If the betting market indicates that Team A is favored to win a game by 3 points and the totals line is 47 points, what is the market's expectation of Team A's total points scored at the end of the game?25 points20 points30 points50 points
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Step 1: Let Team A's expected points be x and Team B's be x - 3 (since Team A is favored by 3). Show more…
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The mean number of points a team scores against a particular opponent is normally distributed with μ=21.5 and σ^2=3. We can be approximately 97.5% sure that the team will score more than how many points in the next meeting against this opponent?
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In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team $A$ is favored by 5 points, and wins the game by 7 points, then a bet on Team $A$ is a winning bet. However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. In games where a team is favored by 12 or fewer points, the margin of victory for the favored team relative to the spread is approximately normally distributed with a mean of 0 points and a standard deviation of 10.9 points. Source: Justin Wolfers, "Point Shaving: Corruption in NCAA Basketball" (a) In games where a team is favored by 12 or fewer points, what is the probability that the favored team wins by 5 or more points relative to the spread? (b) In games where a team is favored by 12 or fewer points, what is the probability that the favored team loses by 2 or more points relative to the spread? (c) Explain the meaning of "the margin of victory relative to the spread has a mean of 0 points." Does this imply that the spreads are accurate for games in which a team is favored by 12 or fewer points?
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