithmetic avg of 2.5 and harmonic of 2.4 which could potentially alter a decision as to value in the bet.

    Could you please confirm which is correct and why?

    Many thanks!

    • 26 April 2013 at 7:05 am #

      Hi Aussiebettor, I think you found an error in the course which needs to be amended. Using the harmonic mean for building average odds is correct.

      Anyway, the course is due for review, and I will attend to it.

  4. 23 April 2013 at 9:43 pm #

    Very interesting article indeed. Would you use harmonic mean average if you we’re say calculating the average shots or corners taken by a given team over the season ?

    • 24 April 2013 at 6:04 am #

      Shots and corners are countable variables; they can be sorted into a natural order and possess a zero point. Therefore, these variables belong to the ratio scale, and for calculating of the average the ‘normal’ average mean is being used. Harmonic and geometric mean are pretty meaningless for this kind of variables.

      You may find this article useful: Correct Assignment of Football Data to Levels of Measurement

  5. 18 April 2013 at 11:09 am #

    Hi Soccerwidow,

    Do you have any idea of how the over/under of a soccer match is priced please?

    I do not think that it is automatically extracted from the 1×2 right ?

    Thanks in advance.

  6. 12 March 2013 at 1:13 pm #

    Hi there,

    Anyone that know where to find the following Calculator:

    1) giving input in the form of odd for Over / under 2,5 & the odd for 1,X,2 outcome.

    Giving estimated fair odd for ALL result from 0-0 to 9-9,

    Thanks in the advance

    • 12 March 2013 at 7:27 pm #

      Hi Goran,

      it’s unfortunately not that easy.

      However, here is a link to a calculator which will give you some probabilities if you put in the goal averages home & away:

      • 25 April 2013 at 7:24 am #

        Thanks for the link, Soccerwidow; unfortunatelly, it seems to be just simple Poisson distribution, that could be easily done in Excel as well, and is known as not really accurate, so nothing special…

  7. 9 March 2013 at 8:02 pm #

    Very interesting. Could one also use a geometric mean? My school maths is rusty but doesn’t a geometric mean provide a “typical value”, while a harmonic mean leans towards smaller figures in the set at the expense of larger ones?

    • 10 March 2013 at 6:36 am #

      The geometric mean is used for describing proportional growth, e.g. in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). In betting, the geometric means calculates the growth rate of success (profits/losses).

      I’m in the process of writing an educational paper on this so keep looking…

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