Leave it to Luke to start a trend. Who knew algorithms could be so interesting, and yet so time-consuming?
I couldn't wait until next week to unveil my analysis, so you're getting it now! How's that for analysis overload in one week?!
Anyways, building upon what I saw as flaws (minor, yet significant) in the previous analyses by Luke and Justina, I decided to partake upon an endeavor to create my own analysis. I wanted to get down to the nitty gritty and figure out who really has had a legit team, and who has not had a legit team. There has been concern about the reliability of the Points Against category, and I hope to address the issue from a different standpoint, and really just determine who deserves to have all the wins and who deserves to have all the losses.
Here's what I did:
1) I went back to all the previous weeks and made a table with all of the points scored by each team on each week.
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2) I figured that on any given week, each team has a certain percentage of games they would win based on how many points they scored relative to how many points other people scored. The team that scored the most points that week would have won regardless of who they were playing, thus that team would have a 100% chance of winning that week. The second highest scoring team would have a 88.89% (forgive the rounding) chance of winning that week, and so on.
Take Week 1 for example: Justina scored 131.8 points, which was more than anyone else that week. So no matter who she played, she would have won. Jeff scored 118.68, which was the second most. The only team he could have lost to would have been Justina, but there would only be a 1/9 chance (11%) of him being matched up with Justina, thus his chance of winning that week would be roughly 89%, because he would have beaten any other team. And so on. Aaron's team would have won 0% of his games, because he had the lowest score. So Justina's Points Against that week was 90.18 (since she played Gabs, the 3rd lowest scoring team that week), but that stat doesn't take into account that regardless of who Justina played, she would have crushed them. It just so happened that she played the 3rd worst team that week. Therefore, these percentages are a better indicator of team strength on any given week.
3) Based on how many points each team scored each week, I assigned them the percentage chance that they would win for that week.
4) I then averaged these values over the span of 8 weeks to determine the probability, on any given week, that a team would win its game.
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The green and the red just indicate actual wins (green) or losses (red) for each week.
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The fall colors are just based on percentage. Portrays trends nicely. Thanks to David for that one.
Here are the rankings based on my analysis (if you're too lazy to open the photo file to look at it, or don't understand it). The percentages represent the average chance that each team would have won on any given week, based on how many points that team scored relative to the other teams each week. Hence, indicative of the strength of their team's performances thus far in the season.
1. JUSTINA OWNS - 69%
2. Rainbow Warriors - 65%
3-T. JohnKasay#1 - 54%
3-T. odoyle RULES - 54%
5. aaronisyourdaddy - 51%
6. Spider Pig - 50%
7. The Debbinator - 47%
8. Terrific Tortoises - 43%
9. THE Pain Train - 36%
10. RelientK - 29%
This information is valuable, because it silences the argument that if a team has had X amount of Points For or Points Against, then that team is weaker or stronger (and hence the team's record could be misleading). Instead, it looks at each individual week to see if that team really deserved to win that week, using probability. This factors in W-L records, points against and points for, etc. etc. all into one nice little chart. At least I think it does.
Basically, it justifies the Yahoo rankings. Even though Justina and Jeff have low Points Against, they have scored enough points relative to the other teams each week, that regardless of who they played, they probably would have won (or lost) anyways, and would have thus had the same rank as they currently have.
The major aberration is Laura, who has seemed to escape last place in the Yahoo Rankings in spite of underperforming each week. I'll attribute that to her victory over me in week 5, with her team scoring the 2nd lowest points and my team scoring the lowest.
Luke and Aaron are also swapped, but that's insignificant to me.
In summation of all of our wonderful analyses, Justina has created a heat map:
It basically provides a nice little comparison of the new rankings v. the Yahoo rankings. It's unanimous that Justina and Jeff should be first and second, respectively. The rest is kind of weird. Besides me being 3rd in all the new rankings. :)
