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Passer Rating, Explained

After reading this you can compute an NFL passer rating and an NCAA passing efficiency rating by hand, explain why the NFL scale tops out at 158.3, and read either number without overrating it.

What passer rating measures

Passer rating is a single number that grades a quarterback's stat line from a game or a season. The NFL version runs from 0 to 158.3. The NCAA version, called passing efficiency, uses a different scale that has no fixed cap and where anything above 150 is very good.

Both formulas take the same four ingredients: completion percentage, yards per attempt, touchdown percentage and interception percentage. Nothing else. Sacks, rushing, fumbles and game situation do not enter. That narrow scope is the whole point and also the main limitation.

Here is the hook. In the 1994 season Steve Young posted 324 completions on 461 attempts for 3969 yards, 35 touchdowns and 10 interceptions. Plug those into the NFL formula and you get about 112.8, an all-time record at the time. The number rewards him for completing 70.3% of his passes while throwing a touchdown on 7.6% of attempts and an interception on only 2.2%.

When to use it, and when not to

Use passer rating to compare passing lines quickly and to settle "who had the better day" arguments where both quarterbacks threw a similar number of passes. It is a fair summary of the four things it counts.

Do not use it to declare who is the better all-around player. A quarterback who scrambles for 60 yards and a touchdown gets no credit. A quarterback sacked eight times pays no penalty. And on very small samples the number swings wildly: one interception in five attempts drives the interception term to its floor and tanks the rating, while three attempts for three touchdowns can pin every term at the ceiling.

Rating is unstable below roughly 15 attempts. A backup who goes 2 for 3 for 40 yards and a touchdown can post a "perfect" 158.3 that tells you almost nothing about his ability.

The NFL formula and the intuition behind it

The NFL rating is the average of four component scores, each scaled so that its middle sits near a typical performance and its edges are clamped. Define the four raw rates first, with C completions, A attempts, Y yards, T touchdowns and I interceptions.

a = \left(\frac{C}{A} - 0.3\right) \times 5

The completion term a takes completion fraction, subtracts 0.3 (so a 30% passer scores zero) and multiplies by 5 (so an 80% passer scores 2.5 before clamping).

b = \left(\frac{Y}{A} - 3\right) \times 0.25

The yards term b centers on 3 yards per attempt as the zero point and gives 0.25 points per extra yard, so 11 yards per attempt reaches 2.0.

c = \frac{T}{A} \times 20

The touchdown term c awards 20 points per unit of touchdown rate, so a touchdown on 11.875% of attempts hits the ceiling of 2.375.

d = 2.375 - \left(\frac{I}{A} \times 25\right)

The interception term d starts at the maximum 2.375 and subtracts 25 per unit of interception rate, reaching zero at 9.5% interceptions.

Each of a, b, c, d is then clamped to the range 0 to 2.375. Finally:

R = \frac{a + b + c + d}{6} \times 100

Add the four clamped terms, divide by 6, multiply by 100. The maximum is four terms at 2.375, which gives \frac{9.5}{6} \times 100 = 158.33, rounded to 158.3. That is where the famous ceiling comes from.

A worked example with the demo numbers

24 of 35 for 285 yards, 3 touchdowns, 1 interception

These are the tool's default values. Work each term to four figures.

  1. Completion rate is 24 / 35 = 0.6857. Then a = (0.6857 - 0.3) \times 5 = 1.929. Inside 0 to 2.375, keep it.
  2. Yards per attempt is 285 / 35 = 8.143. Then b = (8.143 - 3) \times 0.25 = 1.286.
  3. Touchdown rate is 3 / 35 = 0.08571. Then c = 0.08571 \times 20 = 1.714.
  4. Interception rate is 1 / 35 = 0.02857. Then d = 2.375 - (0.02857 \times 25) = 1.661.
  5. Sum is 1.929 + 1.286 + 1.714 + 1.661 = 6.589. Rating is \frac{6.589}{6} \times 100 = 109.8.

So the demo line scores about 109.8 on the NFL scale. A number above 100 signals a clearly good game.

The NCAA passing efficiency formula

College football uses a different, older formula that is not averaged or clamped. It weights the same four inputs directly.

