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For Mr. Tthree and other mathematically-inclined members:
Let's assume that there is a hypothetical NFL team, New Orleans Voodoo. http://en.wikipedia.org/wiki/New_Orleans_VooDoo
For 20 NFL seasons, through various GMs, coaches and players, this team (using a secret voodoo ritual@ ) had managed a unique feat -- the team NEVER loses two games in a row. They could win 16 consecutive games, but they never lose 2 consecutive games.
For simplicity, let's further assume:
1. Each NFL season consists of 16 regular season games, and up to 4 playoff games.
2. After a win (regular and post-season), the next game has a 50% win probability. After a loss (regular season), the next game has a 100% win probability.
3. The team's streak continues from regular season to post-season, i.e., if they lose their last regular season game, the chances for the first post-season game win is 100%.
4. Pre-season results are ignored. The first regular season game has a 50% win probability.
5. This team's lowest record ever is 8-8 (Duh!) @ In such a case, there is no playoff appearance for them that year.
6. If this team ends with 10-6 or better, they win the Division, and plays only 3 post-season games (Div, Conf, SB).
7. If this team ends with 9-7: half-the-time, they go home, half-the-time, they play as Wild Card with 4 post-season games (WC, Div, Conf, SB).
If the pattern holds ... in any given year, what is the probability that Voodoo will:
1. Go 8-8 and miss the playoffs?
2. Go 9-7 and miss the playoffs?
3. Get in the playoffs as "Wild Card" (50% of 9-7)? And win on that round? Lose that round?
4. Get in the playoffs as "Div Leader" (10-6 or better record)? And win on that round? Lose that round?
5. Win their Conference?
6. Win the SuperBowl?
7. How do the probabilities #1 to #6 change depending on whether they win or lose their 1st regular season game?
Thanks,
MD
Addendum: Maybe a further simplification could be to lump the wins together ... thereby reducing the 65,536 win-loss matrix into 8 wins plus 256 win-loss matrix?
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