Probability and Undefeated Seasons

BUCKfutter's picture
February 25, 2013 at 6:38 pm

Before I get into this - caution: nerd alert.  That said, there have been a few thread topics floating around the last few months about another undefeated season next year.  A common argument that such a season is likely seems to be "show me a game we are going to lose" or something of the like.  I agree, when taken individually, we should win every game we play next year (and, I would argue that for the last decade, save 2004 and 2011, going into each game, the majority of us would have argued that we should have won just about every game we played).  That, however, does not mean that chances are we will go undefeated.
For a 12 game schedule, even if your chance of winning each individual game is 95%, your chances of going undefeated are .95^12 = 54%.  A 95% chance of winning each game is absolutely not realistic- much too high - but the 54% overall chance GIVEN the 95% chance of winning is tellingly small.  If you take it down to a 90% chance of winning each individual game (still really high in my opinion), your chances of going undefeated drop significantly to .9^12 = 28%.  Add a B1G title game and a national championship game and you're really starting to get lower.
With that as a prologue, I am going to go through each game in our 2013 schedule, assign a percentage chance of victory (going to be very generous to OSU, as you will see), and see where we come out at the end (hint: the chances aren't great).
Game                            Chance of win
Spring Game (yee haw)   100%
Buffalo (H)                     99.9%
SDSU (H)                       95%
Cal (A)                           90%
FAMU (H)                      99.9%
Wisky (H)                       90%
NW (A)                          85%
Iowa (H)                        95%
State Penn (H)               95%
Purdue (A)                     95%
Illinois (A)                       95%
Indiana (H)                     97%
scUM (A)                        85%
Chance of undefeated reg season = 43.8%.  Again, I feel like I've been pretty generous to OSU in assigning these percentages (see: 95% chance of winning in West Lafayette AKA the Buckeye house of horrors).  We haven't even delved into the postseason yet:
Game                         Chance of win
B1G Title                        85% - rationale: again, being very, very generous.  Assuming scUM will be the best team in the legends next year - the advantage they                     gain by having seen us the week before offsets the game being at a neutral site.
NCG                              50% - assuming we play Alabama or equivalent.  Given the status of both current rosters, 50% here is more than generous to us.
43.8% * 85%* 50% = 18.6% chance of a 14-0 season, once again, using EXTREMELY generous win probabilities.
Not saying I don't want it to happen, or don't think it can happen; only by no means is it a sure thing, or for that matter, even a probable thing.  Go Bucks.

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