Given this statistical analysis - do we actually believe in him?
Children visited
There are roughly 2 billion children worldwide. However, assuming Santa doesn't visit the children of Hindu, Muslim, Jewish, atheist and so on parents, that leaves the 35 per cent or thereabouts whose parents consider themselves Christian. That's still an impressive 700,000,000 children in a night. Assuming three children per household, that's 233,000,000 stops for Santa and his sleigh. There may be a few households where all the children have been naughty, but we are going to discount them for statistical purposes.
Distance travelled
If we assume that the 233,000,000 good Christian households are distributed evenly around the world , and the planet's surface area is 510,000,000km (and for the sake of simple calculations we are going to treat the Earth as a square map, rather than a globe), then each stop between households will be around 1.47km (0.91 miles) apart. Santa will therefore have to travel a total of 342,510,000km (212,030,000 miles).
Speed of sleigh
If he's clever about it, and travels from east to west with the Sun, maximising his available night-time, Santa has about 32 hours to work with (assuming children sleep for eight hours, he has 24 hours plus those eight to finish). Travelling 342,510,000km in 32 hours equates to a speed of 10,703,437.5km/hr (6,650,807.72mph), or a little under 1,800 miles per second, assuming he takes no time actually to deliver the presents or stop for any comfort breaks. The fastest-moving man-made object in history, the space probe Voyager 1, manages a rather less impressive 10.8 miles per second.
Number of calories consumed
Assuming one mince pie (250kcal for the Co-operative Own Brand in the author's cupboard) and one 50ml glass of sherry per household (58kcal, according to weightlossresources.co.uk) we have 308 calories times 233,000,000 households, or 71,764,000,000 calories total. The recommended daily allowance for an adult male, according to the Department of Health, is 2,550kcal. Santa will therefore eat 28,142,745.1 times his daily dues. If Santa is a 300lb (21 stone) man (not an unreasonable assumption) he will have to walk more than 450 million miles at three miles an hour to burn off his night's excesses.
Amount of alcohol consumed
The aforementioned 50ml glass of sherry works out at around one unit of alcohol, according to the UK definition. So Santa would be expected to knock back 233,000,000 units over the course of the evening. The daily recommended maximum for a man is four units, meaning that Santa is endangering his health by drinking 58,250,000 times the DoH limits. Worse, he is likely to be in no fit state to drive his sleigh. The legal blood alcohol limit is 80mg per 100mls of blood, or roughly four units (although this of course would be less for a big man). So Santa would also be at least 50 million times the legal driving limit as well, and would probably have his licence revoked.
Weight of gifts carried
Assuming each child gets the Transformer Optimus Prime, the leader of the Autobots, for a present, in his box, Santa will be carting 659g (1.45lb) per child. That's 461,300 metric tonnes, or about the same in imperial tons, total. For comparison, a Boeing 747-8I airliner can carry 237.5 tonnes in passengers, luggage and fuel.
Cost of gifts
Optimus Prime is worth £42.99 new. Santa will therefore have to spend a grand total of £30,093,000,000 to provide each child with one, or risk arrest by having his elves make illegal copies. This is the equivalent of the gross domestic product of Costa Rica.
Number of reindeer required
Assuming reindeer are capable of pulling around 150kg (330lb) each, and that the sleigh itself weighs nothing, then Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Dunder and Blixem will need to hire some help, to the tune of a further three million reindeer, to drag the 461,300-tonne present payload. The percentage of those reindeer required to have red noses is not known. They have a further problem of teaching the new recruits to fly at hypersonic speeds, but they can cross that bridge when they come to it.
Amount of energy required to drag the sleigh
Assuming that each reindeer is an adult male weighing 600lb (272kg), then the three million required to pull the sleigh will add up to 816,000 tonnes to add to the 416,300 tonnes of toys. To get that up to a speed of 6,650,807.72mph would require around 700 quintillion joules of energy, or the equivalent of 210,000,000,000,000,000 kettles boiling. This assumes that Santa is travelling above the atmosphere, to avoid drag from the air. Of course, when the sleigh descends again into the atmosphere, it, Santa, all the reindeer, and all the presents will immediately be vaporised in the incredible heat of re-entry, thus rendering the whole exercise somewhat pointless.