How To Set Asian Handicap Odds
Sep 13th, 2012 - Posted by Mark_Taylor in Betting Theory, Football
NFL and football fan. I've seen my two favourite sides, Stoke and the San Diego Chargers play at the new Wembley....and both lost.
How do you calculate fair odds for Asian Handicap markets? It's one of the most popular forms of football betting and today on the blog, Mark Taylor shows us how it's done and even gives us an Asian Handicap calculator to download.
Asian handicap betting is fast becoming one of the most popular methods of wagering on the outcome of a football match. The attractions are to be found in the elimination of both draws and very short priced favourites, resulting in a wager where usually the underdogs receive a handicap start and the prices available for each team under these revised conditions are in the region of even money.
There are already many fine explanations of this type of betting to be found on this blog, so in this post I'll try to show you how to use your own estimations of a team's chances of winning, losing or drawing a game to formulate your own prices for the corresponding Asian markets.
What Are The Odds?
Bookmakers express their odds in a variety of different ways, decimal or fractional being the two most common, but the underlying language that they use is probability. An even money chance, 1/1 in fractional terms or 2.0 in decimal implies that the event being described has a 50% chance of occurring or a probability of 0.5.
While probabilities of all possible outcomes, such as a home win, away win or a draw in an event in the real world must add up to 1.0, individual bookmakers will add an "overround" to each probability to give them a margin for error and increase the likelihood that they are offering less generous odds on each possible outcome.
In short, if they think two possible outcomes are true 50% chances, they will offer returns at around 1.9 each of two instead of 2.0.
It is therefore vital that anyone who intends placing a wager should be able to calculate the true odds of an event occurring. This allows comparison with the odds available to determine whether those odds are more or less generous than your own estimation of the true probability of the event happening.
A Couple Of Assumptions
Much of the previous paragraphs will be common knowledge to anyone interested in sports betting, the concept of "value betting" relies upon obtaining better prices than the true odds of an event unfolding as expected. If you consistently obtain even money about true 10/11 shots, then long term you should be guaranteed a profit.
So my second assumption is that readers will be comfortable framing their own true match odds. If not, then I thoroughly recommend Cassini's series of posts which intend illustrating the use of The Poisson Distribution to calculate true home, away and draw odds. Use of the Poisson to calculate football odds does have minor, well described faults, but as an introduction to using slightly more advanced mathematical techniques to begin to model football matches, it is without equal.
Getting Started
The first step towards becoming comfortable in framing your own match odds for Asian betting is an understanding of the concept of expectation. A truly fair coin has a probability of turning up heads of 0.5. This corresponds to fair decimal odds of 2.0 or even money. Therefore, in an ideal world over 100 such trials, if we consistently bet heads and were offered odds of 2.0, we would win 50 such bets. We would have staked 100 units, one unit for each bet and we would have lost 50 of those units on the 50 occasions when the coin fell as tails.
But on the 50 times when the coin fell as heads we would have won a grand total of 50 units as well as our 50 staked units. So by receiving fair odds our long term expectancy is that we receive in winnings plus returned stake exactly what we place in bets. In short, we break even.
We now have a route to derive true Asian odds provided we have an informed opinion regarding the usual home, away and draw odds for a match and as we move to the more exotic examples, a view on how likely a team are to triumph by exactly one and two goals.
Stepping Through An Example
The simplest Asian handicap to understand is the 1/2 ball or -0.5 handicap. The underdog is given an imaginary half a goal start meaning that for betting purposes they "win" the game if they win outright or draw. The half goal start is added to the stalemated draw score to give the "victory".
Now imagine Team A is playing Team B and our estimations are that Team A has a win probability of 0.52, Team B's is 0.19 and the Draw has a probability of occurring of 0.29, we can use our theoretical returns expectation over 100 matches to calculate the fair odds given those three respective probabilities.
I'll now outline the expectation process that allows us to convert these probabilities into the true decimal Asian odds for each team. Don't worry about the actual calculations, if you're simply after a way to convert to Asian odds, there will be a link to a spreadsheet at the end of the post, but often a deeper understanding of odds setting can reap rewards.
