Hold time, not traffic, sets the run hours
Each arrival keeps the light on for as long as somebody is there plus the hold period afterwards. On the defaults that is 4 minutes of presence and 15 minutes of hold, so every arrival costs 19 minutes of light for 4 minutes of use. Eighteen arrivals at 19 minutes is 5.7 hours if none of them overlap.
They do overlap, and that is what stops it being worse. If arrivals are spread randomly through the window, the light is off at any moment only if nothing has arrived during the preceding hold period, so the fraction of the window with the light off is e to the minus the arrival rate times that period. With 18 arrivals across 14 hours the rate is about 1.29 an hour, the period is 0.317 hours, and the off fraction works out at about 0.666. So the light is on 33.4 percent of the window: 4.68 hours rather than 5.7.
Set that beside the occupancy. Eighteen arrivals at 4 minutes each is 1.2 hours of anybody actually being in the room. The light runs 4.68 hours, which is very nearly four times as long, and 3.48 hours of it is an empty room being lit. None of that is a fault in the sensor. It is the hold time doing exactly what it was set to.
The setting is worth more than the hardware
Drop the hold from 15 minutes to 5 and rerun it: the period becomes 9 minutes, the rate is unchanged, and the on-fraction falls to about 17.5 percent, or 2.46 hours a day. That is 2.23 hours a day less light from changing a setting, which is a bigger reduction than most people expect from anything short of removing the fixture.
Compare that with what the sensor itself achieved. Against a baseline of 8 hours on a manual switch, the sensor at a 15-minute hold saved 3.32 hours a day. Shortening the hold saves another 2.23 on top, for free. So about 60 percent of the available reduction came from the hardware and 40 percent from a setting nobody usually touches, and the setting is the part that costs nothing.
There is a real limit on how far to take it. A hold shorter than the gap between movements the sensor can see leaves people waving at the ceiling, and a light that cycles is worse than one that stays on — for the occupant and, on some lamp types, for the lamp. The point is not that shorter is always better; it is that the number is a decision and it should be made rather than inherited.
The money is small, and it is worth saying so
Three fixtures at 45 W is 135 W. Saving 3.32 hours a day is about 164 kWh a year, which at 17 cents is around $28. A single fitted sensor at $28 therefore pays for itself in about a year, which is a genuinely good result — but it is a good result because there are three fixtures on the circuit and the baseline was eight hours a day.
Change it to one 9 W lamp in a hallway that was on for two hours and the same sensor saves a couple of dollars a year and never pays back. That is not an argument against fitting it; it is an argument for being honest about why. Convenience, hands full of laundry, and a garage that is never dark are perfectly good reasons. Energy payback, in a house that has already changed its lamps, usually is not one, and the LED conversion savings calculator is where the wattage side of that gets settled.
One caveat on the model. It assumes arrivals are independent and evenly spread, which real traffic is not — people go to the garage three times in ten minutes and then not at all until evening. Clustering makes arrivals merge more than the model predicts. And the formula assumes the pattern was already running when the window opened, which adds about another one percent. Both errors run the same way, so the run hours here are slightly high rather than slightly low, which is the right direction to be wrong in.
Questions people ask
Why is my motion sensor light on so much more than the room is used?
Because each arrival buys a full hold period regardless of how briefly anyone was there. On the defaults here, 18 arrivals of 4 minutes each is 1.2 hours of occupancy and 4.68 hours of light, so the room is lit about four times longer than it is used. The ratio is roughly the hold time divided by the stay, tempered by how often arrivals merge into a run that was already going.
What hold time should I set?
Short enough that the light does not burn for a quarter of an hour after somebody walks through, long enough that it does not switch off on somebody standing still. That trade depends on the space and on what the sensor can see, so the page shows two settings side by side instead of recommending one. On the defaults, going from 15 minutes to 5 cuts run time from 4.68 hours a day to 2.46.
Do more visitors mean proportionally more run time?
No, and this is the useful counterintuitive part. Once arrivals are frequent relative to the hold period, extra ones land while the light is already on and extend the run rather than starting a new one. Doubling arrivals from 18 to 36 on the defaults takes run time from 4.68 hours to 7.8, not to 9.36. Busy spaces saturate, which is also why a sensor saves least exactly where it is used most.
Is an occupancy sensor worth it for the energy?
Sometimes, and the honest answer depends heavily on the connected load and the old habit. Three 45 W fixtures that used to run eight hours a day give about $28 a year at 17 cents, so a $28 sensor pays back in roughly a year. One 9 W lamp that ran two hours gives a couple of dollars and never pays back. Put your own numbers in; the page will tell you which case you are in rather than assuming.
How accurate is the overlap model?
It assumes arrivals are independent and spread evenly through the window, which gives an exact answer for that assumption and a close one for spaces with steady traffic. Real traffic clusters, and clustering causes more merging than the model allows. A second and smaller effect works the same way: the formula assumes the pattern was already running when the window opened, which is worth about another one percent. Both push the same direction, so the run hours here come out slightly high rather than slightly low for a bursty space such as a garage, and that is the direction worth erring in.