Today, we look at conference strength. I do the conference thing every so often because people cannot wrap their brains around the idea that it is not an absolute thing. Yes, certain conferences are very good on average. "Average" means over the span of years, and simply does not apply to a single season. One of the pillars of scientific (and so statistical) thought is this:
Never attempt to apply a specific case to a general one, and never attempt to apply a general case to a specific one.
This is why Moneyball works over the course of a season and then gets thrown out the window in the playoffs (kind of - I really hate the shift, but if Ted Williams can learn to hit against it these others should have to learn as well).
I broke this down in depth here. It suffices to say that conference strength isn't what most people seem to think it is.
Who's the Best?
"But what's it all mean, Ray?" As per the link above, these are relative rankings based on the sum of the average 1st, 2nd, and 3rd level points for each team in each conference.
For example, the ACC score is 0.3827. That is derived from each ACC team's 1st, 2nd, and 3rd level points.
The sum of all ACC 1st level points is 2.8111, and the average is 0.2008. Do the same for 2nd and 3rd level points (1.3808 & 0.0986 and 1.1653 & 0.0832 respectively). Then sum the averages to get 0.3827
"Ok, great, but how do we use the info?" Going back to the above link again, it works like this:
If
2 conferences were exactly tied, and we took an "average" team from
each conference and made them play 1000 games, we expect each team to
win 500. Pretty basic, right?
The B1G is top dog right now. The ACC is only 67.3% as good as the B1G. That means that if we took an average team from each conference and made them play 1000 games, we would expect the ACC team to win 337 games (rounded up) and the B1G team to win 663 games. In other words, we expect the ACC team to win 67.3% of the 500 games they should win if the conferences were equal. We would also expect the B1G to win its 500 plus the 163 unrealized wins from the ACC (500x67.3%=337; 500-337=163).
Clear as mud? Here's the thing: you can't use rankings to determine if your conference is good or not. I found this post that is more in depth than I can follow, but it produced a few nuggets for us. Most importantly, voted rankings are ordinal.
"Ordinal data is classified into categories within a variable that have a natural rank order. However, the distances between the categories are uneven or unknown."
You cannot math ordinal rankings or classifications. This is very explicitly evidenced by RJ Young's "tiers." What is the actual distance between #1 and #2? No clue. There is literally no way to tell with Young or Klatt or the AP or USA Today or the CFI committee.
Knowing this, to say that your team is better because it beat 3 ranked opponents to only 1 by the other team is ignorant. I don't mean that as an insult. It's an adjective describing a lack of knowledge.
You good people no longer have that excuse!
"But wait, Ray. You rank teams, too!" Yes I do, but I don't vote. I measure, and that is all the difference in the world. Every number including the relative positions of each team is derived from a calculation using real numbers (wins, losses, scoring differentials, averages, and more). You can tell the gap between #1 and #2 just by looking at the spreadsheet:
Maybe I should change the gap number to a percentage? 14.6% difference here between #1 and #2. Does that mean the Irish are 14.6% better than Wisky? No. It means that Notre Dame has done 14.6% more work, if you will. Imagine 2 teams shoveling sand into sandbags. The number of sandbags is the number of wins, and the amount of sand in each bag represents the "worth" of that win, i.e. a better team is a heavier sandbag. Now take all the sand bags for each team and weigh them. Notre Dame's sandbag total is 14.6% heavier than Wisconsin's. Make sense?
We can do the same thing for conferences, only we need to use averages because of differing numbers of teams per conference (my team points are also modified to account for number of games played).
So we take the Big 10's 14 teams and have them fill their sandbags, then we weigh them all. Let's say that they shovel 7.9561 tons of sandbags (from all 1st, 2nd, and 3rd level teams...er, shovel full?). Then we look at the Big 12's 10 teams' sandbags which weigh 4.9077 tons. You see the problem with just adding things up. We instead take the averages:
Big 10: 7.9561/14=0.5683
Big 12: 4.9077/10=0.4908
The B1G shoveled 13.6% more sand when normalized for the number of teams. Put another way, the average Big 10 win was worth 13.6% more than the average Big 12 win.
And yes, I hate that they won't fix the conference names.
Look, this is one of those things that isn't readily apparent to us because all we see are the rankings from people who vote (ordinals, remember?). It's incredibly difficult to have a conversation regarding this because people hold so tightly to their beliefs, and they hold more tightly the more you challenge them. When the next person says, "My team is better than yours because we beat 3 ranked teams and you only beat 1," ask him/her "How much better?" Then stand firm. They won't be able to answer, but you can give them a hint. Ask by what percentage are they better. When they throw out some made up number, challenge them to show you the math. You won't change his/her mind, but you may just get a bystander to think a little.
Baby steps.
No comments:
Post a Comment