From the superior Team A's perspective, they will actually win 52 of the 100 games, both in reality and on the Asian handicap. The 0.5 goal start for Team B will ensure an Asian loss for Team A in the 19 drawn games and the 29 games that are lost in reality. Therefore the fair odds for Team A must ensure that our 100 one unit bets return exactly 100 units from those 52 occasions when Team A won in reality and on the handicap.
In short we have an equation with one unknown, namely the Asian decimal odds for Team A.
52 * Asian Decimal Odds * One Unit Stake = 100 Units.
If we rearrange this equation, we find that the fair Asian decimal odds based on our own win/lose/draw probabilities is obtained by 100/52 which equals 1.923. If we now take the reciprocal of these decimal odds we convert back to probabilities. 1.923 is equivalent to a probability of 0.52 and as we are dealing with "true odds" here, the only remaining outcome, a handicap "win" for Team B takes the remaining probability of 0.48 or 2.083 in decimal odds.
Hence our estimation of the fair odds for Team A conceding half a goal start is 1.923 and for Team B receiving the same start is 2.083 and if the odds available exceed these prices, then we have a value bet.
Another Example
Next, I'll run through an actual example from the Newcastle vs Aston Villa match earlier this season. Newcastle was asked to give +0.75 of a goal start at home to Villa. This is an example of a split ball Asian handicap, if you side with Newcastle, half of your unit stake is placed on Newcastle -0.5 and the rest on Newcastle -1.0, hence the quote of 0.75 or 3/4 of a goal handicap.
We therefore need to know how often a team will win by exactly one goal. This can be modelled from such devices as the previously mentioned Poisson Distribution or through data collection. Below I've plotted the frequency at which teams win by exactly one goal, given a certain likelihood that they will merely win the match.
If we return to the Newcastle-Villa game, we need a view on the following scenarios. Newcastle would reasonably expect win these type of games 56% of the time, 25.5% of the time by exactly 1 goal & therefore 30.5% of the time by 2 or more. So we can now begin to construct our expectation equation for this particular match.
Looking at the expected returns from the viewpoint of a Newcastle backer on the Asian handicap, we find:
If Newcastle lose we receive no returns.
If Newcastle draw we receive no returns.
If Newcastle win by exactly 1, then you are returned half your stake multiplied by the decimal odds (from the -0.5 goal part of the bet) and half your stake is merely returned (from the -1 goal part of the bet). This happens on average 25.5 times in every hundred bets. You've had a partially successful bet.
If Newcastle win by 2 or more goals, your returns are your stake multiplied by the decimal odds. This happens on average 30.5 times in every 100. Both parts of your wager have been successful.
If we now add up the potential returns, along with their relative frequencies over 100 bets we get the following expression of Newcastle (-0.75)'s long term fair expectation:
(25.5 * Asian Decimal Odds * 1 * 1/2) + (25.5 * 1 * 1/2) + (30.5 * Asian Decimal Odds * 1/2 * 2) = 100
This shakes out to fair Newcastle odds of 2.017 and the complimentary Aston Villa odds are 1.983. One popular online firm had Newcastle available at 1.91, shorter than our fair odds estimation and Villa at 2.03, slightly longer than our fair odds estimation. Thus Villa (+0.75) was a value long term proposition.
Some Final Thoughts
The process above is similar for all the available Asian odds and the algebra involved is straightforward, if a little tedious. To automate the process we've uploaded a spreadsheet for download. Merely enter your own match probabilities and the probabilities of the favourite winning by exactly one or two goals from the table provided and the fair price for a range of Asian markets will be calculated.
If your estimates are sound your fair price should be very near to the price being offered by the bookmaker. Often the prices on offer won't represent any value, but occasionally the books will offer a better price than your fair price estimate.
Download the Excel Spreadsheet Asian Handicap Calculator.
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Very interesting and informative article, especially as it is about a subject that a lot of punters misunderstand...keep up the good work!
Thanks for a good article. I learned a lot
nice and usable excel, yust one question:
are this probailities given only for english leagues, or just Premier League or is it europan (world) average?
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awesome calculator! Jus a few questions.![[image]](/assets/js/editor/images/emotes/face-smile.png)
1) inputting the percentages of home win / draw/ away win, can I use average early odds ?
2) if bookmakers set the odds too far off true odds, what does it represent?
Thanks in advance if you could help