+ Reply to Thread
Results 1 to 6 of 6

Thread: How to calculate the odds that Team A will beat Team B given their records to date?

  1. #1

    How to calculate the odds that Team A will beat Team B given their records to date?




    I would like to find a formula to calculate the probability that Team A will beat Team B taking into account just their records to date.

    For example, suppose these 6 teams have these records against the rest of the league, which includes 30-40 other teams. Assume that each of these teams have played each of the other teams more or less the same number of times.
    Code: 
    Team  Wins  Games   %
       A    40     50  80.00%
       B    30     50  60.00%
       C    25     50  50.00%
       D    20     50  40.00%
       E    10     50  20.00%
       F     0     50   0.00%
    Is there a good formula for calculating the probability that each of these teams will beat each of the others?

    If P(x,y) is the probability that Team X will beat Team Y, where x & y are the winning percentages from the table above, then P should have the following properties:
    1. 0 <= P <= 1
    2. P(x,x) = 0.50 (Two teams with the same record should have 50% odds against each other.
    3. P(x,y) + P(y,x) = 1 (The complementary probabilities should sum to 1.)
    4. P(x,0.5) = x (Since Team X's record is against the entire league and the average of all the wins and losses for all of the teams in 50%, if Team X plays a team with a record of 50%, it should be like playing the entire league, which is what its record is. I am not sure about this one,m but it seems right to me.)
    I have tried a couple of formulas, but they all have flaws. I'd appreciate suggestions.


    Two that I tried are:
    1. P(x,y) = (x-y+1)/2
    2. P(x,y) = x/(x+y)

  2. #2
    Points: 1,470, Level: 21
    Level completed: 70%, Points required for next Level: 30

    Posts
    50
    Thanks
    0
    Thanked 5 Times in 4 Posts

    Re: How to calculate the odds that Team A will beat Team B given their records to dat

    The Log5 method seems to be what you're after:
    http://home.ptd.net/~artnpeg/Log5.pdf
    Only winning percentages are considered.

    p(x,y) = (x - x*y)/(x + y -2*x*y)

    Art

  3. The Following 2 Users Say Thank You to ArtK For This Useful Post:

    Jennifer Murphy (02-23-2016), Outlier (02-22-2016)

  4. #3
    Points: 3,571, Level: 37
    Level completed: 48%, Points required for next Level: 79
    Jennifer Murphy's Avatar
    Posts
    37
    Thanks
    3
    Thanked 0 Times in 0 Posts

    Re: How to calculate the odds that Team A will beat Team B given their records to dat

    Quote Originally Posted by ArtK View Post
    The Log5 method seems to be what you're after:
    http://home.ptd.net/~artnpeg/Log5.pdf
    Only winning percentages are considered.

    p(x,y) = (x - x*y)/(x + y -2*x*y)

    Art
    Thanks, Art. This does appear to be exactly what I was looking for. I even attempted this very derivation, but fell short. I see now where I went wrong.

    Thanks so much.

    How do you know about this?

    Do you know why they call it the "Log5" method?

    Only winning percentages are considered.
    Are you sure? I don't see where it says that?

  5. #4
    Points: 1,470, Level: 21
    Level completed: 70%, Points required for next Level: 30

    Posts
    50
    Thanks
    0
    Thanked 5 Times in 4 Posts

    Re: How to calculate the odds that Team A will beat Team B given their records to dat

    Jennifer, you're welcome. I learned of the log5 while doing internet searching for
    a solution. I don't know why the name log5 since it has nothing to do with
    logarithms. When I say "only winning percentages are considered" I mean that
    the analysis is simplistic since it doesn't allow for known significant factors
    such as home field advantage (several percent), etc. If you internet search
    along these lines you'll find formulas that do take such factors into
    consideration.

    Art

  6. #5
    TS Contributor
    Points: 7,284, Level: 56
    Level completed: 67%, Points required for next Level: 66

    Location
    MD, USA
    Posts
    465
    Thanks
    8
    Thanked 11 Times in 11 Posts

    Re: How to calculate the odds that Team A will beat Team B given their records to dat

    This one
    ". . .provide a terrific estimate. . ."
    kinda' jumped out at me.

    How does this author define "terrific"? (I thought stats was quantitative, not qualitative - objective, not persuasive).

  7. #6
    Omega Contributor
    Points: 38,374, Level: 100
    Level completed: 0%, Points required for next Level: 0
    hlsmith's Avatar
    Location
    Not Ames, IA
    Posts
    6,998
    Thanks
    398
    Thanked 1,186 Times in 1,147 Posts

    Re: How to calculate the odds that Team A will beat Team B given their records to dat


    I have not read the posts above, but I also recall seeing a program that does the same thing, but incorporate if you had teams head-to-head records as well.
    Stop cowardice, ban guns!

+ Reply to Thread

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats