Just an interesting problem

[Thanatos 2,847]

Okay, so I was just looking at the playoff possibilities for our league, and I noticed one of the teams has an 87% chance of making it, (87.5 actually but it rounds down for some reason). The league assumes that a team has a 50/50 shot to win games, so this team has a 1 in 8 chance of missing- they would have to have two specific teams win and lose themselves in order to miss the playoffs. However, I'm not seeing this as an actual possibility. See if you can figure out how this team, Mustangs, could miss the playoffs with two spots left to be taken.

 

Tiebreakers are as follows:

1. Best Head to Head Record, (in ties of 3+ teams, only applicable when one team has beaten all the other teams or lost to all the other teams).

2. Division Record, (only applicable if the teams are in the same division).

3. Most Avg Points/Game. (For simplicity's sake, just total points scored).

 

Teams fighting for the last two playoff spots:

 

South Division

Mustangs: 6-6 Overall. 2-5 Division Record. 1284 total points.

Big Daddy: 5-7 Overall. 4-4 Division Record. 1511 total points.

 

North Division

Need for Speed: 5-7 Overall. 3-4 Division Record. 1097 total points.

Fuel: 5-7 Overall. 3-5 Division Record. 1139 total points.

 

Head to Head Records:

Mustangs: 0-2 vs Big D. 1-0 vs N.F.S. 1-0 vs Fuel.

Big Daddy: 2-0 vs Mus. 0-1 vs N.F.S. 0-0 vs Fuel, (they play each other this week).

Need for Speed: 0-1 vs Mus. 1-0 vs Big D. 2-0 vs Fuel.

Fuel: 0-1 vs Mus. 0-2 vs N.F.S. 0-0 vs Big D.

 

Obviously, if Mustangs win, they are in.

 

There are four different scenarios if they lose which result in the following records:

 

Scenario A

Mustangs: 6-7 Overall, 2-6 Division Record.

Need for Speed: 6-7 Overall, 4-4 Division Record.

Big Daddy: 6-7 Overall, 4-4 Division Record.

Fuel: 5-8 Overall, 3-5 Division Record.

 

Scenario B

Mustangs: 6-7 Overall, 2-6 Division Record.

Need for Speed: 5-8 Overall, 3-5 Division Record.

Big Daddy: 6-7 Overall, 4-4 Division Record.

Fuel: 5-8 Overall, 3-5 Division Record.

 

Scenario C

Mustangs: 6-7 Overall, 2-6 Division Record.

Need for Speed: 6-7 Overall, 4-4 Division Record.

Big Daddy: 5-8 Overall, 4-4 Division Record.

Fuel: 6-7 Overall, 3-5 Division Record.

 

Scenario D

Mustangs: 6-7 Overall, 2-6 Division Record.

Need for Speed: 5-8 Overall, 3-5 Division Record.

Big Daddy: 5-8 Overall, 4-4 Division Record.

Fuel: 6-7 Overall, 3-5 Division Record.

 

In both scenarios B and D Mustangs are in, (two playoff spots left and two teams at 6-7).

 

That leaves us with A and C.

 

Scenario A gives us a 3-way tie between Mustangs, NFS and Big D. No team has beaten both of the others, (Mus beat NFS, but lost to BD; BD beat Mus, but lost to NFS; NFS beat BD, but lost to Mus). Division record is not applicable since NFS is not in the same division, so it goes to total points. Unless someone scores 400 points, Big D wins the 5th seed by virtue of that tiebreaker.

 

Now we have a two-way tie between Mustangs and NFS which is broken by the Head to Head tiebreaker in favor of Mustangs.

 

Scenario C gives us a 3-way tie between Mustangs, NFS, and Fuel. This is immediately broken by head-to-head as Mustangs has beaten both of these teams and so they take the #5 seed.

 

So is the projection wrong, and there is no way for Mustangs to miss the playoffs, or am I screwing something up here?

Edited December 2, 2011 by Thanatos19

[Vin+ 3,121]

I just want to say that I am a big fan of option D.

Edited December 2, 2011 by Vin

[oochymp 2,393]

if I'm reading the tiebreakers right, then if there's a three way tie involving teams in both divisions that can't be broken by head to head record then the only applicable tiebreaker is avg points per game, in which case NFS could end up ahead of the Mustangs, not likely at all, but it's mathematically possible, the system must just take the top two in that category rather than advancing the top one and reverting back to the head to head record

[Thanatos 2,847]

if I'm reading the tiebreakers right, then if there's a three way tie involving teams in both divisions that can't be broken by head to head record then the only applicable tiebreaker is avg points per game, in which case NFS could end up ahead of the Mustangs, not likely at all, but it's mathematically possible, the system must just take the top two in that category rather than advancing the top one and reverting back to the head to head record

 

If that is the exception, then it's weird that it would count it as a loss if Scenario A played out. It would seem to far more likely be a win for Mustangs than a loss.

 

That's the only thing I can come up with though.