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jptrader
06 Feb 13 09:36
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Date Joined: 26 Mar 08
| Topic/replies: 30 | Blogger: jptrader's blog
Assume that the expected number of goals scored by a team in a match is distributed in the following way:
0 goals: 10%
1 goal :  40%
2 goals: 30%
3 goals: 20%

Assume also that the probability of a goal is the same in any minute of the match. If there is still no goals scored at half time, what would be the distribution of expected goals at that time?
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Report Andriy February 6, 2013 11:25 AM GMT
Typically, across the top European leagues over last few seasons, an average of about 43.5% of goals have been scored in the first half, varying maybe a % or two from country to country. So whatever goal rate you've used for the initial calc, multiplying it by 56.5% should give a decent measure of second half goal expectancy.

However your assumption of goal prob being the same in any minute gives the impression that you're considering half goals will occur in first half and half in second assuming same added time) - which would be wrong  (but then again your goal distribution seems to be built on sand as well). I suspect i probably haven't answered your question, and that you haven't heard of Poisson.
Report JLivermore February 6, 2013 11:45 AM GMT
Not trying to be annoying but the question is contradictory, so can't be answered.

If we assume that the probability of a goal is the same in any minute of the match then each of these probabilities implies a different goal rate.

Goals Prob Implied Goal Rate/Min
0    0.1     0.0256
1    0.4     0.0102
2    0.3     0.0133
3    0.2     0.0179


so we're a bit farked
Report JLivermore February 6, 2013 12:26 PM GMT
Ok, if we ignore
"Assume also that the probability of a goal is the same in any minute of the match"

then we could assume that Distribution of goals in H1 is same as H2, but then we get problems because you've assumed 0% chance of > 3 goals....

So we have to change your distribution.  The closest I can calculate is:
Goals per team in match
0    13%
1    34%
2    32%
3    15%
4    5%
5    1%
6    0%

which makes:
Goals per team in either half
0    36%
1    48%
2    12%
3    4%
Report jptrader February 6, 2013 5:30 PM GMT
Thanks for your replies. Realized after posting that the question was flawed. I guess my assumption of same prob of goal each minute would lead to Poisson being the right tool, and that was just what I was trying to avoid, due to the mismatch of Poisson for 0-0, 0-1 and 1-0 scores.
Report cpfc4me February 9, 2013 4:07 PM GMT
You need to modify your Poisson for zero-inflation.

http://www.bettingexpert.com/blog/how-to-calculate-probabilities-for-footbal...
Report Coachbuster February 12, 2013 12:00 PM GMT
off the top of my head and a quick calculation i make it

0 goals  40%
1 goal 40%
2 goals 15%
3 goals 5%

this isn't allowing for any more goals btw ,and don't forget more goals are scored second half in reality
Report Coachbuster February 12, 2013 12:02 PM GMT
during a game you don't really get much time to work on poisson distributions and games vary anyway  - they're Football matches) not very good mathematical models
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