TWISTR is an iterative least-squares, score-based ratings system built in the spirit of an Elo model. Team ratings are agnostic to the final result of a game - only the scoring margins are important, as no additional benefit is provided for a win or penalty for a loss.
The SoS rating represents the expected winning percentage of a strong team against that school's schedule. The SoS rating is calculated twice, once for the All Classes ratings and once for the Class ratings. A lower SoS rating represents a lower expected winning percentage and, thus, a tougher schedule.
The TWISTR ratings calculate All Classes and Class-specific SoS ratings, as what constitutes a bad schedule for a 4A team may represent a good schedule for a 1A team. The aims of teams when prepraring for the tournament are different from Class 1A through Class 4A, so in the Class ratings, teams' schedules are only compared to similar schools'.
TWISTR uses a 90th-percentile team, either overall or within the team's class, as the reference for SoS ratings. This roughly represents the average sectional champion in a given class, or an average regional finalist in a single-class setup.
Determining an SoS metric is an inexact science, but the TWISTR SoS calculation is predominantly driven by a desire to recognize two factors: (1) that most SoS discussions center around contending teams - hence the 90th percentile reference point - and (2) that playing 10 great teams and 10 bad teams probably represents a tougher schedule than playing 20 average teams.
A team's SoR rating compares the team's actual winning percentage in rated games to its SoS rating. Like SoS ratings, SoR is calculated twice, once for the All Classes ratings and once for the Class ratings. A positive SoR rating indicates a better record than a strong team would be expected to have, while a negative SoR rating indicates a worse record. Note that SoR ratings remove any effect that head-to-head results may have had on an opponent's rating.
The SoR rankings can be considered as TWISTR's poll ballot if it had a vote. It's also designed as a great candidate to seed teams, as it does not consider a team's margins of victory or its potential, only its objective accomplishments against the schedule the team has played. To a degree, team ratings can be gamed, but SoR cannot be on a nightly basis.