E = \frac{8.4 Y + 330 T - 200 I + 100 C}{A}

Here Y is yards, T touchdowns, I interceptions, C completions and A attempts. Each completion is worth 100, each touchdown 330, each yard 8.4, and each interception costs 200, all divided by attempts.

Run the demo line through it: 8.4 \times 285 = 2394, plus 330 \times 3 = 990, minus 200 \times 1 = 200, plus 100 \times 24 = 2400. That sums to 5584. Divide by 35 attempts and you get 159.5. Notice this is close to the NFL number here by coincidence; the scales are not comparable in general.

A common reference point: an NCAA efficiency of 100 is roughly average, 150 is strong, and single-game marks above 200 happen when a passer throws several touchdowns on high yardage with no picks.

Reading and interpreting the number

On the NFL scale, treat the ranges below as rough guides for a full game or season, not hard cutoffs.

Rough interpretation of NFL passer rating
RatingReadingExample line (35 att)
Below 70Poor15 comp, 150 yd, 0 TD, 2 INT
70 to 90Average21 comp, 230 yd, 1 TD, 1 INT
90 to 110Good24 comp, 285 yd, 3 TD, 1 INT
110 to 130Excellent27 comp, 330 yd, 3 TD, 0 INT
158.3Perfect (clamped)All four terms maxed

The chart below shows how the rating moves as you change one thing at a time, touchdowns, starting from the demo line of 24 of 35 for 285 yards and 1 interception.

Each touchdown adds about 9.5 points until the touchdown term clamps at 2.375 (near 4 touchdowns on 35 attempts), after which extra scores add nothing.

See the clamping for yourself

With 24 of 35 for 285 yards and 1 interception, adding touchdowns raises the rating by about 9.5 points each until roughly the fourth touchdown, where the touchdown term hits its 2.375 ceiling and the rating freezes at 109.8. That flat top is the clamp at work.

Common mistakes

The errors below account for most wrong answers people get by hand.

  • Forgetting to clamp. If you compute c = 3.5 for a five-touchdown game and leave it, your rating is too high. Clamp each term to 2.375 first, then average.
  • Using percentages instead of fractions. The completion term uses C/A as a fraction like 0.686, not 68.6. Multiply by 5 after subtracting 0.3, not by 5 after subtracting 30.
  • Mixing scales. A 158.3 is the NFL maximum; a 158.3 in NCAA terms is merely a solid game. Never compare the two numbers directly.
  • Averaging by 4. The final divisor is 6, not 4, because the maximum term sum is 9.5 and the designers wanted the top to land at 158.3.

Related tools

If you like reducing a box score to one honest number, these calculators do the same job for other sports. For baseball hitting, see the Batting Average & OPS Calculator, and for pitching the ERA & WHIP Calculator. Basketball scoring efficiency lives in the True Shooting % Calculator. To estimate wins from points scored and allowed across several leagues, use the Pythagorean Expectation Calculator. Cricket fans can track a chase with the Cricket Run Rate Calculator.

Frequently asked questions

Why is a perfect passer rating 158.3 and not 100 or 150?

Each of the four terms caps at 2.375, so their sum caps at 9.5. Dividing by 6 and multiplying by 100 gives \frac{9.5}{6} \times 100 = 158.33, shown as 158.3.

Can passer rating be negative?

No. Each term is clamped at a floor of 0, so the lowest possible rating is 0, reached when completion, yards and touchdown rates are at or below their zero points and interceptions are at or above 9.5% of attempts.

What is a perfect NFL line?

Any line where all four terms hit 2.375: at least 77.5% completions, at least 12.5 yards per attempt, a touchdown on at least 11.875% of attempts, and zero interceptions. Many different stat lines qualify.

Why does NCAA efficiency have no upper limit?

The college formula adds weighted counts and divides by attempts without clamping any term, so a game with many touchdowns and high yardage can exceed 200. It was never designed to fit a fixed 0 to 158.3 range.

Does passer rating count rushing or sacks?

No. Both formulas use only completions, attempts, yards, touchdowns and interceptions from the passing line. A modern statistic called Total QBR adds rushing, sacks and context, but that is a separate model.

These figures are educational estimates for sport and training purposes, not professional coaching advice.

Try it yourself in the tool

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