Chapter 1.5, Problem 40E

a.

To determine

The player’s plus-minus rating for game 1; for game 2.

Answer to Problem 40E

The player’s plus-minus rating for game 1 is +2.

The player’s plus-minus rating for game 2 is -3.

Explanation of Solution

Given:

The player is assigned a positive point (+1) each time his team scores while he is on the ice.

The player is assigned a negative point (-1) each time opponent team scores while he is on the ice.

The player is assigned no point each time if the scoring team has more players on the ice than the other team.

The table below shows the points awarded to a player in two games:

Concept Used:

The sum of the positive and negative points is considered the player’s plus-minus rating.

Calculation:

In game 1;

Positive points obtained = $+3$ ;

Negative points obtained = $-1$ .

Therefore, player’s plus-minus rating = $(+3)+(-1)=+2$ .

In game 2;

Positive points obtained = $+2$ ;

Negative points obtained = $-5$ .

Therefore, player’s plus-minus rating = $\left(+2\right)+\left(-5\right)=-3.$

Conclusion:

  $\text{The player's plus-minus rating for game 1 is +2}\text{.}$

  $\text{The player's plus-minus rating for game 2 is -3}\text{.}$

b.

To determine

The total plus-minus rating of the player for the two games.

Answer to Problem 40E

The total plus-minus rating of the player for the two games is -1.

Explanation of Solution

Given:

The player’s plus-minus rating for game 1 is +2.

The player’s plus-minus rating for game 2 is -3.

Concept Used:

The sum of theplayer’s plus-minus rating for the two games is considered the player’s total plus-minus rating.

Calculation:

As per the given problem;

The player’s plus-minus rating for game 1 = +2.

The player’s plus-minus rating for game 2 = -3.

The player’s total plus-minus rating = (+2) + (-3) = -1.

Conclusion:

The total plus-minus rating of the player for the two games is -1.

c.

To determine

To explain: The player had a better plus-minus rating in game 1 or in game 2 ?

Answer to Problem 40E

The player had a better plus-minus rating in game 1.

Explanation of Solution

Given:

The player’s plus-minus rating for game 1 is +2.

The player’s plus-minus rating for game 2 is -3.

Calculation:

As per the given problem;

The player’s plus-minus rating for game 1 = +2.

The player’s plus-minus rating for game 2 = -3.

As (+2) > (-3), The player had a better plus-minus rating in game 1.

Conclusion:

The player had a better plus-minus rating in game 1.