London cycle hire forecasting

The question

An operator of a bike scheme sends vans to move bikes. A dock that runs empty loses a trip. A dock that runs full blocks a return. Those two costs are not the same, so the right number of bikes to leave at a dock is not simply the number you expect to be taken.

So the forecast has to say how sure it is, not only what it expects. This project forecasts departures and returns for each dock for the next 24 hours, issued every morning at 06:00 UTC, and then tests whether knowing the spread changes the decision.

It sits next to LapByLap. Both predict first and optimise second, but this one has real operating data and no Formula 1.

The data, and what is wrong with it

The base is TfL’s public journey data: 18.1 million trips from June 2024 to May 2026, turned into hourly counts per dock. I picked 80 docks, 40 that are busy at the weekday morning peak and 40 that are busy at weekends, each open under one name for the whole period. Forecast weather comes from Open-Meteo, bank holidays from GOV.UK, school terms from Housemait and Tube strike dates from a list I compiled and checked against a TfL freedom of information response.

Most of the work was finding where the data lies.

• Trips taken are not trips wanted. An empty dock records no demand. The archive has no dock availability, so I score only docks that are rarely empty and say so beside every headline number. I also flag hours where a normally busy dock logged nothing, which is a floor on how much demand is hidden.
• A dead day. On 5 August 2025 the whole network logged 188 trips against about 30,700 on a normal Tuesday. That is the data failing, not demand. It had been sitting in a scored window as zeros, so it is now missing, and so are the days that read it.
• Closed docks. A dock silent for a day or more, when it normally logs plenty, is closed, not unpopular. 2,016 dock-hours match events I can name: the Hyde Park docks around Winter Wonderland, the Notting Hill Carnival, New Year at Waterloo. They are treated as missing.
• A feature that did nothing. School-term dates for 2024/25 were missing, so I compiled them by hand from five borough calendars. The flag moved the score by 0.0003, with an interval spanning zero. It stays in because it costs nothing, but I do not credit it.

How the model works

The count of bikes leaving a dock in an hour is a small whole number: the average is about two, and 44% of hours are zero. That shape matters, because a model built to hit the middle of a smooth curve behaves badly on it.

• Step one, the average. A LightGBM model, trained on all 80 docks together, predicts the expected count for each dock-hour. It reads the same hour in each of the last four weeks, the last day and the last six hours, the hour and weekday, bank holidays, school terms, Tube strikes and the weather forecast for that morning. It uses Poisson loss, the standard choice for counting events.
• Step two, the spread. A negative binomial turns that average into a range. It is a distribution for counts that are usually near the average and sometimes burst. How bursty depends on how busy the dock is, so each volume level has its own setting, fitted by maximum likelihood on spare mornings.
• Step three, the safety margin. A conformal step checks the range against recent mornings the model did not train on and nudges it wider or narrower, separately for each hour of the day and for busy and quiet docks. It targets 80%, and on whole numbers it lands higher, because a range has to round outward when 44% of outcomes are zero.

How I tested it

The test is a rolling backtest. Each forecast uses only data from before 06:00 UTC on its day, and the weather it sees is the forecast that was stored then, not what actually happened. There are nine windows of 28 mornings across two years, and a test fails if any feature can see the future.

The fair baseline is the quantiles of the same hour over the last eight weeks, with no fitting. I added it after noticing that “same hour last week” was an easy bar: it scored half the error of my first model, and the real gap was a seventh of that. ARIMA, which had looked like progress against last week, turned out to be worse than the no-fit baseline.

Spring 2026, which includes the April Tube strike, was kept locked. I opened it once, on 29 October 2026, after every model, setting and cost was fixed. The code refuses to run it a second time.

I also checked my own dock selection. The 80 docks were first picked with the whole two years in view, which can flatter results. Re-picking them from the first six months only, and scoring on the six later windows, moved the count model’s mean pinball from 0.349 to 0.348 and left the ranking untouched. 65 of the 80 docks were the same.

How it did

Lower is better in the first two rows. Mean pinball loss scores the whole range, not only the middle guess. All five models are scored on the same dock-hours.

The ranking was the same in the nine earlier windows and on the locked-away spring: the count model is 16% better than the fair baseline in the first and 18% in the second. Strike and bank-holiday hours are harder for everyone, but its gain over the baseline is larger there, about 27% and 32% against 16% on ordinary hours.

The range is not perfectly calibrated and I would rather say where. Across the nine windows the 8am peak was the weak spot, with the range holding 85% against 92% overall. In spring 2026 it did not show up. One window of 56 mornings is a result, not a fix.

Where the gain came from

My first count model beat plain LightGBM by 4%, but it differed in four ways at once. Before crediting the clever part, I changed one thing at a time.

So about half the lead was just more history, and the other half was the count distribution. The model I thought was clever was less than half of the story, and I would rather know that.

What it is worth to someone sending vans

The test: for each dock and a four-hour window, the operator picks how many bikes to have there at the start. Changing from half full costs a van stop. Policies are scored on what actually happened, with costs for a lost trip, a blocked return and a stop.

Docks per station come from TfL’s live listing (13 to 55, average 29). A lost trip costs 1.65, the pay-as-you-go fare. Assume a van holds 18 bikes. The cost of a van stop, 10, is my arithmetic, since no UK operator publishes one, so I swept it from 3 to 50.

The clearest result is that the model beats last week’s counts by a lot. A noisy single number sends vans that were not needed, and was worse than doing nothing at the quiet docks. Having the forecast at all is where most of the gain is.

The spread adds little in this setup. Planning against the whole forecast beats planning from the average by about 0.02 per window, 0.3% of total cost, and on spring 2026’s 56 mornings that gap is within noise. Even an oracle saves only about 8% of total cost, because most of the cost is the busiest third of docks, where four hours of demand exceeds the docks whatever anyone does.

So I tried a harder version. A real operator has a van that can make only so many stops a morning, so the forecast has to choose which docks to visit.

A limited van

Each morning one van can make at most so many stops across the 80 docks. “Van already paid for” means a stop costs only the handling, 0.4 a bike. Otherwise a stop costs 10.

Here the spread earns its place. Ranking docks by the whole forecast saves about 7 to 16% more than ranking by the average when a stop costs 10, and up to 24% more when a stop costs only the handling. The reason is the textbook one. A lost trip costs about twice a blocked return, so the right stocking level is well above the average, and a plan built on the average under-stocks.

The honest summary is that the spread matters when moving a bike is cheap compared with a lost trip, and adds little when every stop is expensive. I would rather show where it helps and where it does not than pick the setup that flatters it. I also modelled departures and returns moving together, with a Gaussian copula. It matched the spread of real outcomes better and changed no decision, so the simple version stays.