Technical factors have about a 30 per cent impact on their decision-making while politics - internal and external - dominate the other 70 per cent. Coe and Mills have months of lobbying to do in the IOC's jungle of smoky bars and busy hotel lobbies before July's vote. Understanding those politics and acting upon them will be crucial.
The most competitive contest for the Games for 20 years is also going to get extremely dirty as the pressure mounts before the vote on 6 July.
In a perfect world, the evaluation commission's report in May on the bids from London, Paris, New York, Madrid and Moscow would have a significant influence on the vote with the IOC members choosing the city with the best ability to stage the Games.
Indeed there are people at the top of the IOC who believe the commission should have far more power and that the final decision should only be taken by the elite members of the IOC's executive board, the body's cabinet, rather then the 117-strong membership.
But the history of Olympic bidding is full of stories of cities who produced brilliant technical bids but still failed to get the Games.
Four years ago Beijing beat Toronto for the 2008 Games even though the Canadians won huge praise for their bid.
Rome arrived at the 2004 vote in 1997 with what influential Italian sports figures thought was an unbeatable concept. But they ended up being destroyed by the lobbying prowess of Athens bid leader Gianna Angelopoulos.
London 2012 chiefs have shown the commission this week that they have a strong legacy argument in regenerating east London and giving the Olympic movement an historic chance to change the face of one of the world's leading cities.
They have also managed to show the commission the growing enthusiasm for a London Olympics, backed by Kelly Holmes's powerful pledge to fill every stadium with fanatical fans.
But when the headlines from this week's visit fade, Coe, Mills and Britain's globetrotting IOC member Craig Reedie will be busy trying to win the arguments for London around the world in important conversations well away from reporters and TV cameras.
It is going to be a fierce contest against the French and Americans who have sophisticated lobbyists on their side.
London are already facing a whispering campaign from rivals who point to Britain's decision to pull out of hosting the 2005 world athletics championships because of the Picketts Lock fiasco as evidence of a lack of Government commitment to sport in this country.
Favourites Paris will tell members they already have their Stade de France stadium in place and that only the French can supply a " norisk Olympics", an important issue after the troubled preparations for last summer's Athens Games.
Opponents will try to propagate the perception that London is a city with fancy proposals but few stadiums in place.
Bid leaders or key officials will not openly brief against London. The damage will be done by lower-profile consultants, spin doctors and influential IOC figures with excellent contacts and years of experience in the Olympic movement. Many members will not even be aware which city is paying them. Their views will be cleverly slipped into seemingly harmless conversations over dinner or drinks.
To counteract this, Reedie will need to do deals with IOC members looking for support in forthcoming elections for top posts in the IOC or in future bidding campaigns.
Coe and Mills will have to increase their support base by persuading more international federation presidents that bringing the Games to London will be good for their sport.
This is a time for horse-trading and back-scratching in the international sports world. The Government, including Foreign Secretary Jack Straw, Sports Minister Richard Caborn and Culture Secretary Tessa Jowell, must use all of Britain's sophisticated diplomatic channels to win support.
In short, by 6 July Coe and Mills must know that they have enough trust among the 117 members to reach a showdown with Paris in the last round of voting.
London has a bid on paper which is easily good enough to beat Paris in this race. Now Coe, the Government and the whole of British sport needs to demonstrate that they are tough enough to pull it off.
