Analysis
NFL passer rating explained: what the formula cannot see
The NFL passer rating explained from the constants up: four capped components, where 158.3 comes from, what the formula ignores, and how to read it honestly.
By CricketTaken EditorialPublished Analysis19 min read
A quarterback finishes a game at 158.3 and the graphic calls it perfect. He was not perfect. He hit four ceilings, and the formula stopped counting.
That single fact does more to explain the NFL passer rating than any walk through the arithmetic, because the ceilings are the point. The rating is not a measurement of quarterback play. It is a scoring rubric written in 1971, adopted in 1973, and left alone ever since, and every one of its famous oddities follows from decisions three men made about how to compress four rate statistics onto one number that a newspaper could print.
The formula survives because it is official. It does not survive because it is good. Those are separate claims, and the interesting work is in the gap between them.
Four rates, four ceilings, and nothing else
Start with what goes in. The passer rating reads five columns of the box score: attempts, completions, passing yards, passing touchdowns and interceptions. From those it builds four rates, each of which is mapped onto its own bounded scale.
a, the completion component, is (completions / attempts - 0.3) x 5.
b, the yards component, is (yards / attempts - 3) x 0.25.
c, the touchdown component, is (touchdowns / attempts) x 20.
d, the interception component, is 2.375 - (interceptions / attempts x 25).
Each result is then clamped. Anything above 2.375 becomes 2.375. Anything below zero becomes zero. Add the four clamped values, divide by six, multiply by 100.
That is the whole thing. It fits on the back of a ticket stub, which was very much the design brief.
Now invert the clamps, because the underlying thresholds are more informative than the coefficients. The completion component reaches its ceiling at a completion percentage of 77.5 and its floor at 30. The yards component tops out at 12.5 yards per attempt and bottoms out at 3.0. The touchdown component maxes at a touchdown on 11.875 per cent of attempts and floors, obviously, at none. The interception component starts at its maximum when a quarterback throws none and reaches zero at an interception rate of 9.5 per cent.
Those eight numbers are the real formula. Everything a passer does outside those bands is invisible.
- 4Components in the rating
- 2.38Maximum value of any one component
- 158.3Arithmetic maximum rating
- 66.7Rating the constants define as average
All four figures are properties of the published formula rather than observations from any season. 2.375 is the ceiling on each component; 158.3 is four ceilings divided by six and multiplied by 100; 66.7 is the rating produced when all four components sit at 1.000, the value the constants treat as average.
Why every component stops at 2.375
The caps are the most criticised feature of the formula and the most defensible one, provided you understand the problem they were solving.
Without a ceiling, a rate statistic computed over a small denominator explodes. A backup who comes on for one snap, completes a 60-yard touchdown and leaves has a completion percentage of 100, a yards-per-attempt figure of 60 and a touchdown rate of 100 per cent. Uncapped, those numbers would produce a rating in the hundreds and it would sit at the top of a leaderboard next to men who had thrown five hundred passes. The caps are, among other things, a containment device for small samples.
They also do something subtler. They stop any single category from dominating the total. The committee wanted four components that each carried a quarter of the weight, and equal weighting only holds if each component has the same range to move in. Give yards per attempt an unbounded upside and it quietly becomes the whole statistic, because it has more room to run than a touchdown rate does. Bounding all four at the same value forces the equal weighting to stick.
That equal weighting is the formula's largest unexamined assertion. It says a quarterback's completion percentage, his yards per attempt, his touchdown rate and his interception avoidance each account for a quarter of what passing is. Nobody demonstrated that. It was assumed, in 1971, and it has been the official position of American professional football ever since.
- Completion percentage39.6
- Yards per attempt39.6
- Touchdown rate39.6
- Interception avoidance39.6
Derived from the formula's own structure, not from any observation. Each component contributes at most 2.375, which after dividing by six and multiplying by 100 is 39.58 rating points. The four blocks are identical by construction, which is the assertion being made. Rounding to one decimal makes the parts sum to 158.4 rather than 158.3.
