Question about use of Poisson distribution

Discussion in 'Statistics and Analysis' started by NoSix, Dec 30, 2003.

  1. tachyon1

    tachyon1 Member

    Apr 23, 2004
    The usual method would be to use the goal expectancies for each team that you used to derive the home win/away win/draw odds to derive correct scores for each half.Around 45% of the goal expectancy is 'scored' in the first half and the rest in the second.Some teams deviate from this usual split,but more often than not the diffrence is transient,so if you choose to make alterations,they should be small.

    Basically you calculate correct score probabilities for each half and use these odds or probabilites to calculate the chances of each of the nine half time/full time double result combos.

    1-0 at halftime followed by 1-2 in the second 45 minute mini match for example generates a Home/Draw combo.

    Looking at your example a home win of 3.35 is around a true 27% chance after stripping out the overround.That equates to a goal supremacy for the home side of around minus 0.4 of a goal.

    For a typical EPL game therefore you're looking at 2.6 total goals.

    That gives the home side about a goal expectancy of 1.1 and the away side 1.5,split 0.495 goals and 0.675 goals respectively in the 1st half and the rest in the second.

    That ultimately equates to a home/home double result of about 15%.(6.66 cp 6.15)

    Away/away=28%
    H/A=2%
    H/draw=5%
    A/H=2%
    A/D=5%
    D/H=11%
    D/A=16%
    and D/D=16%

    For the halftime result you just do a standard poisson,but to 45% of each team's full match goal expectation.

    T
     
  2. arrplayr

    arrplayr New Member

    Sep 14, 2006
    Thank you very much for your prompt answer. I dont think this will work for me since I dont have a clue to calculate correct score probabilities.

    Is it possible to draw those odds without knowing goal expectancy. I do have fixed odds (H D A) and I want to generate HalfTime/Fulltime from fixed odds. Do you think this is possible without knowing goal expectancy? Same goes for Halftime result.


    Thank you.
    A.
     
  3. CaptainJack

    CaptainJack New Member

    Aug 2, 2006
    As I understand it you take the probabillitites in half time and multiply it with the probabillities in full time and then you get the half time / full time odds. But can it really be done this simple?

    I mean, the result in half time will highly affect the result in the second half. I would say (without base it on any statistics) that if the favourite is down 0-1 in half time the chances for them to win the second half is much bigger than if they are up 1-0 in half time! I would therefore say that the result in half time will affect the result in second half and you cannot treat it like two seperate halfs and just multiply the probabillities calculated before the match. Do you agree tachyon1?

    I get the feeling that most bookies are using tables for ht/ft and that they calculate it in a different way. My odds for 1/2 and 2/1 is not in line with that the bookies have when I use the formula mentioned above.

    BTW tachyon1, thanks for the answer in my previous question!
     
  4. tachyon1

    tachyon1 Member

    Apr 23, 2004
    Hi CJ,

    you can certainly tweak the poisson to better mimic reality,especially in it's ability to correctly predict the likelyhood of low scoring games.

    As regards what happens in the first half influencing second half events,then the pre game goal expectation estimates(if they are initially reasonably accurate) do a pretty good job.

    In short goal laden first halves don't on average lead to similarly goal laden second halves.Neither do goaless 1st halves mean goal droughts in the second period.

    The pre game prediction is better than following what happen in the 1st period and subsequently up or downgrading you goal expectations accordingly.

    The bookies odds can vary compared to what you'd expect them to post for loads of reasons.

    Due to the high true odds on offer for the less likely outcomes,I imagine they operate a fav/longshot bias on the outsides,whereby they shrink the larger prices and slightly expand the odds of the more likely outcomes.Primarily to guard against unlucky runs of unlikely outcomes and then to maintain a decent overround per runner to give the illusion of fair prices.

    T
     
  5. arrplayr

    arrplayr New Member

    Sep 14, 2006
    Hi Tachyon1, I do have H D A odds and I want to set HalfTime/Fulltime from fixed H D A. Is this possible without knowing goal expectancy? Same goes for HalfTime result. Thanks.
     
  6. tachyon1

    tachyon1 Member

    Apr 23, 2004
    You can certainly get a regression line to derive the likelyhood of say a fav winning at both HT and to still be winning at FT from the match odds for the fav to win outright.*

    But if you're just using a bookies odds I carn't really see the point,you may as well look at the double odds he's posted and strip out the overound or if you've derived your own match odds then surely it's just a small step to find the double result odds by one of the methods outlined?

    *Fav/Fav double result %=0.72956*(fav's win percentage)-6,does it for fav odds of between 37% and about 72% in the EPL.So a fav with a 54% of winning outright has about a 33% chance of winning at both full and half time.

    T
     
  7. tachyon1

    tachyon1 Member

    Apr 23, 2004
    Adding,

    37.8-(0.4757*fav's win%)=Percentage chance of the outsider winning at both half and full time.

    So if a fav's true chance of winning is expected to be 54%,then the true chances of the outsider leading at HT and FT is about 12%.

    Again works for fav's winning percentages between 37% and around 70%.

    T
     
  8. happyforever

    happyforever New Member

    Jun 16, 2004
    I have been paying quite some attention to this lately and have yet to find any significance in this. What I am referring to is team name depedent deviation. Obviously lower scoring teams create more draws and this should be reflected, but that is just one simple factor that has been included in my model.
     
  9. tachyon1

    tachyon1 Member

    Apr 23, 2004
    I agree(i think).

    If you take all the 'draw specialists' from one season and look at their combined results the next season,they always end up drawing games that are much closer to the normal league split.

    Same for so called home specialists.Teams that win at home much more readily one season don't carry this into the next season.

    You're just looking at random fluctuation that's always going to happen if you have large enough sample.Expecting these trends to continue isn't wise.

    It may be different in other sports like the NFL where there is scope for different playing surfaces/areana designs etc.

    The Denver Broncos are accepted as having an elevated HFA(appropriately as a result of the altitude),although the theory that teams tire at Mile High that was isn't really bourne out by the Broncos scoring split by quarters.(They concede proportionally less and score more in the 1st two quarters....in the second half they're actually just a 'run of the mill' NFL home side).

    If I found a soccer team maintained a team dependent deviation over a concerted period of time(for example Liverpool and their rate of gaining corners compared to how you'd expect a team of their quality to perform),then I'd still be inclined to go with the league wide stat to a large degree.

    Eight parts league to one part individual team as a rule of thumb.

    T.
     
  10. tachyon1

    tachyon1 Member

    Apr 23, 2004
    Re team dependent deviation.

    So called 'draw specialists' records in subsequent seasons.From the English divisions since '86.

    'Draw specialists' drew 931 games out of 2276(41%),in the next immediate season they drew 614 out of 2278(27%).

    However you slice and dice the figures its very,very rare you can extrapolate these trends into future games.

    T
     

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