This site will host updates of my pointshare power rating system that covers College and Pro football, College and Pro Basketball, Major league Baseball and Pro Hockey.
I started outlining the pointshare system at dontsaveapitcher.blogspot.com but moved it to this site.
In June 2012 I modified the pointshare system by incorporating a more realistic prior distribution rather than a flat prior.
To do this I used a beta distribtution. To do this I had to convert a team’s score to a percentage of the maximum score. So I had to determine the maximum score a team in each sport can achieve. To do this I estimated the number of opportunities a team has to score and assumed they scored on all of them.
So for NFL the maximum score is the average number of drives (11.5) by 7 (TD) is 80.5. In basketball I used the average number of possessions, for hockey the average number of shots, in rugby league the average number of scores plus kicks plus errors, in aussie rules I added the number of scores to the number of errors (calculated from the effective distribution rate and the number of distribution), for rugby union I guessed 12. For soccer I will use the average number of shots. For baseball I used the average number of plate appearances which is incorrect as a baseball team has an unlimited number of scoring opportunities if they keep scoring. Although I find that a small change in the total doesn’t make much difference.
The beta distribution requires two parameters a and b. The mean of the beta distribution is a/(a+b) while the variance is ab/((a+b)^2 *(a+b+1)). Therefore is you know the mean of the scoring rate in a league you can set the ratio of a to b and if you know the variance of scoring you can then set the value of a to match this (I used solver).
(See version 2.0 in documents for the data table)
The beta distribution set by this simple method fits high scoring sports (basketball, Aussie rules) very well, medium scoring sports (rugby, American football) slightly less well and low scoring sports such as hockey and baseball even less well but all are a significant improvement on a flat prior so I will use them.
To show the difference here are the prior and post distributions of an NFL that scores 10 points. The effect of using the league average to set the prior rather than a flat prior is that the distribution of the posterior is less extreme as shown in the figure below.
To show the effect of the average based prior on a flat prior in evaluating the game outcome function. Here is the posterior scoring rate PDF for a 21-7 NFL game.
The game outcome function is calculated by determining whether a value drawn from the winner distribution is greater than a value from the loser. So Blue vs red (flat prior) or light blue vs yellow (average based prior). Using the average prior has the effect of slightly reducing the GOF function of wins.
FAQ of version 1.0
What is pointshare?
Pointshare is a sports ranking system which ranks teams based on their score against their opponents the strength of the opponents and the venue.
How good are these rankings?
It is almost impossible to determien how good a system is. My college football and college basketball rankings are listed on Ken Massey's compariosn site where normally they are in the bottom quarter in terms of deviation from the consensus. http://www.masseyratings.com/
NFL and College football picks are also tracked on prediction tracker.com http://www.thepredictiontracker.com/
Where I can do an objective evaluation I list this in the evaluation page.
Where do you get the game data from?
NHL NFL and NBA data come from the sports reference family of websites e.g.
College basketball and College football scores are courtesy of Dr. Peter Wolfe's website.
For the 2011-12 college basketball season I have used the score database on Ken Massey's website http://www.masseyratings.com/data.php
How does the System actually work?
The system has three components
Game Outcome Function
The score in each game is converted to a game outcome function between 0% and 100%. The game outcome function is an estimate of how often a team would win if the game was replayed an infinite number of times at the same venue based solely on the score of the one game that took place.
Each sport has a different score:GOF conversion table depending on the simplified model of the game I use.
Football and Basketball
Football and basketball is treated as a binomial process. Each game is treated as a series of possessions for each team with a team scoring on a fraction of them. In football a touchdown is treated as a success any other score is treated as a partial success. So if a team scores 21 points that is three successes if it scores 24 points that is 3.42 success (24/7). In basketball a success is counted as 2 points so the score is divided by 2 to find the number of successes. This method actually recreates thw beta distribution with the alpha and beta factors equal to the numberof sucessful possesions plus 1 and the numberof unsucessful possesions plus one respectively.
The total number of possessions was calibrated against the Vegas closing line for point spread, totals, and straight up odds so for example the money line indication of proportion of games won by a 3 point favourite in a 47 o/u game is close to the GOF of 25-22 score. For football this equates to 7 possessions and in basketball 68 possessions.
The GOF table is calculated as follows.
For each score the likelihood of that score happening is calculate if the team’s true scoring rate is 1% of possessions, 2% of possessions etc. up to 99%. So if a basketball team scores 100 points that is 50 successes out of 68 possessions. If the team is truly a 1% scoring team the probability is 1%^50*99%^(68-50) all of these likelihoods are summed and divided by the total to get the percentage of each scoring rate.
Now that we know the distribution of scoring abilities of the team and the opposition you can work out how often each team would win a rematch.
Hockey is treated as a poisson process.
Again the likelihood of each score is calculated as for football and basketball but for hockey the likelihood is based on assuming a team scores 0.1, 0.2 up to 9.9 goals per game.
Home field Advantage adjustment
HFA is calculated by looking at the average ratio of GOFs for home and away. as home teams will have a larger ratio this average is then used to reduce the GOF of teams. So if in one game the home team, (Team A) had a GOF of 60% and so the road team (Team B) was 40% this is a ratio of 1.5 (60/40). If the average for HFA is 1.2 the ratio is reduced by dividing 1.5 by 1.2 = 1.25 so the Gof is then 55.5% for team A and 44.4% for team B. This means that a close loss by a road team will lead to a gof greater than 50%.
Pointsharing between teams.
This works by an iterative process
Step 1 Each team starts with 100 points.
Step 2 Each team contributes 1/n of their points into the “pot” for each game they have played to date where n is the number of games played by the team in the league who has played the most games.
Step 3 The points contributed from each team into the pot are then shared between the two teams according to their HFA adjusted GOFs (hence the term pointshare)
Step 4 the new number of points for each team is calculated by determining the number of points they have gained and lost through the point sharing method.
Step 5 Return to step 2 until the differences between the ratings at each step 4 stabilises.
When new games are played the entire system is repeated from step 1.
I also calculate this as a series of simultaneous equations and solve them using matrices in excel. Spreadsheets of how I do this are available on request.
Exceptions and dealing with unusual situations
I have noticed that the relationship between the moneyline and pointspread are for football Pointspread = 9*ln(ML) and for basketball Pointspread = 7.2*ln(ML) where ln is natural log and ML is the moneyline adjusted for the overround. So these are provided to see how well the system compares to the Vegas lines. The effect of HFA is also calculated in a similar way.
What this system doesn’t do.
Injuries and momentum cannot be taken in to account and the HFA is the same for all teams. So a team that wins its first 6 games and loses its last 6 is treated the same as a team that loses its first six and wins its last six if the winning margins and opponents are the same
How to use this system to make predictions of who will win.
Multiply the home team's rating by the homefield advantage (not the Home field pointspread equaivalent) divide this by the road teams rating. This is odds the away team will win.
e.g. team A is at home to team B. Team A rating is 120 team's B rating is 100. The HFA is 1.10. The odds of the away team winning is 120*1.1=132/100 or +132 in US odds and so the home teams odds should be -132.