Show the numbers
| Item | Value |
|---|---|
| Completion percentage | 39.6 |
| Yards per attempt | 39.6 |
| Touchdown rate | 39.6 |
| Interception avoidance | 39.6 |
The cost is severe and it is paid at both ends.
At the top, the caps destroy information exactly where the reader most wants it. Two quarterbacks who both complete above 77.5 per cent of their passes score identically on that component whether one of them completed four fifths of his throws or all of them. The formula's discrimination is best in the middle of the distribution and worst at the extremes, which is the opposite of what anybody wants from a statistic used to sort the very best passers in the sport.
At the bottom, the floors are a mercy the game does not extend. A catastrophic afternoon cannot be punished beyond a point. Once a passer's interception rate passes 9.5 per cent, further interceptions are free. Once his yards per attempt drops below 3.0, further failure costs nothing. The worst possible rating is 0.0, and reaching it requires simultaneously failing all four tests, which means the formula compresses disasters into a narrow band at the bottom in the same way it compresses greatness into a narrow band at the top.
There is a third cost that nobody mentions. As the league's passing efficiency has risen over the decades, more quarterbacks now operate close to the completion-percentage ceiling than did in 1973. A component set at the outer edge of what was achievable in the 1960s is nearer the middle of what is routine now, and every passer who saturates it has part of his performance discarded. The formula's resolution degrades as the sport improves.
Where 66.7 and 158.3 actually come from
The commissioner asked the league's statistical committee for a standard in 1971. The group that built it was headed by Don Smith of the Pro Football Hall of Fame, Seymour Siwoff of the Elias Sports Bureau and Don Weiss of the league office, and they set their performance standards from qualified passers across the 1960 to 1970 seasons. The result went into use in 1973 and has not been touched since.
The calibration is where the constants come from, and you can read it straight off them.
Set each component to exactly 1.000 and solve backwards. The completion component equals 1.000 at a completion percentage of 50. The yards component equals 1.000 at 7.0 yards per attempt. The touchdown component equals 1.000 at a touchdown rate of 5 per cent. The interception component equals 1.000 at an interception rate of 5.5 per cent. Those four figures are the committee's picture of an average passer in the decade they studied, embedded in the coefficients and preserved there ever since like a fly in amber.
Four components at 1.000 gives 4, divided by 6, times 100. Which is 66.7.
So the number the formula calls average is average for a league that has not existed for fifty years. Passing has become dramatically more efficient since, in every one of the four categories, for reasons that have nothing to do with quarterbacks getting better in isolation: rule changes protecting receivers and passers, the spread of concepts designed to produce high-percentage throws, and the professionalisation of everything from route timing to weather-day ball preparation. The league publishes its current averages every season and they are not 50 per cent completions and 7.0 yards per attempt. A rating of 66.7 today does not describe a competent starter. It describes somebody being replaced.
This matters more than it sounds. Every reader's intuition about what a given rating means was formed by exposure to current numbers, not by the formula's own definition of average, which means the scale has drifted underneath the intuition. There is no version of the rating that has been recalibrated, because recalibrating would break every historical figure in the record book. The league chose stability over accuracy, and it was probably the right call, but the price is that the statistic's own internal notion of "average" is now simply wrong.
And 158.3? Four times 2.375 is 9.5. Divided by 6 is 1.5833. Times 100. That is all it is. A ceiling produced by an arbitrary bound chosen so that the average would land on a round-ish integer, dressed up half a century later as perfection.
Watching a stat line become a rating
The formula is easier to hold in your head once you have pushed one line through it. The stat line below is invented, and chosen so the arithmetic stays legible.
- Start with five box-score columns24 completions, 35 attempts, 280 yards, 2 touchdown passes, 1 interception. Nothing else about the game enters the calculation, and nothing else ever will.
