Fare's fair

I really don't understand the mathematics behind taxi fare calculation.

As a fully paid-up geek I am bound to attempt to analyse every situation I find myself in, especially if it involves some numbers. Most of the time this constant analysis goes unnoticed by most people, but sometimes it forces itself to the surface. On occasion, I have the opportunity to do a bit of socialising, and when I'm socialising with certain people, we tend to end up in the same places. Now, I'm partial to the odd ale, and as a responsible member of society this means I can't drive.

So I often take a taxi. Every time I do, I have noticed that the fare is different. And not just by a matter of pence, or even a pound or two- a rough calculation of the range from memory is about £10, which I feel is quite large for a relatively short journey (3-4) miles. The geek in me is desperate to know why, and it has been contemplating the variables:

• Distance - This varies very little with each journey. The vast majority are from only one or two locations within a quarter of a mile or so of each other, and the end location is always the same: my local Sainsbury's.
• Journey time - Again, this varies very little, although the very fact that I require a taxi means that certain of my facilities are somewhat diminished during each trial. It seems sensible to me that the largest time-changers in play would be traffic lights (there are two or three sets) as junctions and roundabouts play only a tiny role in this factor due to the time of day that we're talking about.
• Time of day - I think most taxi companies charge more after midnight, but that shouldn't make a difference because the majority of the journeys are after midnight anyway, and usually at a similar time: somewhere between 1 and 3am (much before that and I probably haven't been drinking, so will have my car with me; much after that and I may as well find a sofa to kip on).
• Taxi firm - Most of the time it's with Kettering's most prolific firm, KLM.

Is it possible that the minute differences between each of these variables from journey to journey can conspire to produce a price difference of as much as £10 over a less than four mile journey? Or is it more likely that the drivers have special buttons that allow them to fleece people who they think are too drunk to notice?

A friend of mine suggested that "there are some things that maths cannot explain," but I cannot think of any such things that don't qualify as fiction: religion and homeopathy, for example, can't be explained by mathematics, but that's because they're made up. Does this mean that taxi fares are fictional? In which case, do I still have to pay them if I don't believe in them?