hi guys,

I have a simple math question, would be nice if you could help me to solve it real quick or verify my result.

two soccer teams, team A and team B play a match.

Team A scored 5 goals in 7 of its previous matches.
Team B scored 4 goals in 7 of its previous matches.

Assuming that both teams will continue to score goals at this rate, whats the probability that we will see a goal in the first half of their match?

I think I know the right answere but im not a 100% certain. Its probably really easy to most of you, so if you could tell me the result and how you have calculated it, I'd be really happy!

Impossible to calculate any probability with the information given since we have no data or assumptions about when scores happen within a match. At best we could say between 0 and X, with X being the chance of any score in the match.

Yes goals could have been scored at any time, doesnt matter when they were scored!

i looked at it like that:

team A scores 5/14 halfs, thats a rate of 0.357 goals/ half.
team B scores 4/14 halfs, thats a rate of 0.285 goals/ half.

0.357 + 0.285 goals makes 0.642 goals per half, so I assume a combined chance of 64.2% that a goal will be scored in the first half of their match.


just tell me if im wrong, its late here, I have a headache and I suck at math, lol

You converted rate to probability, which is not correct. If instead of 9 goals total it was 15, that would give you a probability greater than 1.0.

Here's one approach. If we assume a Poisson distribution with mean 0.624 goals per half, the probability that at least one goal will be scored is 1- exp(-0.624) = 1-0.536 = 0.464.

Look up the Poisson to see if it fits-- the most important characteristic is a constant rate of occurrence of independent events.

Just to add a few words on what statmanhal said, what you calculated (9/14) is the number of goals you see on average in a half. See that it's a different concept from "the probability to see at least one goal". The expected number of goals can well be bigger than one, while the probability cannot.

statmanhal's formula is correct, but he made a typo and plugged the wrong number. However, the final result is very similar (47.4212%).

thanks for the response! Now im confused, could you please explain me what the difference is between a "rate" and a "probabily"? Can the probability for this never be greater than 1.0 because we can never expect a probability higher than 99.9% that a goal will be scored in the first half, even if in the previous 5 matches, team A scored 5 million goals?


To be honest, I dont think that goals distribute the same as poisson, but maybe I missunderstand what statmanhal is saying. Team A or B probably scored their goals against teams with a weaker defense rather than against teams with a stronger defense so most likely they werent evenly distributed but I dont want to take that into account. So I'd rather assume an average distribution.


The reason Im asking this is because I was looking at the odds of a sportsbetting event. Team A is playing Team B and the bookie is laying odds of 2.8 for a bet that no goals will be scored in the first half of the game. So if I put my money on that bet that there will be no goal in the first in 35.7% or higher, I will make profit. So im trying to calculate how likely it is based on both teams record over their previous 7 matches. Maybe thats a nonsense approach anyway. How would you guys approach this problem?

guys, please help me understand this, I feel stupid right now

probability has no unit of measure, it's just a number between 0 and 1. rate of goals scored per half has a measure [goal/half].

you could try solving it without Poisson like this: suppose that unit of measure is goals per minute. team A scores 5 goals in 7*90 minutes, so that's 5goals/630min = 1/126 goals/min. so, team A scores 1 random minute out of 126 minutes.
team B scores 4 in 630, or 1 random minute out of 157.5 minutes.

it's easier to calculate opposite event: both teams not scoring in a half. that would be (125/126)^45 * (156.5/157.5)^45 = 0.5246

so, a goal to happen in the first half would be 1-0.5246 = 0.4754 or 47.54%. that's assuming every team is equally likely to score each minute. funny how it's almost the same as poisson formula.

so, fair odds for no goals in first half would be 1/0.5246 = 1.91 and this would be a valuebet at odds 2.8. but a real match is more complicated. maybe both teams have a history for playing boring in first half? maybe it's more likely a goal will fall closer to half time? strikers are injured? ...

Interestingly, it looks like it is 'relatively' flat distribution of goals per 5m interval in soccer (8 years of English Premiership data used), but definitely less in the first half.

Ignore 45-50, as this includes more than 5 minutes.

interesting diagram, thanks. also reflects the bookies odds for more goals in the 2nd half!

@md46135: thanks a lot, that definitly helped! think I got it now! I dont really know why the bookies were laying such good odds for a goalless first half. One of the teams actually has pretty good offense, so maybe the bookies thought that the last 7 games were a poor reflection of their striking qualities. Maybe they just ran a lot bellow EV in their first seven games, I dont know That seems to be the hardest thing to me in sportsbetting, to look beyond their results and see how good or bad they really are, just filtering out all the luck and bad luck but I dont really know how to do that.


anyway, thanks everyone!

Hello! sorry to bring this up again. I have a slightly different problem now and Im not sure how to adjust the formula in this case and I dont want to risk to make any mistakes. Assuming team C scores 1.5 goals per game and team D scores 1 goal per game on average. Whats the probability that we will see 3 goals or more in a match of these two?

In general, whats the easiest way to convert a rate to probability?

The Poisson distribution is exactly what you are looking for. Have you searched for information on it? It gives a very simple formula to answer questions such as this. The assumptions underlying the Poisson distribution seem to hold for professional soccer games.

Treat the total number of goals scored in a game as the variable of interest. In your example, the average number of goals scored by the two teams combined is 2.5.

Using 2.5 as the key number, the Poisson distribution will give you estimates of the two teams scoring any number of goals you want such as 0, 1, 2, 3, 4, 5, 6, etc.

If you need help understanding or applying the Poisson formula, let us know.

thanks. I wanted to use statmanhals poisson formula but I didnt know what exactly to fill in. Is this correct?


3 - exp( - 2.5) = 2.91


I mean shouldnt the result be something like "0.xx" for a x% chance of 3 goals happening? 2.91 cant be a probability, right? What did I do wrong?

Have you looked up the formula for the Poisson distribution probabilities?

I can post it but I'd rather you find it for yourself.

Just Google "Poisson distribution probability".

It is a very simple formula.

I googgled it and found this on wikipedia, I guess thats what you ment?



So I guess the probability of 3 goals or more is 0.213 + 0.133 ect.. ?

Nice. That's correct. To calculate P(goals>=3), instead of summing P(3)+P(4)+P(5)+ ... + P(n), you can calculate 1 - P(0) - P(1) - P(2), which is easier. Basically you evaluate the chance of having less than 3 goals; the other part is what you are looking for.

Yes, processes that follow the assumptions underlying the Poisson distribution have a standard formula for their probabilities.

If there is a Poisson process that averages A occurrences over a given time interval, then the probability of achieving K occurrences in that given time interval is:

P(K) = (A^K) * exp(-A) / K! for K=0,1,2,3,4,5,...

where K! is "K factorial".

So calculating P(K) is pretty simple. And if you are seeking P(K>Z), nickthegeek gives the best way to find that.

nick and whosnext: big thanks! Now I've got something to work with!

Q really is how much r u gonna bet?

100 play money dollars decided not to get invested until I have a little more understanding of the market.


edit: nvm, found my mistake