- Completion componentCompletion percentage is 68.6. Subtract 0.3 from the fraction and multiply by 5, which gives 1.929. The ceiling of 2.375 sits at 77.5 per cent, so this line is comfortably under it and every completion still counts.
- Yards componentYards per attempt is 8.0. Subtract 3 and multiply by 0.25, which gives 1.250. The ceiling sits at 12.5 yards per attempt, a long way above this.
- Touchdown componentTwo touchdowns from 35 attempts is a rate of 5.7 per cent. Multiply by 20, which gives 1.143. The ceiling sits at 11.875 per cent, which would need roughly twice as many scores from the same number of throws.
- Interception componentOne interception from 35 attempts is 2.9 per cent. Multiply by 25 and subtract from 2.375, which gives 1.661. This component runs backwards, starting at its maximum and falling to zero at 9.5 per cent.
- Clamp anything outside the rangeNothing here needs clamping. On a sharper line the completion component would have been cut down to 2.375 and the excess simply discarded.
- Add, divide by six, multiply by 100The four components total 5.982. Divided by six that is 0.997, and multiplied by 100 the rating is 99.7. The division by six has no meaning beyond making the average land on 66.7.
- Notice what never enteredNo sack, no scramble, no fumble, no down, no distance, no score, no opponent. If this passer was dropped four times and ran for two first downs, the rating above is unchanged.
The stat line is invented for this article and deliberately round: 24 completions from 35 attempts, 280 yards, 2 touchdowns, 1 interception. No real performance is being described. Every constant and cap shown is a property of the published formula.
Two things about that worked example are worth pausing on.
The first is how little movement there is in the middle of the range. All four components landed between 1.14 and 1.93 on a scale that runs from 0 to 2.375, which is to say the formula produced a rating just under 100 out of a maximum of 158.3 from a line that is unremarkable in every category. The scale is not linear in any intuitive sense, and the distance between ratings does not correspond to any fixed quantity of football.
The second is the clamp step, which did nothing here and does a great deal elsewhere. Take the same invented line and improve only the completions: 30 of 35 rather than 24 of 35, same 280 yards, same two scores, same interception. The completion component now computes to 2.786, which is discarded and replaced by 2.375. The rating becomes 107.1 rather than the 114.0 an uncapped version would have produced. The ceiling on that component sits at 27.125 completions from 35 attempts, so three of the six extra catches were paid for in full, the fourth was paid for in part, and the last two were worth nothing at all.
What passer rating pays, converted into yards
Here is the most useful thing you can do with the formula, and almost nobody does it. Because every component shares the same denominator, you can work out what each event is worth in the only currency the formula understands with a unit: yards.
Adding one yard raises the yards component by 0.25 divided by attempts. Turning an incompletion into a completion, holding yards fixed, raises the completion component by 5 divided by attempts. Set those equal and the attempts cancel. One completion is worth exactly 20 yards, always, at any volume.
Run the same exercise on the other two. A touchdown, measured against a non-scoring completion of the same length, is worth 80 yards. An interception, measured against an incompletion, costs 100 yards.
Those are not estimates. They fall out of the published constants, and they are the formula's actual opinion about football.
Look at the touchdown column. The NFL formula prices a passing touchdown at four times what adjusted net yards per attempt does, and the gap is not a matter of taste. Touchdown rate is heavily determined by how often an offence reaches the red zone, and how often an offence reaches the red zone depends on the running game, the defence, special teams and field position. A quarterback whose team gives him a short field twice a game will out-earn an identical quarterback whose team does not, and the formula will call it quarterback play.
The interception column has the opposite problem. Weighting an interception at 100 yards is roughly double the empirically derived penalty, and it makes the rating an unusually harsh judge of one specific failure while remaining completely blind to several others. This is not a neutral choice. It systematically favours the passer who avoids risk over the passer who takes it, and it does so with a number that was picked because it made the scale come out tidily.
