What passer rating is, and what it is not
Passer rating is a weighted average of four passing rates, rescaled so that the league-average performance of the early 1970s produced a rating near 66.7 and a theoretical maximum produced 158.3. The NFL adopted it in 1973 after a committee chaired by Don Smith of the Pro Football Hall of Fame was asked to replace a ranking system that shuffled quarterbacks by their standing in each category rather than by any absolute measure.
It rates the pass, not the quarterback. Rushing yards, sacks taken, fumbles, third-down conversion and the ability to keep a play alive are all outside the formula. A quarterback who runs for 700 yards and 8 touchdowns gets no credit at all. So does a quarterback who takes 55 sacks avoid all penalty. This is the formula's most important limitation and the reason ESPN's Total QBR and the various expected-points-added measures exist.
The 0 to 158.3 scale confuses almost everyone who meets it. It is not a percentage and it is not out of 100. The ceiling exists because each of the four components is capped at 2.375, and four capped components give (4 × 2.375 ÷ 6) × 100 = 158.333, printed as 158.3. The floor is 0 because each component is also floored at zero.
The four components and the caps that shape them
Each component converts one rate into a number that is 0 at a defined floor and 2.375 at a defined ceiling.
a — completion percentage. a = (Cmp÷Att − 0.3) × 5. Zero at a 30% completion rate, capped at 77.5%. In 1973 a 30% completion rate was a plausible bad game; today it is nearly unheard of, which is one reason modern ratings drift high.
b — yards per attempt. b = (Yds÷Att − 3) × 0.25. Zero at 3.0 yards per attempt, capped at 12.5. This is the component that separates quarterbacks in practice, because completion percentage and touchdown rate cluster tightly while yards per attempt does not.
c — touchdown rate. c = (TD÷Att) × 20. Zero at no touchdowns, capped at 11.875% — a rate roughly double what a very good season produces, so this component almost never caps over a full year.
d — interception rate. d = 2.375 − (Int÷Att) × 25. This is the only component that runs downward. It reaches its 2.375 ceiling at zero interceptions and hits zero at a 9.5% interception rate.
Clamp before you sum. This is where hand calculations fail. Each component is clamped to [0, 2.375] individually, then the four are added, divided by six and multiplied by 100. Summing raw values and clamping the total gives a different, wrong answer whenever any component is outside the range — which is exactly what happens on a perfect-rating line, where the raw completion component is 3.5 and the raw touchdown component is 5.0.
The college game uses a different formula entirely: (8.4·Yds + 330·TD − 200·Int + 100·Cmp) ÷ Att, with no caps. It rewards deep passing far more heavily and produces numbers on a wider scale, running from −200 to a theoretical 1,261.6. The two are not interchangeable and a college rating cannot be compared to an NFL one.
Worked example: Peyton Manning, 2004
Manning completed 336 of 497 passes for 4,557 yards with 49 touchdowns and 10 interceptions. Compute each component, clamp, then combine.
- a. 336 ÷ 497 = 0.676056. (0.676056 − 0.3) × 5 = 1.88028. Inside the range.
- b. 4,557 ÷ 497 = 9.169014. (9.169014 − 3) × 0.25 = 1.542254. Inside the range.
- c. 49 ÷ 497 = 0.098592. × 20 = 1.971831. Inside the range, though close.
- d. 10 ÷ 497 = 0.020121. 2.375 − (0.020121 × 25) = 2.375 − 0.503018 = 1.871982. Inside the range.
- Sum. 1.88028 + 1.542254 + 1.971831 + 1.871982 = 7.266347.
- Divide and scale. 7.266347 ÷ 6 = 1.211058. × 100 = 121.1.
No component was capped, which is typical of a great full season: the caps bind on single games, not on 497 attempts. For contrast, run a perfect line through the same steps — 20 completions in 20 attempts for 250 yards with 5 touchdowns and no interceptions. Raw a = (1.0 − 0.3) × 5 = 3.5, clamped to 2.375. Raw b = (12.5 − 3) × 0.25 = 2.375, exactly at the ceiling. Raw c = 0.25 × 20 = 5.0, clamped to 2.375. Raw d = 2.375. Sum = 9.5, and 9.5 ÷ 6 × 100 = 158.333.
Run Manning's line through the NCAA formula for comparison: (8.4 × 4,557) + (330 × 49) − (200 × 10) + (100 × 336) = 38,278.8 + 16,170 − 2,000 + 33,600 = 86,048.8, and 86,048.8 ÷ 497 = 173.1. Same passing line, completely different scale.
How to read a passer rating
Read the rating against its era, because passing efficiency has risen steadily. When the formula was adopted, a rating near 66.7 was intended to represent an average season and the low 80s marked a good one. In the modern NFL a league-average season sits closer to 90, roughly 100 marks a genuinely good year, 110 and above puts a quarterback among the best in the league, and anything below 75 is a starting job in danger. A 158.3 over a full game is a rare event; over a season it is impossible.
