Math 192 Homework Assignment #8

Perfect Games in MLB

• Say a binary logistic regression model was estimated in MTB to predict the probability that a pitcher throws a perfect game in their career and the following output was obtained (predictors are career stats):

  Logistic Regression Table

  Predictor Coef SE Coef P

  Constant -1.75546 1.87272 0.049

  Starts 0.0023050 0.0026987 0.030

  BB 0.0021953 0.0013091 0.001

  HPB 0.0048585 0.0083649 0.645

  ERA -0.137675 0.389389 0.024

  Correctly interpret in a sentence the “ERA” predictor variable.

• Suppose Randy Johnson faces the following lineup once through whose career batting average vs. Johnson is given:

  Hitter Avg

  1 0.202

  2 0.296

  3 0.198

  4 0.256

  5 0.312

  6 0.245

  7 0.191

  8 0.222

  9 0.241

  What is the probability that Randy Johnson gets everyone out the first time through the order? (Assume no errors can be made and Johnson cannot hit or walk anyone).

MLB Shortstops

1. Using the statistics provided below, does Jose Reyes have a significantly higher average and on-base percentage than Jimmy Rollins?
Player   AB   H   BB   HBP   SF
Reyes   3206 919  241   5    11
Rollins 5269 1461 426  30    31
OBP = (H+BB+HBP)/(AB+BB+HBP+SF)

2. Using the statistics provided below, does Jimmy Rollins have a significantly higher fielding percentage than Jose Reyes?
Player   Errors   Fielding %
Reyes    75       .975
Rollins  93       .982
Chances = -errors/(FP-1), where chances is number of trials.
Non-errors = chances-errors, where non-errors is the number of events.

Sports Stats NHL Shootout Homework

1. What is the probability that the average league player will achieve the same length of streaks as Jussi Jokinen (nine consecutive shootout goals) and Trent Hunter (thirteen consecutive shootout attempt misses), assuming that the league average for shootout goals is 33.91%?

2. Using Minitab, pick one goalie from each conference and simulate a shootout, similar to the activity done in class, using three shooters (or more if tied after three shooters), to determine a winner in this all-star shootout. Assume that the shooters have equal ability for both conferences in this example, and use the goalies’ all-time shootout save percentage as their given ability for the shooter to miss an attempt. Show the results and determine the winning conference.

Western Conference

Goalies:

Player	Team	All-Time Shootout Save %
Jean-Sebastien Giguere	Anaheim	68/104 = .654
Niklas Backstrom	Minnesota	42/74 = .568
Roberto Luongo	Vancouver	100/139 = .719

Eastern Conference

Goalies:

Player	Team	All-Time Shootout Save %
Carey Price	Montreal	35/51 = .686
Henrik Lundqvist	New York (R)	128/169 = .757
Tim Thomas	Boston	91/123 = .740