Sports Simple Rating System Implementaion in R - r

Question

I am attempting to implement the sports Simple Rating System in R and am having a lot of trouble. I can do it in excel, which you can see in this video: http://www.screencast.com/users/Sports-Reference/folders/PFR/media/cea8d1e3-ed91-431f-a0df-1336c03b1268
To test this out I am using the same data (basically) as in the video, which you can access here: https://drive.google.com/file/d/0Bzr6jaapQdMRUFhpU0h4NDBNaTQ/view?usp=sharing
The first lines lines of the data frame could be built like this, but there are 206 records:
dat$Week <- c(1,1,1)
dat$Team <- c("Arizona Cardinals", "Arizona Cardinals", "Arizona Cardinals")
dat$Location <- c("HOME", "AWAY", "HOME")
dat$Opponent <- c("San Francisco 49ers", "Jacksonville Jaguars", "Indianapolis Colts")
dat$Points.For <- c(16, 31, 10)
dat$Points.Against <- c(20, 17, 31)
I set up the data with the following code:
library(dplyr)
## Load data
dat <- read.csv("data/footballsrstestdata.csv", stringsAsFactors = FALSE)
## Delete last row
dat <- dat[-207,]
## Create MOV and adjusted MOV variables
dat <- mutate(dat, mov = Points.For - Points.Against)
dat <- mutate(dat, adjMOV = mapply(function(x, y)
{if(y == "HOME") x - 1.3529 else x + 1.3529}, dat$mov, dat$Location))
## Create SRS df
srsTable <- data.frame(teams = unique(dat$Team), stringsAsFactors = FALSE)
## Create average MOV
srsTable <- mutate(srsTable,
avgAdjMOV = sapply(teams, function(x) {
mean(dat$adjMOV[dat$Team == x])
}, USE.NAMES = FALSE))
## Create placeholder varaiables
dat$oSRS <- NA
srsTable$SOS <- NA
srsTable$SRS <- NA
In excel, you would have two sheets that are referenced to each other creating a circular reference that iterates until they reach stability. Each line in the games data would have the opponent's SRS, and on the team SRS sheet, the SRS would be equal to the avgAdjMOV + the average opponents SRS from the game data sheets. I am assuming that I need to create a function with a series of equations and use the optim function to solve them, but can't figure how to set this up so that they work over both the game data dataframe and the teams dataframe simultaneously.
Does anyone have any ideas on how to proceed?
Thank you!

Answer 1

So I suggest setting up everything as a System of Equations Problem :
Ratings = adjMOV+(1/nGames)*Sched*Ratings
Where Ratings is a size N vector with the ratings of each team, adjMOV a size N vector with the adjusted Margin of Victory for each team, and Sched a NxN matrix of how many times each team faced each other. The order of rows in the vectors and rows and columns in the matrix should be the same. Now with some linear algebra your system of equations should look like:
(I-(1/nGames)*Sched)*Ratings = adjMOV
Now it is easy to solve it using any Non-Linear Solver, I have used the lsei() method in the limSolve package, so your code should look like:
library(limSolve)
A = (diag(N)-(1/nGames)*Sched)
b = adjMOV
solution = lsei(A=A,B=b)
Ratings = solution$X
I know it has been a more than a year but I hope this helps.