Then look at which component is driving the number. The calculator's component table exists for this. A rating of 95 built on a 70% completion rate with 6.4 yards per attempt describes a checkdown offence; the same 95 built on 60% completions with 8.6 yards per attempt describes a vertical one. Yards per attempt carries the real information, because the other three components compress into narrow ranges across the league.
Finally, mind the sample. The formula is unstable at low attempt counts — a single 40-yard touchdown on eight attempts can swing a rating by more than 40 points. The NFL requires 14 attempts per scheduled game to qualify for the passing title precisely because of this.
What each component needs to reach its ceiling and its floor
| Component | Formula | Value giving 0 | Value giving 2.375 |
|---|---|---|---|
| a — completions | (Cmp/Att − 0.3) × 5 | 30.0% completions | 77.5% completions |
| b — yards | (Yds/Att − 3) × 0.25 | 3.0 yards per attempt | 12.5 yards per attempt |
| c — touchdowns | (TD/Att) × 20 | 0.0% touchdown rate | 11.875% touchdown rate |
| d — interceptions | 2.375 − (Int/Att) × 25 | 9.5% interception rate | 0.0% interception rate |
The ceilings follow directly from the formulas: 0.3 + 2.375/5 = 0.775; 3 + 2.375/0.25 = 12.5; 2.375/20 = 0.11875; 2.375/25 = 0.095.
Mistakes that produce a wrong passer rating
- Summing the raw components and clamping the total. Each component is clamped individually, before the sum. This is the error that makes hand calculations of high-rating games come out wrong.
- Forgetting the 0 floor on component d. A 20% interception rate gives a raw d of −2.625, which is clamped to 0, not carried through as a negative.
- Using the NCAA formula on an NFL line. The college formula has no caps and a completely different scale. A 173.1 college rating and a 121.1 NFL rating can describe the same passing line.
- Subtracting sack yardage from passing yards. Passer rating uses gross passing yards. Net yards after sacks belong in adjusted net yards per attempt, a different statistic.
- Reading the scale as a percentage. The maximum is 158.3, not 100, and the value has no direct probabilistic meaning.
- Comparing across eras without adjustment. The 1973 calibration put an average season near 66.7. A modern average season is closer to 90 on the identical formula.
Where the formula comes from
The NFL adopted the passer rating in 1973 on the recommendation of a committee that included Don Smith of the Pro Football Hall of Fame, Seymour Siwoff of the Elias Sports Bureau and Don Weiss of the NFL. The four components were calibrated against historical league data so that an average performance scored 1.0 in each component — giving a rating of (4 ÷ 6) × 100 = 66.7 — and a performance at roughly the record level for that category scored 2.375. The NFL Record and Fact Book publishes the formula unchanged each year. The NCAA adopted its separate, uncapped passing efficiency rating in 1979.
What to use instead of, or alongside, passer rating
Passer rating's blind spots are structural, not fixable. It ignores sacks, rushing, fumbles and situation. Three widely used alternatives address different parts of that gap.
Adjusted net yards per attempt (ANY/A) folds sacks and sack yardage into the denominator and applies bonus and penalty terms for touchdowns and interceptions, all on a yards-per-play scale that is easy to reason about. It correlates better with team scoring than passer rating does.
Total QBR incorporates every play a quarterback is involved in, including scrambles and sacks, weights each by its expected-points impact, and adjusts for the strength of the defence faced. It is proprietary and cannot be computed from a box score, which is its main practical drawback.
Completion percentage over expected uses tracking data to estimate how likely each individual throw was to be completed given its depth, the receiver's separation and the pressure on the passer, then measures the quarterback against that expectation. It is the passing equivalent of expected-goals models in soccer and hockey.
The same design tension — simple box-score rate versus context-adjusted model — runs through every sport. True shooting percentage and save percentage are the box-score end of the spectrum in basketball and hockey; expected goals and shot-quality models are the other end. On the baseball side, on-base percentage and slugging percentage combine into OPS the same way passer rating combines four rates, and with the same objection: the weights are conventional rather than derived from run or point values.
Key terms
- Component cap
- The clamp of each of the four terms to the range 0 to 2.375, applied before summing. It is what produces the 0 and 158.3 endpoints of the scale.
- Perfect passer rating
- 158.3 — achieved when all four components sit at 2.375, which requires at least 77.5% completions, 12.5 yards per attempt, an 11.875% touchdown rate and no interceptions.
- NCAA passing efficiency
- The uncapped college formula, (8.4·Yds + 330·TD − 200·Int + 100·Cmp) ÷ Att. Rewards yardage far more heavily and uses a different scale.
- ANY/A
- Adjusted net yards per attempt — a sack-aware alternative that expresses passing efficiency in yards per dropback rather than on an abstract scale.