# Predictions

Betting line.  The betting line is taken to be that posted by William Hill at the time the predictions are made.  If no betting line has been posted by William Hill at that time, the betting line is taken to be one posted by MGM Resorts, Wynn Resorts, Stations, CG Technology, or Caesars Entertainment.  In cases where no betting line has been posted at the time the predictions are made, the betting line may (depending on availability) be taken to be one posted subsequently.

Expected difference in score.  By definition the difference in score is the score of the first team minus the score of the second team.  The expected difference in score reflects the relative ratings of the two teams and (unless the game is to be played at a neutral site) the home-field advantage.  The expected difference in score is either positive or negative depending on which team is “more likely” to win (or is 0 in the case of a “toss-up”).

Table.  In the table of probabilities, k represents the score of the first team minus the score of the second team.  And the probability associated with each value of k represents the probability of that difference in score exceeding k.  Note that the the probability of any “outcome” or collection of outcomes can be determined from the entries in the table.  For example,  if the entry in the table for k = 7 were 0.341 and that for k = 6 were 0.409, then the probability  of the first team winning by exactly 7 points would be 0.409 – 0.341 = 0.068.  And if the entry in the table for k = -1 were 0.611 and that for k = 3 were 0.486, then the probability of the first team winning would be 0.611, the probability of the second team winning would be 1 – 0.611 = 0.389, and the probability of the second team either winning the game or losing it by no more than  3 points would be 1 – 0.486 = 0.514.