Please help me solve this dispute

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SportsNmath

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Nov 20, 2012
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In my fantasy football league there was a trade offer to a guy that we feel would be clearly out of the playoff race because their are only 4 games left. However, he won this week, but because we run a point system he is still currently in 8th place (Team 8)....Please help me solve this problem and help me prove that statistically he still can't make the playoffs (and or couldn't make the playoffs just by his standings in Week 10). Please help me mathematically and statistically figure this out in a equation and tell me his odds of making the playoffs ... before week 10 and after week 10.


Week 10:
team 1 record 7-2 points 1457.56
team 2 record 6-4 points 1636.77
team 3 record 6-4 points 1438.22
team 4 record 6-4 points 1410.89
team 5 record 6-4 points 1415.93
team 6 record 6-4 points 1383.47
team 7 record 4-5 points 1413.28
team 8 record 4-5 points 1310.56 (He played Team 3 this week)
*Team 9 & 10 are out

Week 11 (He beat Team 3 to move to 5-6) He now has to play Team 6(week 12 as shown below), Team 4 (week 13), & Team 1 (week 14) to make the playoffs

New Standings as of yesterday
team 1 record 8-3 points 1611.64 plays team 9 week 12
team 2 record 7-4 points 1791.77 plays team 5 week 12
team 3 record 6-5 points 1597.27 plays team 4 week 12
team 4 record 6-5 points 1521.33
team 5 record 6-5 points 1498.54
team 6 record 6-5 points 1483.61
team 7 record 5-6 points 1558.54 plays team 10 week 12
team 8 record 5-6 points 1482.27 plays team 6 week 12
*Team 9 & 10 are out

Thank you so much for your help!
 
SportsNmath said:
In my fantasy football league there was a trade offer to a guy that we feel would be clearly out of the playoff race because their are only 4 games left. However, he won this week, but because we run a point system he is still currently in 8th place (Team 8)....Please help me solve this problem and help me prove that statistically he still can't make the playoffs (and or couldn't make the playoffs just by his standings in Week 10). Please help me mathematically and statistically figure this out in a equation and tell me his odds of making the playoffs ... before week 10 and after week 10.


Week 10:
team 1 record 7-2 points 1457.56
team 2 record 6-4 points 1636.77
team 3 record 6-4 points 1438.22
team 4 record 6-4 points 1410.89
team 5 record 6-4 points 1415.93
team 6 record 6-4 points 1383.47
team 7 record 4-5 points 1413.28
team 8 record 4-5 points 1310.56 (He played Team 3 this week)
*Team 9 & 10 are out

Week 11 (He beat Team 3 to move to 5-6) He now has to play Team 6(week 12 as shown below), Team 4 (week 13), & Team 1 (week 14) to make the playoffs

New Standings as of yesterday
team 1 record 8-3 points 1611.64 plays team 9 week 12
team 2 record 7-4 points 1791.77 plays team 5 week 12
team 3 record 6-5 points 1597.27 plays team 4 week 12
team 4 record 6-5 points 1521.33
team 5 record 6-5 points 1498.54
team 6 record 6-5 points 1483.61
team 7 record 5-6 points 1558.54 plays team 10 week 12
team 8 record 5-6 points 1482.27 plays team 6 week 12
*Team 9 & 10 are out

Thank you so much for your help!
Click to expand...

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217


We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.
 
SportsNmath said:
In my fantasy football league there was a trade offer to a guy that we feel would be clearly out of the playoff race because their are only 4 games left. However, he won this week, but because we run a point system he is still currently in 8th place (Team 8)....Please help me solve this problem and help me prove that statistically he still can't make the playoffs (and or couldn't make the playoffs just by his standings in Week 10). Please help me mathematically and statistically figure this out in a equation and tell me his odds of making the playoffs ... before week 10 and after week 10.


Week 10:
team 1 record 7-2 points 1457.56
team 2 record 6-4 points 1636.77
team 3 record 6-4 points 1438.22
team 4 record 6-4 points 1410.89
team 5 record 6-4 points 1415.93
team 6 record 6-4 points 1383.47
team 7 record 4-5 points 1413.28
team 8 record 4-5 points 1310.56 (He played Team 3 this week)
*Team 9 & 10 are out

Week 11 (He beat Team 3 to move to 5-6) He now has to play Team 6(week 12 as shown below), Team 4 (week 13), & Team 1 (week 14) to make the playoffs How in the world can he go from 4-5 to 5-6 after one game. The problem does not seem well defined. After week 10, three teams seem to have played only 9 games (although it is possible that tied games are ignored in your calculations). After week 11, all the teams seem to have played 11 games. Something seems goofy.

New Standings as of yesterday
team 1 record 8-3 points 1611.64 plays team 9 week 12
team 2 record 7-4 points 1791.77 plays team 5 week 12
team 3 record 6-5 points 1597.27 plays team 4 week 12
team 4 record 6-5 points 1521.33
team 5 record 6-5 points 1498.54
team 6 record 6-5 points 1483.61
team 7 record 5-6 points 1558.54 plays team 10 week 12
team 8 record 5-6 points 1482.27 plays team 6 week 12
*Team 9 & 10 are out

Thank you so much for your help!
Click to expand...
You are asking a question about subjective probabilities, which means that there is no unique answer because the probabilities assigned can be disputed. To put it a different way, you are making an estimate, and estimates are not exact.

A very simple way to make the estimate is this:

\(\displaystyle Probability\ that\ team\ 8\ will\ win\ three\ games\ in\ a\ row\ = \left(\dfrac{5}{11}\right)^3 \approx 9.4\%.\)

The logic here is that the win-loss history of team 8 shows that it has a probability of winning a single game of 5/11.

A somewhat less simple way to make an estimate is this

\(\displaystyle Probability\ that\ team\ 6\ will\ lose\ game\ against\ team\ 8\ is \dfrac{5}{11},\) based on the win-loss history of team 6.

\(\displaystyle Probability\ that\ team\ 4\ will\ lose\ game\ against\ team\ 8\ is \dfrac{5}{11},\) based on the win-loss history of team 4.

\(\displaystyle Probability\ that\ team\ 1\ will\ lose\ game\ against\ team\ 8\ is \dfrac{3}{11},\) based on the win-loss history of team 1.


\(\displaystyle So\ probability\ that\ team\ 8\ will\ win\ three\ games\ against\ those\ teams = \left(\dfrac{5}{11}\right)^2 * \dfrac{3}{11} \approx 5.6\%.\)

Those seem to me like reasonable upper and lower bounds. If you average them, you get:

\(\displaystyle \dfrac{0.096 + 0.054}{2} = \dfrac{0.15}{2} = 7.5\%,\) which is a nice round number that can be easily explained.
 
Very Helpful

Thanks for taking the time to explain this all to me, I appreciate it. Had no clue how to go about it.
 
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