The completion column is the quiet one. A completion, in this formula, is worth 20 yards regardless of what it achieved. A four-yard checkdown on third and 12 is credited at 20 yards plus the four it gained. A throwaway on the same down, which surrenders nothing and preserves field position, is credited at nothing and costs the passer a completion. The formula prefers the failed completion to the sensible incompletion, and it is not close.
The sack is the hole in the middle of it
Of everything the formula ignores, the sack is the one that changes conclusions rather than merely adding noise.
A sack does not appear anywhere in the passer rating. Not in attempts, not in yards, not in any component. A quarterback who is dropped six times for 45 yards has, as far as the formula is concerned, played a game consisting only of the passes he did throw.
Follow that through to its logical end and something absurd appears. Consider a passer under pressure with nowhere to go. He can throw the ball away, which costs him an attempt, a completion and the yardage he did not gain, dragging two components down. Or he can hold the ball and take the sack, which costs his team down, distance and often field position, and costs him nothing at all in the rating. The formula does not merely fail to penalise the worse football decision. It actively rewards it relative to the better one.
That is not a hypothetical edge case. It is the single most common quarterbacking decision in the sport, made dozens of times a game, and the league's official passing statistic has an opinion about it that is exactly backwards. Any serious account of quarterback play has to price the plays where the ball never left his hand, which is why how often a quarterback is pressured and what he does about it became a separate field of study rather than a footnote.
Rushing is the second absence, and it has grown from a quibble into a structural failure. The passer rating credits nothing to a quarterback who scrambles for 60 yards and two touchdowns. Nothing. A designed quarterback run on the goal line that scores is worth zero, while the identical situation converted with a one-yard pass is worth the full touchdown weighting of 80 yards-equivalent. Two quarterbacks who produced the same points by different means are separated by the formula purely on the basis of which body part they used.
Fumbles are the third. Quarterbacks fumble more than any other position, mostly on strip sacks and botched exchanges, and a lost fumble is a turnover with the same consequence as an interception. The rating punishes one turnover at 100 yards-equivalent and the other at zero.
Add those three together and the passer rating is missing the negative side of the ledger almost entirely. It sees one way for a quarterback to lose the ball and one way for a play to go wrong, and it prices those two heavily while pretending the rest do not happen.
Down, distance and everything else the formula never asked
The exclusions above are omissions of things that appear in a box score. The next set are omissions of context, and they are harder to fix because the box score never contained them in the first place.
The rating does not know the down. A nine-yard completion on third and 15 and a nine-yard completion on third and 8 are the same event to the formula and opposite events on the field. One is a punt and one is a first down. This is the gap that the arithmetic of fourth-down decision-making exposed most brutally, because once you start valuing football states rather than football counting stats, the idea that a completion has a fixed value stops being tenable.
It does not know the score or the clock. Yardage accumulated against a soft zone with the game decided counts the same as yardage produced in a two-minute drill. Quarterbacks on bad teams throw a great many passes in that first situation, which is one reason ratings and won-lost records diverge so often.
It does not know the opponent. No adjustment exists for the quality of the defence faced, the weather, the surface or the venue, and there is no way to add one without abandoning the formula's chief virtue, which is that it can be computed from a newspaper. Opponent adjustment is the whole premise of the efficiency ratings that compare drives against situational baselines, and it is precisely the sort of thing a 1971 committee could not have attempted.
It does not know who did the work. A completion is a completion whether the ball travelled 25 yards in the air into a tight window or two yards to a running back who then made three men miss. Yards after the catch belong to the passer's line in full. Two offences built on entirely different principles will produce similar ratings while asking completely different things of the quarterback.
It does not know about drops, either, which cuts the other way and is worth saying out loud. A perfectly thrown ball that bounces off a receiver's hands lowers the completion component exactly as much as a throw into the third row. The formula's blindness is not uniformly flattering.
And it counts things the game does not really regard as passes. A spike to stop the clock is recorded as a pass attempt and an incompletion, so a quarterback managing the end of a half competently is penalised for it. Two-point conversion passes, meanwhile, are kept in a separate statistical category and never enter the totals the rating is built from, so a scoring play that a team deliberately chose is worth less than nothing to the passer's rating. It is worth exactly nothing, which is somehow worse.
