Some statistics on year-to-year consistency, 2005-2007

[Bongle]

I made a bunch of these last year comparing 2005 and 2006 performance among teams. Basically, I made some scatter plots that showed that performance in a given year basically absolutely doesn't predict performance in the next. Top seeds in 2005 were ending up anywhere from top seed again to nearly dead last in 2006.

With the 2007 regionals done, I again collected all the data. Since 2005 and 2007 are purported to be similar, it would stand to reason that well-performing teams in 2005 would again do well in 2007. Does the data support this? Not really, though someone in stats class could probably do some tests to see if there is any statistically significant trends going on.

How to read the charts:
A team's performance in a year is given a value from 0 to 1, indicating the average percentage they placed in whatever regionals they went to that year. So a team that came 10th out of 60 and 20th out of 40 would be plotted along some axis as a 0.33 ((0.167 + 0.5)/2 = 0.33). Along the x axis is their performance in the earlier year, and along the y axis is their performance in the later year.

Areas:
Top left: teams that did well in the earlier year, poorly in the later year
Top right: Teams that did poorly both years
Bottom left: teams that did well both years
Bottom right: teams that did poorly in the earlier year, then got better in the later year.

Things you can kind of draw from these graphs:
-Teams that got top seed in a given year tend to not turn into bottom-performers the year after
-Likewise, teams that got near bottom seed in a given year tend to not turn into top seeds the year after
-There seems to be LESS correlation between 2005 and 2007 performance (both arm years) than between 2005/2006 or 2006/2007. I explain this by saying that since students graduate, there is much possibility for team quality varying as time passes. Even though you have the constructed 2005 arm, if everyone that knows about construction, maintenance, and operation of it has graduated, then it isn't going to help you.
-So long as you're not bottom seed or top seed, it is difficult to predict much about your performance the following year
-I plotted average performance for the 3 years versus team number. There is a VERY slight correlation between team number and performance.

Graphs:
20052006.PNG - 2005 performance along x axis, 2006 performance along y axis
20062007.PNG - 2006 performance along x axis, 2007 performance along y axis
20052007.PNG - 2005 performance along x axis, 2007 performance along y axis
teamPerformance.PNG - Team number versus averaged performance in years 2005-2007. So if a team placed 20% in 2005, 15% in 2006, and 10% in 2007, then they would be plotted at position (teamNumber,0.15). Remember, lower is better!

That's enough explaining of graphs. I also looked at some other stuff:
Of the 418 teams for which I have data (many 2005 regionals are missing standings so I don't have the whole set), only EIGHT had an average top 20% placing in each of the three years. Those teams are 365, 118, 25, 254, 703, 126, 987, and 111. If you restrict it to top 10% placing in each year, then only 365 gets that honour.