Solutionfinder
New member
- Joined
- Apr 28, 2017
- Messages
- 2
Hi All,
To start with this post I will say that I am very much at a loss as to correct terminology and jargon, I did try to work through this on an excel forum but thought I could start here and have a better chance to isolate what I need to do on paper.
Bottom line is I am trying to calculate probabilities of teams winning a regular sports season. As it would be working off no historical figures (every team starts the season at an equal chance of winning and no handicap or known advantage to speak of). Known variables are:
# of Teams = 10
# of Rounds = 10
Maximum amount of points that can be accrued in any one season = 120
As an addition; Teams would play each other once, and games are determined similar to baseball rules (i.e. turn-based, and cumulative total at the end of each game determines the winner UNLESS in the final round where the team with the last turn has more points before the start of their last turn (the winner would be declared a turn early), this does not include tiebreakers with separate rules but there would still be a measured points distribution.
So far I have been able to establish the game parameters to calculate points, round distribution etc. and I have used a Cartesian Product table in Excel to calculate the total number of scenarios (i.e. Team A after 10 rounds has 120 points. Team B after 10 rounds has 2 points et al) which doesn't really bring me any closer to solving the HOW to calculate likelihood of a scenario occurring but also how to use the results after each round to update the probability.
To use the example I quoted in the other forum; in a 10-round season with 10 teams, Team A (who have won all games) would be at a 90%/100% chance of winning the season(?) whereas in contrast, Team D who have LOST all games would be at a 0% chance of winning the season (as the rules for points allocation in one game) would negate their chance BUT they may have a chance to place second-last.
So my questions are:
1) How do I calculate each team's probability of winning the season (based on the variables above)?
2) How do I include rounds played vs. rounds remaining to be included in the probability?
3) How do I express each team's probability in a mathematically-sound manner that reflects each other?
Thank you so much for having a read and would love to hear your feedback.
To start with this post I will say that I am very much at a loss as to correct terminology and jargon, I did try to work through this on an excel forum but thought I could start here and have a better chance to isolate what I need to do on paper.
Bottom line is I am trying to calculate probabilities of teams winning a regular sports season. As it would be working off no historical figures (every team starts the season at an equal chance of winning and no handicap or known advantage to speak of). Known variables are:
# of Teams = 10
# of Rounds = 10
Maximum amount of points that can be accrued in any one season = 120
As an addition; Teams would play each other once, and games are determined similar to baseball rules (i.e. turn-based, and cumulative total at the end of each game determines the winner UNLESS in the final round where the team with the last turn has more points before the start of their last turn (the winner would be declared a turn early), this does not include tiebreakers with separate rules but there would still be a measured points distribution.
So far I have been able to establish the game parameters to calculate points, round distribution etc. and I have used a Cartesian Product table in Excel to calculate the total number of scenarios (i.e. Team A after 10 rounds has 120 points. Team B after 10 rounds has 2 points et al) which doesn't really bring me any closer to solving the HOW to calculate likelihood of a scenario occurring but also how to use the results after each round to update the probability.
To use the example I quoted in the other forum; in a 10-round season with 10 teams, Team A (who have won all games) would be at a 90%/100% chance of winning the season(?) whereas in contrast, Team D who have LOST all games would be at a 0% chance of winning the season (as the rules for points allocation in one game) would negate their chance BUT they may have a chance to place second-last.
So my questions are:
1) How do I calculate each team's probability of winning the season (based on the variables above)?
2) How do I include rounds played vs. rounds remaining to be included in the probability?
3) How do I express each team's probability in a mathematically-sound manner that reflects each other?
Thank you so much for having a read and would love to hear your feedback.