## So you're telling me there's a chance?

Penn State Basketball has a chance to get an at-large berth in the NCAA Tournament.  A probable chance? A realistic chance?  That's what I'm trying to find out.

Assumptions:

--16 or less wins gives PSU a 0% chance to make the tournament
--17 wins gives PSU a 10% chance to make the tournament
--18 wins gives PSU a 50% chance to make the tournament
--19 wins gives PSU a 90% chance to make the tournament
--20 or more wins gives PSU a 100% chance to make the tournament
--PSU's chances to win any given game on a neutral court are proportional to the team's Colley Matrix rating and are calculated as (PSU's rating) / ((PSU's rating) + (opponent's rating))
--Home court advantage is worth a 5% boost in a team's chances to win
--The Big Ten standings will remain the same for the sake of seeding in the Big Ten Tournament.  This means Penn State will be the 7 seed and play Indiana followed by Purdue.
--If Penn State goes into the Big Ten Tournament needing more than 2 wins to get to 17 wins, PSU isn't getting in.  This means at a bare minimum, PSU must finish 5-6 down the stretch.

What follows is a spreadsheet calculating the odds of winning any individual game and the likelihood of any given record in the last 11 regular season games:

So what are the odds that PSU gets to exactly 17 wins, where PSU has a 10% chance of getting in?  This amounts to the odds that PSU will either win exactly 7 games down the stretch and none in the BTT OR win 6 games down the stretch and exactly none in the BTT OR win exactly 5 down the stretch and two in the BTT.

Exactly 5 down the stretch AND Indiana AND Purdue: 5.5%
Exactly 6 down the stretch AND Indiana AND NOT Purdue: 6.5%
Exactly 7 down the stretch AND NOT Indiana: 6.4%
Total Chance: (5.5%+6.5+6.4) * 10% = 1.84% chance that PSU will make the tournament and that they will do it with exactly 17 wins

18 wins, 50% Chance
Exactly 6 down the stretch AND Indiana AND Purdue: 5.0%
Exactly 7 down the stretch AND Indiana AND NOT Purdue: 4.3%
Exactly 8 down the stretch AND NOT Indiana: 2.9%
Total Chance: (5 + 4.3 + 2.9) * 50% = 6.1% chance that PSU will make the tournament and that they will do it with exactly 18 wins

19 wins, 90% Chance
Exactly 7 down the stretch AND Indiana AND Purdue: 3.2%
Exactly 8 down the stretch AND Indiana AND NOT Purdue: 1.9%
Exactly 9 down the stretch AND NOT Indiana: .9%
Total Chance: (3.2 + 1.9 + .9) * 90% = 5.4% chance that PSU will make the tournament and that they will do it with exactly 19 wins

20 or more wins, 100% Chance
Exactly 8 down the stretch AND Indiana AND Purdue: 1.5%
Exactly 9 down the stretch AND Indiana: 1.1%
10 or more down the stretch: .4%
Total Chance: 1.5 + 1.1 + .4 = 3% chance

The total chance that PSU gets an at-large berth: 16.34% chance.  About exactly 1 in 6.

Don't give up hope: the most likely thing to happen (wins over Iowa, Wisconsin (1), Michigan, Northwestern (1), Minnesota (1), and Indiana in the BTT, losses everywhere else) only has a .023% chance of actually happening.  Making the tournament is approximately 720 times more likely than the most likely individual scenario.

Don't bet the farm either.

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