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Problem of the Week
Problem B
On-Base Probabilities

In baseball, OBP stands for On-Base Percentage. It is the number of times the player makes it on base divided by the total number of times they step up to bat, rounded to three decimal places. For \(10\) players in the MLB, suppose we have the following OBP statistics.

Player OBP
Jake Bauers \(0.357\)
Vladimir Guerrero \(0.500\)
Ian Happ \(0.156\)
Kyle Schwarber \(0.278\)
Andrew Vaughn \(0.267\)
Alex Call \(0.857\)
Jarren Duran \(0.091\)
Aaron Judge \(0.581\)
Sal Stewart \(0.600\)
Masataka Yoshida \(0.571\)

  1. Order the given OBP data on the probability line below from least likely to get on base to most likely to get on base.

    A number line from 0 to 1. Five evenly spaced tick marks divide the line into four intervals. The tick marks, from left to right, are labelled: Impossible (at 0), Unlikely, Even chance, Likely, and Certain (at 1).

  2. Choose any three of the ten players and answer the questions that follow. If they step up to bat \(10\) times, how many times would you expect each of these three players to get on base? What about \(20\) times at bat? \(25\) times?

  3. What would be a reasonable explanation for the OBP of Jasson Dominguez, a brand new player with an incredible OBP of \(1.000\)?

  4. A new player has an OBP of \(0.400\) after \(10\) times at bat, but wants to increase their OBP to \(0.550\). How many times must they make it on base in their next \(10\) times at bat?

Theme: Data Management