How the ratings and strength of schedule work

Each set of ratings covers one group of teams, like FCS football. Every number uses only games where both teams are in that group that season. For FCS, a trip to an FBS power is left out, so buying one doesn't inflate a schedule. A game against a Division II or III school is left out too, so scheduling one doesn't drag a schedule down. Those games still appear on each team sheet, labeled with the opponent's level, for example "Arizona (FBS)".

Strength of schedule is an average per game, not a total. A team that has played eight FCS opponents and one that has played five are measured on the same scale: how hard each game was, on average.

The ratings use only game results. They don't use any poll, including ours.

Each team gets a strength in points: how many points better than an average team in its group on a neutral field. Strengths come from the margin of every counted game:

margin(home − away) ≈ strength(home) − strength(away) + home field

• Margins count up to a cap (for FCS football, 35 points). Running up the score earns nothing past it.
• An overtime game counts as at most 3 points either way, because overtime is close to a coin flip.
• Home field is estimated from the games each week. The fitted value is printed with every run, and neutral-site games get none.
• Before any games, each team starts at a share of its final strength last season. That starting point counts like a couple of games, so by midseason a team's own results dominate. A team new to the group starts below average, because reclassifying programs usually are.
• The math is least squares with that starting point (Bayesian ridge regression). Strengths are centered so the average team is 0.

For schedule numbers, each opponent's strength is computed without its games against the team being measured. Blowing a team out lowers that team's strength, and it shouldn't also lower your own schedule. The NCAA's RPI does the same thing by dropping head-to-head games.

Every schedule number is measured against one fixed yardstick, a #25-level team: a team as strong as the 25th-best team in these ratings usually is at the end of a season (strength B, the median over recent seasons). It comes from these ratings, not from any poll, and it stays fixed for each method version. For each counted game, ask how often a #25-level team would lose it:

p = Φ( (opponent strength + opponent's site edge − B) / σ )
SOS = average p over the team's counted games, shown 0–100

Φ is the normal curve. σ is how many points a game typically misses its expected margin by, fitted from past results. The opponent's site edge is plus home field if they hosted, minus it if they visited, and zero on a neutral field.

Example for FCS football (B = 8.98, σ = 14.72): an opponent 5 points better than a #25-level team, at their place (about +2), gives p = Φ(7 / 14.72) = 0.683. That game adds 68.3 to the average.

Why a #25-level yardstick instead of averaging opponent strengths? For a contender, one great opponent plus one terrible one isn't the same as two average games, and a plain average would treat them as equal. The yardstick is fixed for each method version, so a schedule's SOS moves only when its opponents' strengths move.

Remaining SOS uses the same p for unplayed games. Teams need 3 counted games for an SOS rank; below that the value shows as a small sample.

Strength of record asks how hard this team's record was to get. Give a #25-level team this exact schedule, at these sites, and work out the exact chance it wins at least as many games:

SOR = P( #25-level team wins ≥ this team's wins ), winning each game with probability 1 − p

Lower is more impressive. Going 10-0 against a strong schedule might be 4%; against a weak one, 30%. Rank 1 is the lowest SOR. A team's own margins never enter, only its wins and losses. This is the default order of the ratings table.

Power is the number for predicting games: a team's strength in points. Team A is expected to beat Team B on a neutral field by Power(A) − Power(B). Recent games can count a little more; each pool's setting is in the table below.

Strength of victory (SOV) is SOS over wins only: how good were the teams it beat. Strength of loss, SOS over losses, is on each team sheet. Higher means more forgivable losses.

Record SOS is the NCAA RPI's schedule part, from records only and counted games only: two-thirds opponents' win percentage plus one-third their opponents' win percentage, leaving out games against the team itself. It's a cross-check anyone can reproduce in a spreadsheet.

Tiers sort each game by p, which already includes the site. Tier 1: the opponent, at that site, would be favored over a #25-level team. Tier 2: it beats that team 25–50% of the time. Tier 3: 10–25%. Tier 4: under 10%. Each team sheet shows its record in each tier, like the quadrants on NCAA basketball team sheets.

Ratings are estimates, and early in the season they lean on last season. Until the teams in a group are connected by games, or average fewer than 4 games each, the whole table is marked provisional. Each team sheet also shows a likely range for its Power rank, from 1000 plausible sets of strengths drawn from the fit's margin of error.

• Scores, sites, and overtime come from ESPN. If ESPN is down during a weekend, final scores from NCAA.com fill in until ESPN returns.
• Who is in each group, and each team's conference, come from ESPN for that season, so moves between levels and conferences are handled.
• Ratings publish on their own once the week's last game is final, usually early Sunday morning, or after a Monday game when the week has one. Score corrections from ESPN are picked up for 10 hours after the week's last kickoff; after that a week's numbers don't change on their own. A game moved to midweek counts the following week.
• Each published week is kept exactly as published, with its method version and a checksum of every input.

These were chosen by replaying past seasons: rate with only the games played so far, predict the next week, score the predictions, and keep the settings that predicted best. The season after the ones used to choose them is the honest test. See each pool's accuracy page.