Why the formula quietly prefers the checkdown
Put the pricing and the omissions together and a coherent bias falls out, one that is stronger than most casual criticism of the rating manages to articulate.
Consider a passer choosing between a five-yard route and a 20-yard route on the same play. The short throw completes at a high rate, gains modest yards, and carries a very low interception risk. The deep throw completes at a much lower rate, gains a great deal when it works, and carries meaningfully more risk.
Now price them. The short throw earns its 20-yard completion bonus almost every time, and the yards component barely notices the difference between five yards and twenty because a yard is worth only a quarter of what a completion is worth, twentyfold. The deep throw wins the yards battle when it connects and loses the completion battle whenever it does not, and every additional interception carries a 100-yard punishment that no realistic quantity of extra yardage will offset.
The arithmetic is not close. An offence that throws short, protects the completion percentage and never risks the ball will out-rate an offence that pushes the ball downfield, even where the second offence is producing more points. And because yards after the catch are credited in full, a well-designed short passing game can keep the yards component respectable while never actually asking the quarterback to make a difficult throw.
This is the deepest problem with the statistic. It is not merely incomplete. It is incomplete in a directional way, and the direction it favours is the conservative one. Any measure used to evaluate people eventually influences the behaviour of the people being evaluated, and a measure that pays 20 yards for a completion, 80 for a touchdown and minus 100 for an interception is telling every quarterback in the sport to take the safe throw.
The college passer rating explained, and why it looks nothing like the NFL's
College football computes its own figure, built from college data across the mid-1960s to the late 1970s, and it shares only its ingredients with the professional version.
The formula is ((8.4 x yards) + (330 x touchdowns) + (100 x completions) - (200 x interceptions)) / attempts.
Three structural differences matter.
There are no caps at either end. Nothing is clamped, nothing is discarded, and the figure is bounded only by what is physically possible on a football field. A single attempt that produces a 99-yard touchdown gives a rating above 1,200. A single attempt that loses 99 yards on a completion gives a rating well below minus 700. Neither has ever been a meaningful season figure, but both are reachable in a game, which is why single-game college efficiency figures are frequently ridiculous and single-game NFL ratings never are.
The weightings are different, and much more moderate on the turnover. Divide each constant by 8.4 and the college formula prices a touchdown at 39 yards, an interception at 24 and a completion at 12. Compared with the NFL's 80, 100 and 20, the college version is markedly less obsessed with touchdowns and less punitive about interceptions. Whether that is better depends on your view of college football, where scoring environments vary enormously between opponents and an interception thrown by a team winning by five scores means something different from one thrown by a team trailing.
The scales are unrelated. The absence of a division by six and of the 0-to-2.375 mapping means college figures live in a completely different range from professional ones. A quarterback's college efficiency figure and his eventual professional passer rating are not on speaking terms, and any draft profile that compares them without saying so is either careless or hoping you are.
The one thing the college version does better is that it does not throw information away. Its top passers are actually distinguished from one another, because nothing saturates. The one thing it does worse is that it can be gamed by volume in a way the capped version cannot, and it is even more exposed to small samples.
Adjusted net yards per attempt, or what happens when you put the sacks back
The most useful fix to passer rating did not come from the league. It came from the statistical community, and its virtue is that it is nearly as simple as the thing it replaces.
Adjusted net yards per attempt takes the four passing inputs, adds the two the formula forgot, and expresses the answer in a unit everybody already understands:
(passing yards + 20 x touchdowns - 45 x interceptions - sack yards) / (attempts + sacks)
Four things happen at once here, and each of them is a repair.
