The following article was a contribution by Groger Ranks member Arjun Nageswaran
On November 3, 2018, ACF Fall mirrors nationwide and even outside of the United States took place, putting to test many beginning college players (and some top college teams, apparently). This set, like other ACF sets, had no powers and was also closed to high schoolers. It would thus seemingly be non-relevant for Groger Ranks, as we only rank high school teams obviously and also require powers in our ranking formula.
ACF Fall, however, also had one dedicated HS mirror at UIUC, and at their UCLA mirror special dispensation was given to a high school to play. With top tier schools like Detroit Catholic Central, University Lab, IMSA, Auburn, and Canyon Crest all playing ACF Fall, a rare tournament at this point of the year with an above hs-regs difficulty, this set would have been the perfect one for our rankings, quite possibly even more important than Penn Bowl 2018 (another college set where HS teams made an impact). Nevertheless, the problem remained: how could we adjust for powers?
After a lot of deliberation, I chose to try to find a new formula for Groger Ranks just for ACF Fall which would increase the weight of PPB, while trying not to inflate or deflate scores as a result. To do so, it would be necessary to see if there was a correlation between PPB and powers per game, find the formula for the aforementioned correlation, and substitute it into the Groger Ranks formula.
To test out this formula, I copied our spreadsheet of the Groger ranks data on IS 177 specifically (since that is our baseline set, with an adjustment of 0 and with the most data) to try to test out what a possible correlation would look like. Using the powers per game and ppb data of the ranked teams, I had this scatterplot filled out, with a line of best fit drawn through it. Using another website to calculate the formula of this regression line, I found that the PPB was equivalent to .9528(powers per game) + 15.7, with an R^2 of .715. To find the inverse, I got that powers per game equaled (PPB-15.7)/.9528 with R^2 staying put.
Now, it came time to test this new formula. I was pretty confident in having such a high R^2, and felt I had solved the problem of a powerless set in a power-dependent rankings system. Using this new formula, I then applied it to the IS 177 teams to see how the Groger Scores would have been affected if IS 177 was hypothetically also powerless and we had used the new formula instead to sort of project the powers per game and then insert that into the Groger Score formula. The results were…not at all good.
A lot of shifts occurred, with Hunter A most notably dropping 12.20492615 Groger Points, making it no longer the top IS 177 team. The largest gain from the new formula was 23.2225021 points. The largest loss was of 26.12925588 points. Given the cluster of teams in the Groger Ranks with very similar Groger Scores, this new formula would mess up everything. It was here that we decided to abandon the idea.
Less than an hour later, after sharing the findings of this disastrous set with Dylan of Uni Lab, he suggested another idea: instead of doing linear regression, to try to do a polynomial regression instead. My impatience with the last test made me skip the graph and the r^2 and everything, and go directly to an online calculator to find an equation for a polynomial graph of best fit. I did get a formula of y = -1.440133015·10^-2 x^2 + 1.366065477 x – 16.74017403. Using the same IS 177 data as I had used before, I calculated new Groger Scores for IS 177 using projected power values and found an average difference in Groger Scores of 0.00000001410846947. This stunningly low number would surely mean that I had found the formula to finally Groger Rank the ACF Fall set. Then, I decided to find the maximum gain and loss in Groger Scores.
Once more, I was to be disappointed. There was a maximum gain of 15.5648515 Groger Points and a maximum loss of 17.80843159 Groger Points. This was better than the line of best fit to be sure, but a variance of 15-18 in the Groger Score was too much to risk for one set.
As a result of these failed ventures to Groger-ify ACF Fall, we have decided to not calculate any adjustment for it and not include it in our rankings. While this is a very important set in terms of both its difficulty and the schools who played it, ultimately it is not worth sacrificing the integrity of our rankings. There will be more high difficulty sets played by top level teams in the future, so that will overcome any potential losses of ignoring ACF Fall.
If there are any suggestions from the community about how we can fix this to adjust for ACF Fall, please let us know by emailing firstname.lastname@example.org or filling out the “Contact” form. Until then, ACF Fall will not be counted. If you were excited to see how last week’s ACF Fall tournaments would shake up the rankings, you may be in for an unpleasant surprise.
Arjun Nageswaran is currently a sophomore at Adlai E. Stevenson High School in Lincolnshire, Illinois