Gonzaga Probabilities

A lot of games on TV will put up statistics way too fast. They're up for a few seconds and its tough to take it all in. Maybe it is the Detroit Lions' total rushing and passing yardage for each of the past three seasons. You got about five seconds to see it and try to make some sense of it. They obviously have some point they are trying to make with all those numbers, but tough to take in. Sometimes you just have to stare at things for awhile.

I did see one a few days ago that didn't have too many numbers in it. Gonzaga is currently the number one college basketball team. In fact they're undefeated. What are the chances they stay undefeated? It's 91%, they claim. They also showed the chance of winning each of their remaining games. Those chances are:

• 98%
• 99%
• 98%
• 96%

How did they come up with those numbers? I'm not sure. They didn't explain that. I tried looking on the internet to find out. That didn't work so well. Different associations (Vegas, ESPN, etc.) have their own different methods. Most of them let you in only partially on how they figure things. Turns out they take a lot of things into account. Your win-loss record, opponents win-loss record, playing home or away, point differentials, injuries, recent win-loss records, etc.

Then how they take all that data and come up with a percent is a mystery. What isn't a mystery is the 91% chance of winning all four of those games to remain undefeated. It is an "and" probability problem, which mean we can just multiply those individual probabilities together.

       (0.98)(0.99)(0.98)(0.96) = 0.9128 or just over 91%

On a related note, the University of Connecticut women's team won their hundredth game in a row last night. Pretty impressive. Impressive especially considering the following:

• A team that usually wins 80% of its games has a (0.8)¹⁰⁰ = 0.00000002% chance of winning 100 in a row.
• The best NBA record ever is Golden State last year. They won 89% of their games. Thus, a 0.00087% chance of winning 100.
• How about a team that wins 99% of its games? They have a 36.6% chance of winning a hundred in a row.

Here is a little higher mathematical problem. What kind of team would it take to have a 50% chance of going on a 100 game winning streak?

• x¹⁰⁰ = 0.5 
• 100(log(x)) = log(0.5)
• x = 0.9931

So you need to usually have a 99.31% chance of winning any single game you would play to have a 50-50 shot at winning 100 in a row.

In your mind this is maybe not the most important math application ever, but many students are into this kind of thing. And it does beat flipping coins and pulling various colored socks from drawers.