Sacks enter the denominator, so a dropback that ends behind the line is finally counted as a dropback rather than deleted. Sack yardage enters the numerator as a subtraction, so the field position surrendered is charged to the passer's account. The touchdown weighting drops from an implicit 80 yards to an explicit 20, chosen from the run-value of a passing touchdown rather than from a desire for a tidy scale. And the interception penalty falls from an implicit 100 to 45, still a heavy charge and a much more defensible one.
The output is a yards-per-attempt figure. Not an index, not a rubric score, not a number out of 158.3, but a quantity with a unit that a reader can reason about, compare across eras and add up. When a metric produces 7.9 rather than 106.4, everyone knows roughly what a movement of half a point means, and nobody is tempted to call any value of it perfect.
Take the invented stat line from earlier, 24 of 35 for 280 yards with two touchdowns and one interception, and give the passer two sacks for 14 yards. His passer rating is unchanged at 99.7, because sacks do not exist in it. His adjusted net yards per attempt falls from 7.86 to 7.05. That is the whole argument in one line: the same game, and one of the two measures noticed that he was dropped twice.
What adjusted net yards per attempt still cannot do is anything contextual. It does not know the down, the score, the defence, or who produced the yards after the catch. It is a better box-score statistic, not a departure from box-score thinking, and that is a real limit rather than a quibble.
What replaced both, and what that cost
The genuine successors abandon the box score entirely. Rather than counting events, they value football situations, asking what a team's position was worth before a play and what it was worth afterwards, and crediting the difference. The expected-points framework that underpins modern football analysis is the general version of that idea, and it dissolves most of the problems above in one move: down and distance are inside it by construction, a checkdown short of the sticks is correctly valued at close to nothing, a sack is a large negative, and a scramble for a first down is credited to the quarterback who made it.
The other successor attacks a different weakness. Completion percentage over expected uses tracking data to estimate how likely each individual throw was to be completed, given depth, coverage, pressure and receiver separation, and reports how far above or below that expectation a passer finished. It answers the question passer rating's completion component asks and answers badly, which is whether a high completion percentage reflects accuracy or an easy menu of throws.
Both are better measures. Both carry a cost that people who advocate for them do not always own.
They are not reproducible from public information. You cannot compute either by hand from a box score, which means you are trusting a model you cannot audit, built by an organisation that may change it. They are versioned, so a figure quoted in one year may be recomputed later and quietly change, which is fatal for historical comparison. Several implementations are proprietary and their exact construction is not published. And the underlying tracking data has not been collected uniformly for the whole history of the sport, so the modern statistics simply do not exist for most of it.
Which is the same argument that runs through every attempt to build a comprehensive value statistic in any sport, and the same one that attends baseball's wins above replacement. Sophistication and auditability trade against each other, and the trade is real.
The honest defence of a bad formula
Having spent several thousand words on why the passer rating is a poor measure of quarterback play, here is the case for it, which is stronger than its critics allow.
It is reproducible. Five columns, four expressions and a division. Anybody can compute it, verify it, and disagree with a published figure on the evidence. No model, no proprietary data, no version number, nobody to ask. That property is rarer than it should be and it is the reason the number can be quoted in an argument without the argument becoming about the source.
It is stable. The formula has not moved since 1973. A rating computed for a season five decades ago means exactly what a rating computed last Sunday means, because the definition is identical. Modern models get retrained, recalibrated and reissued, and when they do, history changes underneath the people who cited it. Passer rating never does.
It is computable backwards. Because it needs only attempts, completions, yards, touchdowns and interceptions, it can be applied to almost the entire recorded history of professional football. No tracking-derived statistic can make that claim, and none ever will.
It is transparent about being arbitrary. The constants are visible. Anyone can see that a touchdown is priced at 80 yards and object to it. A model that produces a number from a hundred inputs and a fitted surface is arbitrary too, in ways that are considerably harder to see and therefore harder to argue with.
It is not that bad at the job. For all the deserved criticism, the rating is heavily correlated with the modern alternatives, because most of what makes a passer good shows up in the four categories it counts. It separates a good season from a poor one reliably. It fails at the margins, at the extremes, and on the specific players whose value lives in the parts it cannot see, which is a real failure and not a total one.
