- Nov 17, 2011
- 7,662
- 2,541
I had to make decisions in order for this to work. 1 for a win. 0 for a loss is standard. OT and SO games are close so I scored them at 0.75 and 0.25 for an OT/SO win and loss respectively.
Since you 'had to make a decision' then the decision becomes non-mathematical in the strictest sense.
The value of K is usually 32, but it is irrelevant. I use 100 because it allows for a larger spread. If we use 32 or 50 or 100 or 768, it just creates a larger spread. The difference is in the fact that sometimes, like in chess, the value of K changes over time. For this ranking each team plays 82 games a year and for me it did not merit changing K.
But a bigger K creating a bigger spread changes the odds and therefore the effect of the result of the next game, does it not? If I am missing the math, I would love to see, with rigor, how it makes no difference. And, I say that as a math geek, with a slight inclination in the back of my mind how that math would come out.
No, not taken into consideration. 41 home games and 41 away games balance out, imo. Determining how much home ice favors a team and how much that impacts their expected score is very subjective and can skew results.
If this is subjective, then the 'guess' as the correct value of OT/SO wins and losses is also, as well as the value of K. And, as described below, there are mathematical ways to determine the value of home ice as a league average.
Yes. Scoring is based on team scores at the time they play. A team can go on a tear and win several games in a row and then go on slump and lose several in a row. The first team to beat them and put them on their slump gets the most points. Beating a team when they are hot is harder to do and earns more points. It's a cold mathematical process and doesn't consider "fair-to-bad" or retroactively update scores.
It is a cold mathematical process, but it can be skewed by the following. Let's say there are 32 teams, instead of 31, so we don't offend anyone, and let's say that the last team in (International Falls, MN) is globally acknowledged to be the worst team in the league. Now, let them win their first 3 games, 1 in OT, because their goalie is particularly hot. Everyone knows that this is a mirage. It won't last. But, their 4th opponent, who beats them, gets major points for this win. And, after they lose 9 more games out of 10, the next opponent, who beats them, gets minimal points. That seems mathematically correct, but not completely sensical to me.
Even though I know that all teams have injuries, and so one team's power level is not the same all year long, so teams do have scheduling advantages of playing some one "at the right time", I feel this system unduly rewards teams with scheduling luck to play weak teams with fast starts.
That could well be your preference, and I wouldn't argue with your preference, but it is really a preference.
That's awesome, please share.
This article (pardon the few typos. I wrote it as a post, and the mods moved it. Had I known it would be an article, I would have proof-read it better) gives the basics. Should you be interested in more mathematical rigor, or how I arranged the spread-sheet to accomplish this, please PM me.
And, it should be noticed that those rankings recalculate from scratch after every game.