Why Vettel's title chance is down to 23 per cent

What happened at the start of the Singapore Grand Prix will unquestionably be a key moment in the battle for the world championship. But what we don't yet know is whether it's the decisive blow against Sebastian Vettel, a mere detail in a Lewis Hamilton championship charge or a bump in the road that the Ferrari man will overcome.

What we can be sure of is that it's slashed Vettel's chances of winning the world championship. If history is a reliable guide, by more than half.

The mathematics of the situation don't make encouraging reading for Vettel. With six races remaining and a maximum score of 150 points, Vettel's current deficit is 18.7% of the total available.

In order to overhaul Hamilton, Vettel requires a swing of either 28 or 29 points in his favour (the lower figure is only enough if it puts him in a position to win on countback). But this season there has been no run of six races where he has gained that much, the best being his 25-point gain over Hamilton during the opening half-dozen races of the year.

The simple way to look at the maths is what Vettel needs to do to be certain of winning the title regardless of what Hamilton does.

It doesn't paint a very positive picture, as he would need to win five out of six races and be in the top two in the other. Even five wins and a second only gives him the title on countback to number of race victories if Hamilton takes five runner-up spots and a victory.

Naturally, this will not happen. The frequency with which Hamilton and Vettel have finished one-two has diminished, with four of the five instances this season happening in the first five races of the year. Since then, it's only been at Spa that they have finished first and second.

Vettel has not necessarily got his disaster in early, with Hamilton now being owed one

The reality is the results will be more scattered, but there's also bad news for Vettel here. Out of this year's 14 races, Vettel has only outscored Hamilton in six of them - and only twice in the past eight races has he done so.

Worse still, over the past six races Hamilton has had a points swing of 52 in his favour. Even if you disregard the Singapore Ferrari wipeout as an anomaly, Hamilton is still going along at an average gain of 5.4 points per race for the preceding five grands prix.

In fact, by every measure the momentum is with the Mercedes driver. Hamilton has won four of the past five races, Vettel has managed just one in eight. As the season has progressed, the pendulum has swung more and more away from Ferrari.

There are, of course, random factors to consider. Hamilton could easily suffer a 2016-style engine failure in next weekend's Malaysian GP and a Vettel win would cut the deficit to three points and transform the situation.

Or Hamilton could be taken out in a crash, be it of his own making or someone else's, just as happened to Vettel in Singapore. But to counter that, so could Vettel.

History is not always the best predictor of things, and it's not as if there is some kind of equal amount of misfortune that must befall every driver over a year. Vettel has not necessarily got his disaster in early, with Hamilton now being owed one. It's just as possible that Vettel could suffer another blow.

What's more, Vettel's situation is made worse by the fact that he might have to take a grid penalty for using extra power unit elements. It's not guaranteed and Ferrari is trying to manage things, but this could be another disadvantage. Doubly so with Hamilton unlikely to be hit with such a penalty.

While the gap itself is not insurmountable - with 25 points for a victory, 28 isn't such a big amount to make up - the way the season is going it's getting harder for Ferrari to land blows on Mercedes.

And just think what would have happened had the Singapore GP start disaster not occurred. It's not just the 25 points that Hamilton gained, it's how the race might have panned out.

Let's say Vettel had won and Hamilton finished fourth, which is where he would have been, based on jumping Daniel Ricciardo at the start and the other three drivers that started ahead of him staying there. In that scenario, Vettel's lead in the standings would be 10 points.

That would make a huge difference to the landscape, and while you'd argue that Hamilton would still be slight favourite given the trends, Vettel would have to do far less to be sure of the title. Going back to the hugely hypothetical scenario in which Vettel and Hamilton are first and second in every race, two wins and four seconds would give the Ferrari driver the title by three points.

Of the three occasions when a gap of equivalent magnitude has been overturned by a driver in the past 30 years, two of them have been achieved by Vettel

Even that might be difficult given the current trend, but it's vastly more likely than the scenario where five wins and a second are the minimum needed to be sure of winning.

Looking at the previous seven seasons in the 25-points-for-a-win era, stretching back to 2010, four times the driver leading with six races remaining has become champion.

