7. Find the win and point-spread ratings for the four-team league with records: W L PF PA 1 40 18 22 3 1 32 3 36 34 0 4 6 40 Team A B C A -11 34 B 13 C13 - 1 2 301 D The league of this exercise can be thought of as the league of Exercise 5 with one extra game played. Who played, and what was the score? How much difference does this one game make in the ratings? 8. Use the win ratings of Exercise 7 to project the final won/lost records over a four-game round-robin schedule. You will need to decide how to round off the ratings to get realistic projections. Note in particular that you cannot predict team R to win a negative number of games: also the
For exercise 7, don't forget to consider both win and point-spread ratings in the last question. For exercise 8, be sure to explain the choices you make!
Solution :-
7.
Win ratings and point-spread ratings can be calculated based on the following formulas:
Win rating (WR) = (Wins + 0.5 * Ties) / Total Games Point-spread rating (PSR) = (Points For - Points Against) / Total Games
Using these formulas, we can calculate the win and point-spread ratings for each team in the league:
Team A: WR = (4 + 0.5 * 0) / 8 = 0.500, PSR = (40 - 18) / 8 = 2.50
Team B: WR = (3 + 0.5 * 0) / 8 = 0.375, PSR = (32 - 22) / 8 = 1.00
Team C: WR = (2 + 0.5 * 1) / 8 = 0.375, PSR = (36 - 34) / 8 = 0.50
Team D: WR = (0 + 0.5 * 0) / 8 = 0.000, PSR = (6 - 40) / 8 = -5.00
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