Wednesday, November 2, 2011

Points Against: What does it really mean?

This "Points Against" argument has been brought up a few times: some teams have a really low "Points Against," and maybe don't deserve their ranking (either high or low).  Personally, I find this a little offensive because it suggests that I don't deserve my #1 - which is also why I loved reading Luke's analysis in the previous post.  But anyway, here's how Tim, Luke, and I tackled the issue:
Here are our teams and Yahoo! ranks, sorted by "Points for."  As you can see, there are only a few differences: Tim has more points than Eric, and David Lin has more points than Aaron - in both cases, the higher-ranked team has a better win/loss record.
Here are our teams sorted by "Points against."  As noted before, Jeffrey's team has the lowest Points against in our league.
Here's where the math comes in.  I totaled the "Points for" of each of the 8 teams each team has played so far, then divided it by 8.  This is the total of the average number of points each team scores per week.  I realize this is an over-simplification, and will address it in the closing points.  But anyway, let's do an example.  Jeffrey hasn't played David Li yet, so I totaled the "Points for" of everyone else's team, divided by 8, and that's how I got 802.11.  That's a 125.07 point difference from what we actually scored against him.  Which means that for whatever reason, we underperform when we play Jeffrey.  Likewise, we play really well against David Lin and Gabs.  Interestingly, we play almost exactly as predicted when we play Aaron.  This probably has interesting implications for future predictions.  So does this mean David's rank isn't indicative of his team's ability?  And more pressing (for me), does this mean Jeffrey's team is grossly overrated?
Maybe not.  Still sorted by "Points against," this shows that Jeffrey's team's "Points for" is 109.775 points higher than my calculated average "Points against."  The only other two teams to come out in the blue are Tim's and mine, with 37.1025 and a decisive 136.1425, respectively.

Here it is in graphical form:

And now for a quick re-ranking, sorted by the difference in "Points for" and my calculated "Points against":
So yes, David Lin might be right.  Even though his team's "Points for" is less than my calculated "Points against" for his team, it's not by much.  The only other team to experience a significant change is Eric's - no doubt boosted by his wins over Jeffrey's and my teams. In the end, I'm mostly relieved that my team still ended up on top.

A few closing points:
  • In general, it makes sense that Jeffrey's and my Points Against are pretty low, because we only face one of the top two scoring teams (ourselves).
  • We realize that this is slightly flawed because it uses the average weekly score from each team, and we all know that our scores vary widely from week to week.  Which is why... We're going to do more analysis next week!  Stay tuned.