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Ryan, Engineer

Category: Complex Math

Satisfied Customers: 9137

Experience: B.S. in Civil Engineering

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I was look at league results as I wish to write a game. I

Customer Question

I was look at league results as I wish to write a game. I would like very much to know how to ask my computer to unravel the end of season results and return a list of how the league games of the season could have been played. I wish to include the Home and aways separately. I wish to divide the goals of the home and away matches fairly to express win and loses. The draw needs to work out evenly so as when all has been done I have no remaining matches and the matches add up to the correct end of season points. wind give 3 its, and loses no its, and draws give both teams 1 pt. If you can help then great. Otherwise could you offer me a good read that ay help?

If I understand your question correctly, you are looking for a way of taking the final league results, which I assume to mean the total record of wins, losses, and ties for each team in the league, and work backwards from that to how each game played could have turned out?

If that is correct, then what you are attempting to do is sort of the mathematical equivalent of unscrambling an egg. It would be difficult, if not impossible, to work backwards from the results to anything that resembled a "true" solution. For example, if I were to tell you that the mean of five numbers is 1520, it would extremely unlikely for you to be able to tell me which specific five values I used to get that mean. There are just too many possible sets of five values that would have a mean of 1520. Certainly, you could easily come up with an answer, but the chance that you would stumble upon the "right" one is extremely small.

Your problem would actually be more difficult than that example though. With the example I gave of the mean of five numbers, you could just arbitrarily select any four numbers, and then calculate the necessary value of the fifth number to get the correct mean. In the case of your league teams, though, it wouldn't be very realistic to assign wins and losses such that one team had all wins and no losses. Thus, there is some added complication in even coming up with a realistic possible solution.

Also, the more teams that are involved in the league, and the more games that are played, the more complicated it will be to find a solution. Particularly a general computer program solution that could be used again in the future.

If you are modeling your game on an actual league, might I suggest searching online for complete season records? That would eliminate the need for deconstructing the consolidated results, and would likely give a more realistic solution than a computer program could come up with. If there is some issue with copy-right protections (I'm not completely up on the laws in the UK, but I appreciate that they may be different than here in the US), could you perhaps start with "real" results, and then alter them slightly to make them different from the "real" results?

If I have misunderstood your original question, please feel free to clarify. I'll be happy to continue to discuss this problem.