Winning probabilties

(10 pts)

In this problem we’re all going to make probabilistic predictions for tomorrow’s NCAA tournament games following the strategy outlined in this presentation. Then, we’ll check them on Friday and see how we’re doing!

Note that we’ll divvy out the games in class. Once you’ve got your game, respond here with:

1. The game you’re asked to predict,
2. The ratings of each team,
3. The Z-score of the difference, and
4. The probability that the higher seed defeats the lower seed.

1. Kentucky v Saint Peter’s
2. KY- 91.23 SP- 74.19
3. z-score = \frac{91.23 - 74.19}{8.5549} = 1.99
4. When plugged into the normal probability calculator this gives us a 97.6705% chance that Kentucky will beat Saint Peter’s
5. lol nvm they sucked

1. This is a prediction for the game between Vermont and Arkansas.
2. Arkansas has a rating of 86.78 and Vermont has a rating of 80.32.
3. The z-score equals about:

4. When this value is plugged into our normal probability calculator we get around a 77.4906% chance that Arkansas will beat Vermont.

This is a prediction for Memphis Vs. Boise St.
The rating for Memphis is 85.47, while the rating for Boise St is 82.49
The z-score = \frac{85.47-82.49}{8.5549} = .3483
When it is plugged into the probability calculator it gives us a 63.62% chance that Memphis beats Boise St

1. North Carolina vs. Marquette
   2.NC:83.99, Marq:81.92
2. Z-score=\frac{83.99-81.92}{8.5549} = 0.2419
3. 59.55%

I chose to predict the Baylor vs. Norfolk State game.
Baylor’s rating is 87.92
Norfolk State’s rating is 71.42
the Z-score of the difference is

When we plug this number in to the normal probability calculator, we get a 97.31 %chance that Baylor will beat Norfolk State.

The game that I am predicting is is UAB (12) vs. Houston (5). The ratings for these teams are…

So, with these values, we can calculate the Z-score, which will be…

When we plug that value into the calculator, we get that the probability of Houston (5) beating UAB (12) is about 79.34%.

New Mexico Versus UCONN
New Mexico has a rating of 77.67
UCONN has a rating of 86.45
The Z score \frac{86.45-77.67}{8.5549}=1.0263
This gives us a probability of 0.8461, or 84.61% that UCONN will win that match.
In reverse, New Mexico has just a 15.39% chance of moving on.

1. This is a prediction for Creighton (9) vs. San Diego State (8)
2. Creighton’s rating is 81.49 and San Diego State’s rating is 83.49
3. The z score is

4. When plugged into the normal probability calculator, the probability that San Diego State beats Creighton is 59.24%

1. gonzaga v. georgia state
2. gonzaga: 96.47, georgia state: 73.48
   3.z-score:

4. there is a 0.996395 or 99.6% chance gonzaga beats georgia state

Prediction for Vermont vs Arkansas.
Vermont’s rating: 80.32
Arkansas’ rating: 86.78
Z-score = \frac{86.78-80.32}{8.5549}=0.7551
Probability: P_{AV}=0.7749
The probability that Arkansas will defeat Vermont is 77.49%.

1. This is a prediction prediction for San Francisco Vs. Murray State.
2. San Francisco has a rating of 83.00 and Murray State has a rating of 81.37.
3. The z-score equal about:

4. When this value is plugged into our normal probability calculator we get around a 57.55% chance that San Francisco will beat Murray State.

1. Indiana vs Saint Mary’s
2. Indiana = 83.01
   Saint Mary’s = 84.32
3. Z score = \frac{84.32 - 83.01}{8.5549} = 0.15312
4. When plugged into the probability calculator we get a 56.08% chance that Saint Mary’s will beat Indiana.

1. Iowa v Richmond
2. Iowa - 89.0 Richmond- 79.9
3. z-score:

4. The probability that Iowa beats Richmond is 85.63%.

1. Tennessee 5 vs. Longwood 14
2. TN - 88.55 & LW 73.41
3. z-score = \frac{88.55 - 73.41}{8.5549} = 1.76
4. When I plug it into the normal probability calculator this gives us an 96.0796% chance that Tennessee will beat Longwood

1. South Dakota State vs Providence
2. Ratings
   South Dakota State: 79.68
   Providence: 82.72
3. Zscore
   z= \frac{82.72-7968}{8.5549} \approx 0.3553519
4. Probability that Providence beats South Dakota State
   63.8838\%

1. Colorado State vs Michigan
2. Colorado state - 81.65
   Michigan - 84.73
3. Zscore

4. The probabilty that Michigan beats Colorado State is 64.0587\%