We can’t use **P(A&B) = P(A) x P(B)** for all multiples. P(A) x P(B) is used in liquid, independent markets to work out the value, such as 1×2 match odds.

AGS doubles are not independent where both players are playing in the same game. The AGS market on the exchange is for each singular event and doesn’t take in to account how one event may affect another.

The odds of the 2nd goalscorer in a game are diminished as there are fewer goals to go round when we need to squeeze two AGSs in to the same game.

To estimate the real odds of P(A&B) for an AGS double we therefore use Total Goals as a variable to adjust for this.

EG:

Salah AGS = 2.4

Firminio AGS = 2.8

Total goals were 3.4**

After the first goal goes in there are 2.4 expected goals left in the game. The avg expected goals between 1st and 2nd goal is 2.9 goals. We can use this ratio to work out the variable to increase the AGS lay odds of each player to work out value.

(2.9/3.4)x100 = 85%

Salah becomes (2.4/.85) = 2.82

Firminio becomes (2.8/.85) = 3.29

Giving the AGS double implied odds of 2.82 x 3.29 = 9.3

A big increase on the odds of 6.72 we would have got if they were playing in different games.

** Total goals worked out as a linear, pro-rata calculation of where evens would lie on the Total Goals market on the exchange.

## Quick Calculation

2.5 to 3 goals is the average amount of goals in the top European Leagues. Where the total expected goals is lower the impact would be even greater.

We can use an average markup so that we don’t always have to perform the full calculation. The adjustment is going to be in the 80-85% (or 15-20% mark up) range in most circumstances so multiply each player’s lay odds by between 1.17 to 1.25 to achieve a reasonable estimate. How about 1.2!

This would be on top of any bookies profit margin if we were using best odds instead of the exchange lay price.

## Other Considerations

The above process is likely to give a worst case scenario for the calculation of two goalscorers in the same game. There will be other factors at work here such as:

What is the style of play of the team(s) concerned – do they try and shut up shop when they go one up or are they the sort of team that continues to attack whatever the score?

What we really need is vast amounts of data to be able to model this properly but at least this gives food for thought – when considering these specific doubles the value may not be what it first seems.

### Alternative view point from BB member Firefox

##### Double Goalscorer Bets (2 players both scoring in the same match)

Ok, first of all the numbers. I’ve placed 94 double goalscorer bets since the start of the 2018 / 19 season. The majority of these have been at £20 / £25 stakes and I’ve made a profit of £580. I’ve taken any bet where the back price is greater than the ags price of player 1 x the ags price of player 2.

Now of course, this doesn’t prove anything. It implies I’m likely to be taking +EV bets but you could claim (quite correctly) that ’94 bets is too small a sample size’ or ‘you might have just been very fortunate with variance’.

So let’s look at the maths. I am going to say a few things here which contradict the advice given in the Bookiebashing article and one thing I will say is that I really don’t want this to come across as negative. I think the guys who run the site do a fantastic job overall and the work done is ever so much appreciated. I think the bet calculations done by the guys who run the site are generally very accurate and this is one of very few occasions that I strongly disagree with what they’ve said.

Now one of the ideas of the Bookiebasher model is that in a football match, ‘there are a finite number of goals available’ (quoted from Discord).

The problem is that this isn’t true. There isn’t a finite number of goals available in a football game. There would be if the 2 teams said (for example) ‘let’s play football until 3 goals have been scored and then stop’.

A 2nd idea in the Bookiebasher model is that once a goal is scored, a goal has been ‘used up’ and so there is one less goal available for anybody else to score – to quote from the article: ‘After the first goal goes in, there are 2.4 expected goals left’ (referring to the example in the article with 3.4 expected goals).

So by that logic, there are 1.4 expected goals left after 2 goals. 0.4 expected goals left after 3 goals. And -0.6 expected goals left after 4 goals. But this is impossible. There cannot be a negative number of expected goals.

So of course, it has to be that the number of expected goals varies throughout the game. It cannot constantly remain at 3.4 because otherwise we can end up with negative expected goals. The idea of ‘using up’ a goal would be correct in the imaginary scenario above of 2 teams saying ‘let’s play football until x number of goals have been scored’.

It’s also correct in other betting situations – e.g. the probability of a specific 2 teams being relegated or the probability of a specific 2 athletes winning a medal in the same race. But that’s because the number of winners is fixed. Only 3 teams can be relegated and only 3 athletes can win a medal. The number of goals in a match is not fixed and so one player scoring a goal does not reduce the available goals for everybody else.

This weekend, I tracked on Betfred’s website the in-play anytime goalscorer odds available on likely goalscorers (Salah, Mane & Firmino) in a Premier League football match (Chelsea v Liverpool). This is obviously only a 1 game sample but it was enough to get a feel for how a bookmaker varies their anytime goalscorer odds throughout the course of a game. I was specifically looking to see whether goals scored by other players resulted in an increase in the ags prices of the players I was following, as the Bookiebashing model would suggest.

I discovered 2 main things:

• the ags prices of all 3 players increased gradually throughout the match. This suggests that (as I would expect) their prices are increasing due to the elapsing of time, meaning they have less time left in which to score

• there was no increase at all in ags prices immediately after a goal by another player. The Betfred ags prices were exactly the same immediately before the market suspended as they were when the market re-opened after the goal (obviously now minus the goalscorer). In other words, Betfred did not take the Bookiebashing view. They did not say ‘oh Firmino’s scored. He’s used up one of the goals. There’s now one less for everyone else to score’. They considered the scoring of a goal by one player insignificant enough to merit a change of odds for other players.

**So what calculation should we use?**

Personally I’m more than happy to multiply individual lay odds. It’s been a profitable strategy for me over 94 bets and the Betfred in-play odds support my opinion that a goal by one player doesn’t significantly reduce the chances of another.

I agree that 2 players scoring in the same match are not 100% independent events due to the nature of a game sometimes changing as a result of a goal. For example, a team who were previously packing their defense can abandon the tactic after falling behind (although this can actually make the bet more favourable due to the game becoming more open).

I also agree that a player’s ags odds following the 1st goal may well be higher than they were pre-match (particularly if the 1st goal takes a long time to arrive). However, this is due to the elapsing of time rather than the scoring of a goal by another player. The bet is placed pre-match and so we should be using the ags pre-match odds rather than ags odds that we anticipate a player will be mid-match.