Predicting Lines (Against the Spread)

The MDS Model is essentially a strength of opponent-adjusted Pythagorean expectation for each team. Thus, each team's rating is designed to estimate "true win percentage" and is bounded by [0, 1], which allows for it to be used to predict matchup win probabilities by Log5.

However, Log5 only gives the probability of Team A beating Team B (and inversely, Team B beating Team A). A major use of modeling sports is for picking games "against the spread", which is considerably harder than picking "straight up" winners: lines (i.e. spreads) are designed to be 50/50 - having even money on each side - and the best professional gamblers in the world win only 55% of these picks.


To predict margin of victory (MOV), I calculate the inverse of the normal distribution for each percentage and multiply this by a parameter for each league. These parameters were derived by minimizing the residuals between the approximate Vegas moneyline to spread MOV and the predicted NORMINV MOV. Predicting MOV also allows for the inclusion of a constant home field advantage.

However, the question arises as to how to calculate this parameter when no Vegas benchmark exists, such as with Ultimate Frisbee, or baseball or hockey (where lines are not 50/50 and thus don't approximate the expected MOV). Since the NORMINV of the win probability gives the expected number of standard deviations from 0 the team should win by, the constant this is multiplied by should simply be the standard deviation in MOV for each league.

The answer to this question came to me when I was building the model for Ultimate literally from scratch: there are no exponents in place, no past models to go by, and certainly no Vegas numbers to use. However, Ultimate presents a challenge because most of the time, teams play to a set score instead of when time runs out. This leads to the distribution of scores to not be normal:

Data taken from a sample of 210 games played by teams from NC, NE, and NH

As the above graph indicates, more weight should be given to the extremes, which is more characteristic of the log-normal distribution. For all other sports, the normal distribution should be a decent fit (which is also how Nate Silver calculates predicts lines). 

In conclusion, these are the parameters I use for predicting lines (which generally are "conservative" in that they favor regression to the mean (a MOV of 0)):

SD for MOV:

NBA:      10.5

NCAAB:    10

NFL:      10.5

NCAAF:    13.5

NHL:      2

Soccer:   1.5

Ultimate: 4

Also, these are the point values I use to include home field advantage:

Home Team Advantage:

NBA:       3 pts

NFL:       3 pts

NCAAF:     3.5 pts

NCAAB:     4 pts

NHL:       0.25 pts

MLS:       0.5 pts

As I am constantly looking to improve my modeling systems, my next project will be to determine if in fact the log-normal distribution should be used instead of the normal distribution. For example, the following scenario seems to fit reality per the 68/95/99.7 rule:

68% of NBA games are within 10.5 points, 95% are within 21 points, and 99.7% are within 31.5 points.

However, is this the case in college football:

Are 68% of NCAAF games within 13.5 points, 95% within 27 points, and 99.7% within 40.5 points? It would seem that more than 0.3% of all Division I games are blowouts larger than 40 points.