Why we publish a median delay, not an average

Every delay figure on this site is a median. Almost every other place you will see train punctuality discussed uses an average. That is a small-looking choice with a large effect on what the number actually tells you, and it is worth ten minutes of your time to understand, because it changes how you should read any punctuality figure anywhere.

The shape of railway lateness

Start with the thing that makes railway delay unusual as a quantity.

A train cannot arrive much before its booked time. It can be a few minutes early, occasionally. It cannot be an hour early, because there is nowhere for it to go and nobody expecting it. So on one side, the numbers stop almost immediately.

On the other side there is no stop at all. A train can be ten minutes late, and it can be nine hours late, and once in a while it is later than that. The distribution has a hard floor near zero and a long tail running away from it in one direction.

Statisticians call that right skewed. What it means in practice is that the extreme values are all on one side, so any calculation that adds them up gets pulled that way.

What the average does to it

An average adds every value together and divides by how many there were. Every value gets an equal vote, including the ones that are nothing like the others.

Picture a train that runs a service ten times. Nine of those runs arrive within about a quarter of an hour of the booked time. The tenth loses most of a day somewhere, which does happen: a failure, a blockage, a knock-on from something else on the same line.

The average of those ten runs is dominated by the tenth. It lands somewhere far above anything that happened on nine of the ten days. It is not describing a typical journey on that train, because there was no typical journey anywhere near it. It is describing a journey nobody took.

The median does something different. It lines every run up in order and reads off the middle one. The very late day still counts, and it still sits at the far end of the line, but it moves the middle only by one position rather than dragging it. The number you get is a run that actually happened, and it sits in the middle of what actually happens.

Which question each one answers

Both numbers are real. They answer different questions, and only one of those questions is the one you have when you are standing on a platform.

The average answers something closer to "how much total lateness does this service produce". That is a genuine question, and if you were rostering staff or costing knock-on effects across a network you might want it.

The median answers "if I take this train, what is the ordinary case". That is the question a passenger has. It is the reason we chose it.

What the median does not tell you

Here is the honest limitation, because a number you trust for the wrong reason is worse than one you do not trust at all.

The median is deliberately unmoved by the bad day. That is its strength when you are asking what usually happens, and it is exactly its weakness when you are asking what could happen. A median of fifteen minutes is entirely compatible with a service that occasionally loses half a day.

So we publish a second figure beside it: the ninetieth percentile. Same idea, different position in the line. Instead of reading the middle run, it reads the one nine tenths of the way along, so nine runs in ten were better than this and one in ten was worse.

Read the two together and you get something a single number cannot give you. The median is the day to plan around. The ninetieth percentile is the day to have a fallback for. If they are close together the service is consistent. If they are far apart it is a service that is usually fine and occasionally is not, which is a genuinely different thing to be told, and it is a difference an average erases completely by blending both into one figure that describes neither.

We also publish the distribution itself where there is enough history to draw one, because the most honest thing you can show someone is the shape of what happened rather than any single summary of it.

Why we say "typical" rather than "average"

You will see the word typical on train and route pages where another site would write average. It is not a stylistic preference. Average has a specific arithmetic meaning that most readers know, and using it for a median would be inaccurate in a way that sounds authoritative. Typical is vaguer, and it is vague in the right direction: it says middle, which is what a median is.

How this connects to everything else here

The same instinct runs through the rest of the site, and it is worth naming because it explains choices that otherwise look overly cautious.

We do not show a punctuality figure for a train until there is enough recorded history behind it to mean something. A median of two runs is not a median of anything. A blank is honest, and it fills in as the archive grows.

We hold a floor under how early a train can be recorded as arriving. A recorded arrival an hour before the booked time is not a very early train; it is a mismatch between our copy of the timetable and the run we matched it to. Publishing it as though the train were early would put a fault of ours into a figure about them.

And where a figure comes from a small sample or an unusual measurement, we say so beside the figure rather than in a footnote at the bottom of the page.

None of this makes the numbers better. It makes them honest about what they are, which is the only thing that makes them worth reading.