Steps in PANTS:
1. Collect the number of powers (if applicable), 10-point tossups, and negs for each team. Also collect the number of games played or tossups heard for each team and each team's bonus conversion.
2. Obtain a "strength of schedule (SOS) factor." This can include:
- Average Tossup Points per Tossup Heard (TPTH) of a site, divided by the average TPTH of all teams (or equivalently tossups per game, but I'm generalizing here).
- Average Bonus Conversion of a site, divided by the average BC of all teams.
- An average of Opponent's TPTH (calculated either using or not using games played against that team) weighted by the number of times a team plays each opponent, divided by the average Opponent's TPTH of all teams
- Weighted average of Opponent's Powers per Tossup Heard, Tens per Tossup Heard, and Negs per Tossup Heard as calculated above (3 different SOS factors)
- Some other statistic that you like using that accurately categorizes how strong each site's field is.
4. Compute the Points Per Game (or PP20H) against an average "normalized" team using the formula:
Adj_Powers*15+Adj_Tens*10+Adj_Negs*(-5)+(Adj_Powers+Adj_Tens)*BC
This (the "PANTS") is a measure of how many points a team would be expected to score in a game against a totally average team in the field.
ADVANTAGES OF PANTS:
- Clearly and unambiguously ranks teams across different sites; furthermore, gives a reasonable assessment of each team's strength expressed in units that make intuitive sense (points per game)
- Takes into account the exact way in which tossups and bonuses affect a team's score
- Works with any number of sites/teams and on any non-terrible format (may work for terrible formats too)
- Depending on what you choose for your strength-of-schedule factor, can be quickly and easily computed with an Excel spreadsheet
- PANTS was developed while thinking about S-values and first computed with 2009 SCT D1 statistics, but it is stressed that PANTS is not intended as an S-value for this or future years. Several critical flaws preclude PANTS as it is proposed; however, it may be possible to modify PANTS to lessen or circumvent these flaws.
- In PANTS, it is always better to answer a question than to not do so. I have not yet looked into forfeits, but one simple idea (stolen from previous ramblings in the S-value thread) is that teams that do not show up receive 0 points in 20 tossups (and do not count that opponent in any weighted SOS factors).
- It is as-yet unknown to what degree intentional gaming of the system to drop to a lower playoff bracket (and thus artificially inflate adjusted tossups) affects the system. It is hypothesized that the SOS factor, if chosen correctly, can account for a team playing in a much weaker field, but does not completely account for a team playing in a lower bracket within the same field.
- It is hypothesized that the average conversion ratio (D2 conversion/D1 conversion) on common tossups/bonuses should yield a measure of how the "D2 average opponent" would compare to the "D1 average opponent." Therefore multiplying the D2 SOS factor by the conversion ratio for tossups and the D2 BC by the conversion ratio for bonuses should adequately scale D2 vs D1 fields/packet sets. Similarly, a conversion ratio should yield a measure of CCCT vs D2 "average performance" on tossups; thus, multiplying the CCCT SOS factor by the conversion ratio for tossups should allow for easy insertion of CC schools into the D2 ICT list (alternatively, one could recalculate everything with the CCCT as an additional site; it is unknown how this will affect PANTS).
- It is unknown whether PANTS "almost always" invites a higher-finishing team over a lower-finishing team with better statistics. Plotting each team's within-sectional reported finish against each team's within-sectional PANTS ranking yields an R^2 of 0.9739, but it is unknown whether this holds for other years/divisions or how the addition of D1 teams playing on D2 sets will affect it.
- A comparison of different SOS factors is possibly necessary.
- I have "proof-of-concept" with 2009 D1 SCT data (largely because I had already calculated most of what I needed back when I was looking at crazier things) and need to verify its usefulness on ACF-style tournaments.
- PANTS can be converted into an expected winning percentage by the formula 1/(1+(T2/T1)^EXP), where T1 and T2 are the PANTS for teams 1 and 2. This formula is similar to that for "Pythagorean" win-loss except that it does not use points against/scored but a team's expected points against an average team. It is yet to be determined what exponent EXP works best. Attempts to convert this to a Bradley-Terry model, which appears to be the more statistically correct thing to do, have so far failed due to improper scaling factors. I'm not sure what the purpose of this would be, but it looks cool.