The correct verdict is narrower than either camp usually states. Passer rating is a poor instrument for ranking the best quarterbacks in a season and a perfectly serviceable one for sorting a hundred passers into rough tiers. It is used almost exclusively for the first job.
Reading a passer rating without being misled
Six checks, in the order that matters.
Check the volume before anything else. The rating is a set of rates and rates are unstable over small denominators. A figure computed from fewer than a couple of dozen attempts carries almost no information, and the caps guarantee that a short excellent stretch produces the maximum. A backup at 158.3 on nine throws has told you nothing.
Ask what happened on the plays that are not in it. Sacks, scrambles and fumbles are the most important missing information and are all publicly available. A quarterback with a strong rating who was dropped repeatedly had a worse game than his rating says, every time, without exception.
Treat any figure near the ceiling as censored. Above roughly 77.5 per cent completions or 12.5 yards per attempt, the formula has stopped listening. Two ratings in the 150s can conceal very different performances and the formula will not tell you which is which.
Convert the components into yards when you want to know why. A rating is four numbers pretending to be one. If a passer's rating is high because his touchdown rate is high, ask how often his offence started inside the opponent's half. If it is high because his completion percentage is high, ask how far the ball was travelling.
Look at a second measure that includes sacks. Adjusted net yards per attempt is calculable from public data in one line and it disagrees with passer rating in exactly the informative cases. When the two agree, you have a much stronger statement. When they diverge, the divergence is almost always about pressure, and pressure is the story.
Never compare a college figure with a professional one. They are different formulas on different scales built from different eras of different sports. The similarity of the names is a trap.
The rating is worth keeping, in the same way an old ruler with worn markings is worth keeping. It measures something real, it measures it the same way every time, and everybody has one. What it will not do is tell you which of two very good quarterbacks was better on a given Sunday, and every autumn a good deal of the argument that surrounds the sport proceeds as though it can.
Ask instead what the number was built from. Four rates, four ceilings, three men in 1971 and a decade of data that ended before most of the people quoting it were born.
Common questions
How is NFL passer rating calculated?
Four rates are computed from the box score: completion percentage, yards per attempt, touchdown passes per attempt and interceptions per attempt. Each is converted onto a scale that runs from 0 to 2.375, with anything above the top capped and anything below zero raised to zero. The four capped values are added, divided by six and multiplied by 100, which is why the arithmetic maximum is 158.3.
Why is 158.3 the highest possible passer rating?
Because all four components stop at 2.375, and four times 2.375 is 9.5, which divided by six and multiplied by 100 gives 158.33. It is a ceiling rather than a peak, so a quarterback who clears every cap comfortably scores exactly the same as one who clears them by a single yard. That is why the phrase "perfect passer rating" describes the formula running out of room rather than a flawless performance.
What does passer rating not measure?
Sacks, sack yardage, rushing attempts, rushing touchdowns, fumbles, down and distance, score, time remaining, opponent quality, weather, drops, pressure and how much of each completion the receiver produced after the catch. It sees five box-score columns and nothing else, so a quarterback who takes a sack rather than throwing the ball away is treated as though the play never happened.
Is passer rating the same as QBR?
No. Passer rating is the league's official 1973 formula, computed by hand from five box-score columns and bounded at 158.3. Total QBR is a proprietary model on a 0 to 100 scale that weights plays by situation, splits credit between the passer and the players around him and discounts garbage time. They answer different questions and frequently disagree.
Why is the college passer rating formula different?
The college figure was built separately, from college data, with its own constants: yards are multiplied by 8.4, touchdowns by 330, completions by 100 and interceptions by minus 200, and the total is divided by attempts. Crucially it has no caps at either end, so a single attempt can produce an enormous or deeply negative figure, and the resulting numbers are on a completely different scale from the NFL's. The two are never comparable, whatever a draft profile implies.
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