Finding a System Using the HO/AO Quotient


Our 7th generation of HDAFU tables introduces the HO/AO quotient as a selection criterion which has the effect of making your systems less volatile and your portfolio of systems more viable.

Furthermore, the HO/AO Quotient removes the need to stay in front of the computer in the last hour before kick-off and allows you to compile your portfolio of bets well in advance, hence reducing the stress factor and possible human error.

Image: StockLite (Shutterstock)

What is a HO/AO Quotient?

The division of HO (Home Odds) by AO (AO Odds) reflects the “strength” of the teams. This makes upcoming games comparable with past matches, of which the results are known.

When building the quotient, we’re not asking ourselves questions like “Are these teams really equal?” or, “Is the favourite priced correctly?” We do not recalculate 1X2 odds; we simply use market prices and assume that the bookmakers have taken statistics into account and reflected public opinion (market pressures) as well as they possibly could do when setting their odds.

The HO/AO quotient is therefore an ideal device for comparing an upcoming match with the nearest batch of equivalent games against teams of a similar perceived strength to the opponent under analysis.

If for example, Liverpool are 1.34 to beat West Ham and West Ham are 11.0 to beat Liverpool, it makes sense to look at comparable matches where other teams carried similar prices in their respective home and away games in the past.

How to Calculate the HO/AO Quotient

As an example we will use the match Arsenal against Liverpool on 22/12/2017.

The evening before the match, the home win (Arsenal) was priced at 2.60, and the away win (Liverpool) at 2.95.

For the HO/AO quotient you simply divide the home odds (HO) by the away odds (AO).

2.60 divided by 2.95 = 0.881

That’s it!

Of course, if you would use the odds at kick-off then your quotient will be different, the home win (Arsenal) was then priced at 2.68, and the away win (Chelsea) at 2.95.

2.68 divided by 2.95 = 0.908

We will have closer look at these difference in the course of this article and explore if they actually matter and how much they matter.

What does the HO/AO Quotient Tell Us About the Comparative Strength of Teams?

When looking at the 2013-18 EPL HDAFU table, the following classifications become apparent when dividing games into ‘perceived strength’:

  1. HO/AO: up to 0.225
    The home team is the clear favourite with a very good chance of winning (the home team is the overwhelming favourite)
    For example, Liverpool vs. Brighton on the 13/5/2018
  2. HO/AO: 0.226 to 0.499
    The home team is definitely stronger than the away team, but there is also a good chance of a draw in the game (fluctuating opinion between home or draw)
    For example, Swansea vs. Stoke on the 13/5/2018
  3. HO/AO: 0.500 to 0.788
    It is not really clear in which direction the game will develop (no overwhelming favourite)
    For example, West Ham vs. Everton on the 13/5/2018
  4. HO/AO: 0.789 to 1.751
    The chance of a draw is quite high as both teams are perceived to be of equal strength (no overwhelming favourite)
    For example, Stoke vs. Crystal Palace on the 05/05/2018
  5. HO/AO: over 1.752
    The home team is perceived as being much weaker than the away team; the public feels that it could be an away win (the perceived favourite is the away team)
    For example, Southampton vs. Man City on the 13/5/2018

If you are in the possession of the 2013-18 EPL HDAFU table then go to the data tab and check a few matches and their HO/AO quotients and see if you agree with the games being in the above classifications.

Alternatively, calculate the HO/AO quotients using before kick-off odds that you can retrieve from any odds comparison site.

Now, continue with the exercise and check against the actual distribution of results. You will quickly see that they hardly distribute according to the expectations (HO/AO clusters). That’s what makes 1X2 betting so very tricky and the HO/AO quotient so handy.

Finding a System Using the HO/AO Quotient

We now come to the practical part of this article. If you have not yet downloaded our HDAFU Show Table, then you can do it now here; all the following examples are being carried out using this show table.

It is a fully functional table and its only limitation is that it is an expired table and cannot be used for the forthcoming season. Of course, it can be used for backtesting its functionality against the previous season (2017-18).

The size of this Excel .XLSX workbook is 4.2 MB

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(1) Find an HO/AO Cluster in the ‘IP’s by HOAO’ tab in which the Curve Goes Steadily Upwards

Image 1: P/L Simulation of ‘Backing the Draw’ in the first half

Above screenshot shows you ‘Backing the Draw’ in the first half.

It is a nice, steady upwards curve and stretched over almost a third of the whole graph. This is why we are going to look at this HO/AO cluster for this article.

(2) Check in the ‘System Picker’ tab what to Expect

Image 2: System Picker example



  1. The expected number of matches to bet on the following season: 53

    To diversify your portfolio, you are looking ideally for at least 500 bets in one season but you certainly want to avoid having too many small individual systems in your portfolio. Just remember, the more restrictive your selection criteria the higher the risk of deviation from the expectations.

    50 bets in an individual system is a very good number (that means that you only have to identify 10 different systems to populate a portfolio with 500 bets in total), and even better if it has been achieved over all five previous seasons.

  2. The expected hit rate: 39.62%

    Please keep in mind that the lower the hit rate the more volatile a system is to longer losing streaks. Here’s an article on that topic: The Science of Calculating Winning and Losing Streaks

    If your system has a probability of 40% to win then the maximum length of a losing streak may be as long as 8 bets in a row.

    Keep that in mind and try to avoid too many low hit rate systems in your portfolio.

