Like most other things in Formula 1, race strategy has progressed far beyond the intuitive seat-of-the-pants style of the old days into something wildly elaborate and scientific. It is an around-the-clock computer exercise involving millions of calculations and scenarios and a full-time staff of half a dozen engineers and mathematicians devoted to analyzing the right combination of fuel load and tire changes and when and how many pit stops to make during a race.
''Gone are the days of someone sitting on the pit wall saying, 'Let's pit now; it's a great idea,''' said Neil Martin, who used to be head of strategic operations at the Red Bull team. ''They would not prevail.''
For the teams race strategy is as important as aerodynamics, mechanics, engine power and the driver, and they have hired numerous specialists to match those in other parts of the factory. The driver serves only to feed them data.
Martin has a degree in mathematics and computer science and another in operational research, which involves the study of risk analysis and mathematical modeling. He started in Formula 1 on a student project applying those disciplines to race strategy. He was then hired by McLaren, where he stayed for a decade before moving to Red Bull last year.
''Before I got seduced by Formula 1, I was headed right into the city doing derivatives and share trading,'' he said. ''And in a sense, this is completely analogous to it.''
Martin said it was thanks to a split in strategies between the Red Bull drivers - one stopped once, the other twice - that one of them, David Coulthard, finished third at the Canadian Grand Prix on June 8.
''All we were doing was like in a financial portfolio, spreading the risk,'' he said.
The Toyota team accurately predicted the timing of a probable safety car period and put its drivers, Timo Glock and Jarno Trulli, on one-stop strategies. They finished fourth and sixth.
But Dieter Gass, Toyota's chief engineer, noted the limits of race strategy.
''Strategy is not strong enough to make a bad car win races or to make a good car lose races,'' he said, ''unless you make really big mistakes.''
He said it can be crucial, however, when a race is disrupted by accidents, rain or the safety car, which neutralizes a race while the track is cleared of debris as happened in Canada.
For example, Kimi Raikkonen's victory for McLaren at the Monaco Grand Prix in 2005 was attributed to Martin's decision to do the opposite of what was expected when a safety car appeared.
But such decisions are based on data analyzed through millions of scenarios on computers that work not only throughout the week before the race, but during the race weekend and the race itself, as the team's results and those of the other teams are added.
Such strategy started to become crucial in the mid-1990s, when refueling and tire changes were introduced, meaning that a car no longer ran an entire race on a single tank of fuel and one set of tires. The importance increased in 2003, after cars were required to start the race with the same amount of fuel that they had used in qualifying. That meant deciding how much fuel to use based on an expected grid position and on the ideal length of the first stint.
The main factors fed into the computers are number of race laps, amount of fuel a car should carry, the car's speed and the duration of its tires, and what the competition is expected to do. And human judgment in all of this?
''There could be two competing strategies, one which gives you the small probability of a shot at a podium, but if that goes wrong, you will end up 17th, 18th or 19th,'' Martin said. ''However, there might be another strategy option that says that we can almost guarantee you seventh place. So the human has to come in, look at the campaign management and say, 'Well, do I really want to bag the 2 points? Or take the small percentage chance of going for the podium?'''
Another human aspect sometimes trumps the decisions: A driver may fail to live up to the plan, or, more rarely, he may exceed expectations.
''We got it wrong,'' said Martin Whitmarsh, the McLaren chief executive, referring to Lewis Hamilton scoring pole position by a wider margin than expected in Canada. ''We could have had more fuel in Lewis's car. You want to be on pole by a thousandth of a second, ideally, if you've done the job right. But Lewis pulled out something a little bit special, which we hadn't programmed into our analysis.''
Lately, Formula 1 has been trying to give fans more insight into strategy.
''For those of us who are involved in it, it's a deeply fascinating sport with many facets,'' Whitmarsh said. ''But we haven't yet done a good enough job to work on providing the fan base with the information and the insights of the complexities of our sport.''
Television viewers depend on specialist commentaries. But for spectators at the track, little was available until handheld televisions from Kangaroo TV were introduced last year for rental during race weekends. These televisions provide a choice of commentary, driver-to-pit radio communications and other data provide by the teams.
But teams draw the line where the information risks giving rivals an advantage. Before the Turkish Grand Prix in May, McLaren kept secret that Hamilton's car had tire problems that required him to make three pit stops while most other drivers made two.
''It is never a good idea to advertise weaknesses,'' Martin said. ''It is no longer an unknown; it is an absolute. And then they can increase the fidelity of their simulations against ours.''