Deconstructing WDL and O/U 2.5 goals odds.
Input odds below (in decimal):
| Home Odds: | |
| Draw Odds: | |
| Away odds: | |
| Over 2.5 Odds: | |
See also Elo Reverse Calculator.
Dixon Coles
Dixon Coles is a method of generating probabilities on football matches. It is related to Poisson but adds a correlation for low scores. It seems to be one of the most accurate public methods. It requires three parameters lambda, mu and rho. rho describes how related low scores are. lambda and mu represent the average goals the home and away team are expected to score.
In this calculator I have fixed rho = -0.13 (more info here and here) and I simply do a brute force search varying lambda and mu to find the values that has the lowest error from the Win Draw Lose and Over 2.5 odds entered. I use the WDL odds and Over/Under odds as they are the most liquid betting markets and you can usually read a very accurate estimate for these off oddschecker or the exchange.
The solutions (from this brute force search described above) for lambda and mu represent the Home team and Away team market implied xG.
Based on these best fit parameters - you can generate a prediction for all scores. By grouping these scores you can easily add up the probabilities to estimate the BTTS markets, Home & BTTS etc, which is what the calculators does for you.
Dixon Coles is built on top of Poisson. A known weakness of applying Poisson to football goals is that it seems to fall apart on high scoring games. So be mindful of probabilities generated above where there is a high likelihood of a huge scoreline.
Half Time
There are less goals scored in the first half than the second half. In the season to date in the Premier League 2022 there have been 712 goals and only 318 in the first half. This is consistent over seasons. I preserve this proportion to estimate each Teams xG for each half - ie Team First Half xG will be Team xG * 318/712.
Half markets can be tricky as there is a clear dependency - goals dictate matches. For example if you are 3-0 up at half time, you may take your foot off the gas, make a few subs. On the other hand the losing team will need to push, or go all out. It clearly affects tactics. I ignore all this for this simple calculator. I assume both halves are independent. A large lead at half time is usually very unlikely, so you are considering an edge case already. Also often the affects can cancel each other out. By throwing extra players forward to chase a lead you are also leaving yourself exposed at the back - so although it may effect total goals the overall effect on the result might be small. So you are talking about a negligible to small affect on a small number of cases. However it is definitely worth bearing in mind for some matches.
The other aspect to be aware of, if a team earns a large unexpected lead at half time, the market might want to scrap the pre match ratings and upgrade the leading teams parameters. For example, the market expected them to be 2.0 for the second half. They go in at half time 3 up and deservedly so. The market might tend to think, "we got their rating wrong, these guys are better than we thought", while simultaneously thinking, "this game is over the manager will want to give some of the youngsters a run". So although the game state may favour goals for the losing team in the second half, the underlying rating upgrade for the winning team will act in the opposite direction.
For markets like Home Both Halves and Away Both Halves I have found the assumption of independence is an adequate approximation.
For the HT/FT markets treating them as independent tends to skew the derived probabilities. The main way to a Home/Home result is you win the 1st half and either draw or win the 2nd half. This is all I estimate. There are other cases where you win the 1st by 2 (or 3 ..) goals and lose the 2nd by less than 1 (or 2 ..). These are the cases where assumption of independence breaks down most. I have found that ignoring them completely gives closer to the market price for that market.
The calculator is just for fun. As you can see from the above there are many simplifications applied and assumptions made. The markets will usually be much more accurate. I do not recommend using these values to take on the betting market. It can be used as a stepping stone to understanding the probabilities/markets and so on. It can also be used as a rough estimate for where there is no market or only a very low liquid market. But the market is always King.
It is also an example of a trick that some advantage bettors use. They can take the betting market odds on big highly bet events. They can deconstruct these odds to find the implied parameters (eg power ratings, expected goals) and then use these implied parameters to build odds for smaller less accurate markets for example alt lines, or for early prices.
Some examples of this are the Bookie Basher game centre, the Unabated alt line calculator and Dan Shan's power rating as described on the Business of Betting Podcast.
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