    As a side note, you will be expecting with this system a hit rate of 39.62%. However, it is very unlikely that it will be absolutely spot on. Compared with the hit rates of the previous five seasons the average fluctuation (deviation) expected is 2.55% but it may be even as high as the maximum deviation which in this case was 5.48%.

    This is a risk measurement and I will address and explain the calculations and their interpretations in another article about ‘How to Construct a Portfolio’.

  3. The Zero Odds: 2.49

    This is actually the most important figure when using the HDAFU Tables to determine if you take the system in your portfolio of bets or not.

    Taking the expected deviation (2.55%) into account you are looking at ‘Zero’ odds between 2.34 and 2.65; even taking the max. deviation (5.48%) into account, the ‘Zero’ odds are still as low as 2.88.

    In this example, everything above the ‘Zero’ odds of 2.49 was a value bet! If you would have aimed constantly for odds above 2.88, you would have been playing on the absolutely safe side.

    As you are looking at a system with average odds of 3.44 (the figure below the ‘Zero odds’ in the above screenshot) the timing of your bet would hardly have mattered. Even if you don’t always have access to the highest odds in the market, e.g. because of territorial restrictions, then it would have been safe to include this system in your portfolio because of the likelihood of achieving draw odds above 2.49 (or even 2.88) ‘Zero’ odds.

    Again, as previously mentioned, the calculations and their interpretations will be addressed in detail in another article.


(3) Decide if to Include the System in your Portfolio

Our example above was definitely a system worthy of inclusion in the 2017-18 portfolio. It had everything you would be looking for:

  • 50 bets minimum per annum
  • an acceptable hit rate and
  • delightfully low ‘Zero’ odds for the draw

Feel free to check yourself how this system would have performed for you during the 2017-18 season.

Here’s the answer: In the end 55 bets were played, of which 21 won (38.18% hit rate) with a profit of over 1,500 units using 100 unit flat stakes.

Why does the HO/AO Quotient Make an Analysis Less Volatile?

Here’s a close up screenshot from the Inflection Point graph above (image 1) and the odds seem to be disorganised and unordered:

Image 3: Inflection Point graph – corresponding draw odds

The HO/AO Quotient is a device for grouping matches into ‘comparable strengths’ of the teams involved (home odds divided by away odds), with the draw variable removed.

If you would be picking your system by odds then draw odds up to 3.54 could be draws odds for all kind of matches; matches between a strong favourite at home, equally matched teams, or the favourite being the away team, and so on.

With the HO/AO Quotient in our example: 0.603 to 1.396 we are only targeting teams in group 3 ≫ It is not really clear in which direction the game will develop (no overwhelming favourite) and group 4 ≫ The chance of a draw is quite high as both teams are perceived to be of equal strength (no overwhelming favourite)

For example, if there is a strong favourite involved in the game then the HO/AO Quotient approach filters these games out, even if the draw odds may be lower than 3.54.

Using the HO/AO Quotient slims down the number of available bets to an average of 53 bets with an expected hit rate of 39.62%. The expected profit is: 2,046.60 units per annum when staking 100 units flat.

Would you have used the ‘IP’s by Odds’ instead you would have likely chosen the odds cluster from 3.30 to 3.65. This would have provided you with a higher number bets per annum (87) but with only a 33.33% expected hit rate and a lower profit expectation of 1,322.40 units. Furthermore, the system would have been more volatile: an expected deviation of 2.78% (as compared with 2.55%) with a maximum deviation of 6.66% (as compared with 5.48%).

By slimming down the number of bet candidates and targeting bet selection via the HO/AO quotient taking the strength of the teams into account, the system becomes less volatile.

Draw systems especially benefit from the HO/AO Quotient, but others as well.

At What Time Should the HO/AO Quotient be Calculated and Which Odds should be Used

All Summer and Winter League HDAFU Tables use 1X2 odds recorded at or close to the end of the ante-post market. In other words, just prior to kick-off in all games. In the majority of cases, these odds are courtesy of Pinnacle, the most popular low-margin bookmaker around. In all other cases, the 1X2 odds used are the highest bookmaker odds at www.Oddsportal.com from a selected panel of their bookmakers according to our own personal settings.

Ideally, the closer to kick-off you calculate the HO/AO quotients for your system(s), the closer you are going to be to the HO/AO quotients calculated and used in the HDAFU simulations. Preferably, you should wait until team news is released before relying on where the odds settle thereafter.

Calculating the HO/AO Quotient at another Time

If you are for some reason unable to calculate the HO/AO quotient close to kick-off on match days then please, don’t worry too much.

Here’s an example weekend from the first half of the 2017-18 EPL season:

Image 4: Calculating HO/AO Quotients at different times

As you can see all four matches that would have fitted the criteria of being in the HO/AO 0.603 to 1.396 quotient cluster would still have been in the group of betting candidates even when using odds at the close of the match.

Only the Swansea vs. Crystal Palace match may have drifted out of the cluster. The other three games remained solidly within their clusters so that it didn’t matter at all how their odds changed during the ante-post market.

I hope this article has cleared up any confusion caused by the introduction of the HO/AO Quotient to our 7th generation HDAFU tables. However, if you are still not sure, then please feel free to ask any questions via the comment section below.

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Last Update: 12 July 2018

Categories:1x2 Betting Betting Systems



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