What the autobrake is actually doing
Reverse thrust is where most of the folklore lives, and untangling it means understanding one thing about the automatic brakes first: they are not a pressure setting.
Select a level and you are not telling the airplane how hard to squeeze. You are telling it how quickly you want the speed to come off, and leaving it to arrange that — exactly as cruise control is told a speed rather than a throttle position, and works out the rest.
Now count what is slowing the airplane down. Three things, and they add together: the aerodynamic drag of the spoilers and flaps, the reverse thrust if you have selected it, and the brakes. Only the last of those is the system's to adjust. It watches what the first two are delivering for nothing, and tops the total up with brake pressure until it reaches the number you asked for.
That single fact explains everything that follows, including two results that look wrong.
You can see the first of them in the airplane's own numbers, and it is worth going to look. Open the landing distances, take a high autobrake setting on a dry runway, and compare the figure with reverse thrust against the figure without it. They are the same. Not close, not nearly — the same distance, to the foot. Two engines' worth of reverse thrust, and the airplane apparently lands no shorter for it.
That is not a misprint, and it is not the tables being lazy. It is the autobrake doing exactly what it was designed to do.
When the target is high
Ask for a firm stop and the target sits well above what the spoilers and the reverse can produce between them. The brakes must make up the difference, and they must do it whether or not the reverse is running.
With reverse selected, the brakes contribute less. Without it, they contribute more. Either way the total is the number you asked for — because that is what the system is regulating to — and the same deceleration from the same touchdown speed takes the same distance.
So at a high setting, on a dry runway, adding reverse thrust does not shorten the landing at all. The reverse simply takes over part of the work: the brakes do less, because the reverse is doing it for them. What changes is not the distance but who absorbs the energy — engines rather than brakes — and the proof shows up somewhere else entirely: the brake cooling time afterwards can go from almost an hour to almost nothing at all.
When the target is gentle
Now go back to those same landing distances and look up a low autobrake setting instead. This time the two figures are not the same. With reverse selected, the distance is genuinely shorter.
Which ought to puzzle you, because nothing about the reverse has changed. Same engines, same dry runway, same thrust — and a moment ago it bought you nothing whatever. Why should it start working now?
Because of the thing the autobrake is regulating to. It is aiming at a rate of deceleration, and at a low setting that rate is modest — modest enough that the spoilers and the reverse, between them, are already producing more than you asked for. The system wants less. So it eases the brake pressure down, and down, and reaches zero, and there it stops. There is no such thing as negative braking. It has run out of adjustment in the direction it needs to go.
Which means the airplane now decelerates harder than you asked for, and stops shorter than the same low setting would have managed without the reverse. You asked for a little braking, and then put reverse on top of it. There is nothing the airplane can do but stop sooner.
Take the reverse away and the system is back in charge: the spoilers alone fall short of the target, so it puts in a little brake, meets the target exactly, and the airplane rolls on for longer.
That gives the result worth carrying, and it is the opposite of the high-setting one: at a low autobrake setting on a dry runway, the reverse does shorten the landing. Not because it is working any harder than it was at the high setting, but because there is now more braking on offer than the requested rate can absorb, and the system has no way left to give the surplus back. It has to take all the braking it is being given and stop the airplane with it. Take the reverse away and the airplane is finally able to obey the gentle instruction it was given, which means rolling on for longer.
The rule underneath all of it
Which reduces to something simple enough to carry into any of these cases.
Reverse thrust changes the distance only when the autobrake has run out of adjustment. Pinned at zero because the target was too gentle, or pinned at maximum because the runway will not give the grip — at either extreme the system is no longer regulating, and whatever the reverse contributes lands directly on the distance. Anywhere in between, while it is genuinely holding the rate you asked for, the reverse changes only which parts of the airplane get hot.
Manual braking sits outside the argument entirely, because there is no target to regulate to. Full pedal is the anti-skid working at the limit of the grip available, nothing is being held to a deceleration rate, and the reverse simply adds. On a dry runway that addition is modest, because grip is good and the brakes are doing most of the work already. On a wet one, where grip is what is limiting the brakes, the same reverse thrust is worth several times as much.
Does reverse thrust actually shorten the landing roll?
Only when the autobrake has nothing left to give. The system is regulating to a deceleration rate and the brakes are the only part of it it can adjust, so while it is genuinely in control it simply reduces braking by whatever the reverse contributes — same rate, same distance, cooler brakes. It stops being in control at either extreme: on a wet runway it cannot reach the rate at all, so the reverse makes up a shortfall and shortens the landing; at a gentle setting on a dry runway the spoilers and reverse together overshoot the rate, the system backs the brakes off to nothing and can do no more, and the airplane stops short of what was asked. With manual braking there is no target at all, so the reverse always adds — a little on a dry runway, a great deal on a slippery one.