dR/dN in simple terms
No calculus needed. This page explains what this site measures, in plain words, for anyone who never took a math class past algebra.
The one idea
dR/dN is a short way to write one question: how much money does one more person in the room bring in?
That is the whole idea. Everything else on this site is about answering that question for a real bar.
A night at the bar
Early in the night, the room is quiet. Each person who walks in orders a drink, and nobody waits long. So one more person means more money.
As the room fills up, the line at the bar grows. Bartenders can only pour so fast. Each new person still buys something, but everyone waits longer, so the drinks come slower. One more person still adds money, just not as much.
Past a certain point, one more person costs you money. The line gets so long that some people give up. They stop ordering, or they leave. The person you let in took the place of drinks you would have sold.
The best crowd size is the point where one more person stops adding money. With fewer people than that, you are leaving money on the table. With more, the crowd is getting in its own way.
The picture illustrative example
Each step covers 10 people. In our made-up bar, Pigfox Cantina — a fictional venue — the best crowd size comes out at 98 people (simulated). Between 40 and 50 people, each extra person brings in about $7.45 an hour (simulated). Between 120 and 130 people, around the posted capacity of 120, each extra person costs about $10.07 an hour (simulated).
Where calculus comes in
Calculus is the math for measuring how fast something changes. Here, it measures how fast money changes as the crowd grows. That is all you need to know about it.
What this site does with it
We build a model of a bar and play out the night many times. Each time, people arrive and leave a little differently. Looking across all of those nights, we find the crowd size where one more person stops adding money.
When a bar sends us its own records, what the till rang up and what the door counted, we read the same answer straight out of its real numbers.
What an owner does with the answer
- Staffing: if your busy nights run past the best crowd size, another bartender can move that point higher, because the bar can serve more people.
- Holding the door: once the room reaches the best crowd size, letting more people in costs you money. That is the moment to hold the line outside.
- Pushing for more: if your room rarely gets near the best crowd size, you have space to fill. That is the night to run a promotion or bring in a band.
Want the full math, with every step shown? Read the science →