# Misunderstanding Purpose of the Line

ESPN posted a terrific piece on one gambler's effort to develop a regression model (i.e., predictive analysis) to aid in his effort to beat the house. Scott Eden touched on several topics covered in Marketing courses including model building, retrodiction, k-means, nearest neighbor, and other analytic concepts. Late in the article, a troubling piece of logic is introduced. The money logic problem:

If I were the general manager of a team,” says (Bob) Voulgaris, “and I had someone building models and doing quantitative work -- if that person could not beat the Las Vegas line, his model wouldn’t be worth anything to me.” The reason? The way he sees it, the best and perhaps the only way to test one’s theories about player value is to take those theories to market. And the only market that’s liquid with money flows in the billions is the betting line, where opinions have a daily price.

The argument appears, at first blush, fine. Voulgaris argues for the use of the line as reflective of the value for the outcome associated with a particular game. A similar argument is made about the price of a bond, stock, or other assets. Except, in this argument, the line does not reflect anything except the house's desire to win.

The house makes money from the vigorish, or vig. The vig is usually 10% of the bet. A simple example of two betters illustrates the relationship between the line and the vig. Two bettors place bets with the same house. Bettor A bets on the home team while bettor B bets on the visiting team. Both place \$25 wagers on their respective team. The home team wins the game. Bettor A will receive \$25. Bettor B will owe the lost wager (e.g., \$25) plus the vig (\$2.50 - \$25 wager * 10% vig). Thus, the house makes \$2.50 (\$2.50 Bettor B's big + \$25 Bettor B's losing wager - \$25 Bettor A's winning wager) from the two bettors.

Few places will take straight up action (i.e., home team beats visiting team regardless of margin of victory). Most places use a betting line (i.e., home team must beat visiting team by six points). If the home team wins the game but the margin of victory is less than six points, then bettors who wagered on the home team will lose their bet because the margin of victory is less than the line (six points in this example). Hence, they will pay the vig to the house.

The line then reflects what the house perceives is the optimal point to attract sufficient return from the vig while drawing sufficient interests from bettors. If the line is too high or too low, then the house will not generate superior financial performance because not enough bettors will place wagers. If the house sets the line incorrectly, then the house will lose money because it will pay more to bettors who placed winning wagers than to losers who will pay the vig.

A model as espoused by Valgorious would have little appeal to an NBA general manager because the general manager is only concerned with winning a game or a series of a games. The margin of victory matters little to the NBA manager because he or she is not being assessed by it. Given the lack of organizational goal centered on the margin victory, the general manager should skip a model devoted to such an outcome.

Eden's piece provides a compelling story of one man's quest to profit by beating the odds with analytics.