The probability of winning
To get the probability of winning, first we compute the distribution of the goal differential:
goal_dist1 = MakeGoalPmf(suite1) goal_dist2 = MakeGoalPmf(suite2) diff = goal_dist1 - goal_dist2
The subtraction operator invokes
Pmf.__sub__, which enumerates pairs of values and
computes the difference. Subtracting two distributions is almost the same
as adding, which we saw in Addends.
If the goal differential is positive, the Bruins win; if negative, the Canucks win; if 0, it’s a tie:
p_win = diff.ProbGreater(0) p_loss = diff.ProbLess(0) p_tie = diff.Prob(0)
With the distributions from the previous section,
p_win is 46%,
p_loss is 37%, and
p_tie is 17%.
In the event of a tie at the end of “regulation play,” the teams play overtime periods until one team scores. Since the game ends immediately when the first goal is scored, this overtime format is known as “sudden death.”