Doctor No
Registered User
Looks like the old threads went the way of the old board setup, so here we will start fresh.
What is a Simple Rating System? As the name implies, it's not that difficult to implement, but it's essentially schedule-adjusted goal differential. One way to rank teams would be to take their goal differentials (goals scored, less goals allowed, divided by the number of games played - for instance, Tampa Bay has scored 36 goals, and allowed 24 goals, in nine games, for a goal differential of (36-24)/9 = 12/9 = 1.333).
However, that ignores the fact that different teams have played different strengths of schedule - particularly this early in the season. This can have a major impact on United States' college football, for instance, but still is meaningful in hockey. So far this season, Tampa Bay has played Florida, Florida, Washington, Pittsburgh, St. Louis, Detroit, New Jersey, Columbus, and Pittsburgh. These teams have a slightly below average combined goal differential (an average of -0.09), which suggests that the Lightning's schedule has been a tad easier than normal. So we adjust their ranking to be (Goal Differential) Less (Schedule Strength) = 1.333 - 0.09 = 1.243.
However, now we have a better sense of each of the Lightning's opponents' strength, and so we need to recompute the strength of Tampa Bay's schedule. This becomes an iterative process (the schedule strengths change, which changes the rankings, which changes the schedule strengths, which changes the rankings, and so forth). The good news is that this almost always converges under "realistic" assumptions, although the bad news is that I've proven that the process matrix is non-invertible almost always. So you actually have to iterate; you can't find a closed form solution.
My intent on posting these during the season is not to claim that they are the best - they are in no sense "the best" at predicting future games. My intent is that this is relatively easy to follow along with, and hopefully they entice people to say "hey, the model doesn't do this, and so I can do it better". It's easy to pick up and say "this should adjust for home-ice advantage" (what I present here will do that) or "blowout wins shouldn't count for a lot more than close wins" (what I present here will not adjust for that). I'd love to see others try this on their own and perhaps learn a bit while doing so (the best way to learn this stuff is to do it).
For any given game going forward, the home team will be expected to win the game by approximately (home team SRS) - (road team SRS) + (value of home ice). When Toronto hosts Los Angeles tonight, they'll be expected to win by (1.438) - (1.152) + (0.205) = 0.491 goals. To convert this into a winning percentage (or a points percentage), you'll have to capture each team's standard deviation of performance as well.
But hey, enough of my yakkin'. whaddaya say? Let's boogie!
http://www.tcm.com/mediaroom/video/...-Tap-Movie-Clip-If-You-Will-Rockumentary.html
What is a Simple Rating System? As the name implies, it's not that difficult to implement, but it's essentially schedule-adjusted goal differential. One way to rank teams would be to take their goal differentials (goals scored, less goals allowed, divided by the number of games played - for instance, Tampa Bay has scored 36 goals, and allowed 24 goals, in nine games, for a goal differential of (36-24)/9 = 12/9 = 1.333).
However, that ignores the fact that different teams have played different strengths of schedule - particularly this early in the season. This can have a major impact on United States' college football, for instance, but still is meaningful in hockey. So far this season, Tampa Bay has played Florida, Florida, Washington, Pittsburgh, St. Louis, Detroit, New Jersey, Columbus, and Pittsburgh. These teams have a slightly below average combined goal differential (an average of -0.09), which suggests that the Lightning's schedule has been a tad easier than normal. So we adjust their ranking to be (Goal Differential) Less (Schedule Strength) = 1.333 - 0.09 = 1.243.
However, now we have a better sense of each of the Lightning's opponents' strength, and so we need to recompute the strength of Tampa Bay's schedule. This becomes an iterative process (the schedule strengths change, which changes the rankings, which changes the schedule strengths, which changes the rankings, and so forth). The good news is that this almost always converges under "realistic" assumptions, although the bad news is that I've proven that the process matrix is non-invertible almost always. So you actually have to iterate; you can't find a closed form solution.
My intent on posting these during the season is not to claim that they are the best - they are in no sense "the best" at predicting future games. My intent is that this is relatively easy to follow along with, and hopefully they entice people to say "hey, the model doesn't do this, and so I can do it better". It's easy to pick up and say "this should adjust for home-ice advantage" (what I present here will do that) or "blowout wins shouldn't count for a lot more than close wins" (what I present here will not adjust for that). I'd love to see others try this on their own and perhaps learn a bit while doing so (the best way to learn this stuff is to do it).
For any given game going forward, the home team will be expected to win the game by approximately (home team SRS) - (road team SRS) + (value of home ice). When Toronto hosts Los Angeles tonight, they'll be expected to win by (1.438) - (1.152) + (0.205) = 0.491 goals. To convert this into a winning percentage (or a points percentage), you'll have to capture each team's standard deviation of performance as well.
But hey, enough of my yakkin'. whaddaya say? Let's boogie!
http://www.tcm.com/mediaroom/video/...-Tap-Movie-Clip-If-You-Will-Rockumentary.html
