Which airline would you choose?
63% versus 77%. The choice looks obvious.
Arrivals board
Flights from the same period.
Illustrative board · fictional flights
You need a flight. Which company would you choose from this board?
The flights behind the percentages
Two fictional airlines, two fictional airports, 100 flights per airline. This ledger is not a real airline ranking.
At North, A leads 90% to 80%. At South, A leads 60% to 50%. Yet B leads overall. Every number can be true at once.
Each square is one flight. Filled = on time; outlined = late. The two rows within each company have the same scale.
Airline A
North: 9 / 10 = 90%
South: 54 / 90 = 60%
Airline B
North: 72 / 90 = 80%
South: 5 / 10 = 50%
A sends 90 of its 100 flights to South, where both airlines have lower rates. B sends 90 to North. The overall board mixes different proportions of the two airports.
Move flights. Keep the route rates fixed.
This next board is a model: it reallocates 100 flights per airline while holding the four percentages above constant. Real route changes need not preserve those rates.
Read the full ledger and calculation
The original totals are A: 9 + 54 = 63 out of 100; B: 72 + 5 = 77 out of 100. At a common 50 / 50 mix, the model gives A: 45 + 30 = 75; B: 40 + 25 = 65.
For a common North share w between 0 and 1: A = 90w + 60(1 − w); B = 80w + 50(1 − w). Subtract: A − B = 10 percentage points at every common mix.
Nobody changed the board
63% and 77% correctly describe all of each airline’s flights in the invented ledger. If the question is which company had the higher overall on-time share in that period, the answer is B. Splitting the data does not erase that result.
But asking what happened at each airport gives a different picture. A has the higher on-time share at both North and South. Most of its flights, however, go to the airport where both airlines have the lower rate.
An overall percentage weights each group by its number of flights. A large group pulls the total further towards its own rate. Different weights can reverse the overall comparison even when every within-group comparison points the other way. This is one form of Simpson’s paradox.
A new mixture asks a new question
“Give both airlines 50 / 50” does not repair the past. It specifies a common mix: half the flights at North, half at South. Holding the route rates fixed gives A 75% and B 65%.
In this model, A leads at every common mixture because its advantage is the same at each airport: 10 percentage points. Send both airlines entirely to North, entirely to South, or divide them another way: that gap remains.
In a real schedule, moving flights could change congestion, departure times and other conditions. The slider does not model those changes. It exposes the arithmetic of mixtures; it does not promise the outcome of a future flight.
So who gets your money?
This ledger cannot book your ticket. A real choice needs at least your route, the observation period, comparable flights and enough data. One group here has only ten flights. If one of those ten arrivals switches from on time to late, the rate drops by 10 percentage points.
A split table alone cannot establish why rates differ. “Always use subgroups” is no universal solution either: the appropriate grouping depends on the question and how the situation works.
The useful souvenir is not a suspicion of every percentage. It is one extra question for any impressive board: “What did you mix together—and in what proportions?”