In 2014, Hamilton turned the tables on Nico Rosberg by overturning potentially winning positions for his team-mate in Russia and the United States, as well as a problem effectively ruining Rosberg's Singapore GP the moment it started. Even then, Hamilton only had a 22-point deficit - though it became an eventual winning margin of 67 points thanks to the fact that Rosberg failed to finish the double-points Abu Dhabi finale in the top 10 thanks to an ERS problem.

But the other two scenarios will give Vettel cause for encouragement because he achieved the reverse. In 2012, he was 29 points behind Fernando Alonso and came through to win the title, albeit with the caveat that Vettel's Red Bull was stronger than the Ferrari in the run-in.

Vettel also did it back in 2010, when four drivers went into the season finale in the hunt and, with six races remaining, Vettel was 31 points behind leader Hamilton and 28 points behind second-placed team-mate Mark Webber.

The circumstances were slightly different, not least because he actually had a 10-point advantage over the driver who actually finished second - Ferrari's Alonso - but it shows that it can be done.

But Vettel 'only' won three of those final six races on his way to grabbing the title and can't expect Hamilton to struggle in the same way this year that he did when at McLaren in 2010 with a car fading in competitiveness.

Another thing that could encourage Vettel is that he turned a gap of 25 points (62.5 if you adjust from 10 points for a win to 25 for a win) into just 11 points (27.5) in 2009 as Jenson Button limped to that season's title. Not enough to win that time, but it would be enough this year. But again, it's hard to see Hamilton only managing the kind of low-key results Button did in the Brawn over the last half-dozen races.

Looking back over the previous 30 runnings of the world championship, it's clear that the driver leading with six races to go generally wins. Only six times have the tables been turned - Hamilton on Rosberg in 2014, Vettel on Hamilton and Webber in '10, Kimi Raikkonen on Hamilton and Alonso in '07, Mika Hakkinen on Eddie Irvine in 1999 (pictured below) and Jacques Villeneuve on Michael Schumacher in '97. So only around 20% of the time has it happened.

Looking further back, such instances were more common. In the 14 campaigns before 1987 (which takes us back to '73, the first season in which there were 15 races on the calendar), there were seven such occurrences. But this was in a very different era from today and probably shouldn't be taken too seriously as an indicator of form.

So the statistics suggest that it's game, set and match Hamilton, then? Not necessarily. Vettel is a driver with a knack for the turnaround.

Of the three occasions when a gap of equivalent magnitude has been overturned by a driver in the past 30 years, two of them have been achieved by Vettel himself. He is a strong finisher, and clearly doesn't give up or lose motivation.

And when you factor in only what might be termed as 'competitive' championships - ie eliminating the walkovers - then the frequency of reversals increases to 46% of the time. Although still only 23% of the time if you include gaps as big as the one Vettel faces.

What you cannot replicate are the circumstances. Nobody has ever tried to overturn this gap with a car with the performance profile Vettel's Ferrari has compared to the one of Hamilton's Mercedes.

The most alarming thing for Vettel is just how big a dent his title hopes took in Singapore. Let's say he'd emerged with the hypothetical 10-point championship lead. Historically, and factoring in only 'competitive' championships with a last-race showdown, he'd be in a position where drivers have won the title 54% of the time.

Out of this year's 14 races, Vettel has only outscored Hamilton in six of them - and only twice in the past eight races

So with the decision to steer left at the start of the Singapore Grand Prix, so Vettel's chances of winning the world championship more than halved - from 54% to 23%.

Of course, this is a one-dimensional metric, based purely on historical data of the past 30 years, but it indicates how he went from slight favourite to outsider in one fell swoop. With it, Hamilton's chances of winning leaped from 46% to 77%.

These figures don't factor in the relative performance of the cars or the characteristics of the circuits to come, and are to be treated as an indicator of the scale of the task rather than any kind of prediction. After all, in one scenario all Vettel had to do was match or be just behind Hamilton over six races. The alternative requires borderline dominance.

But with the position Vettel is in and what history tells us about it, combined with the recent trend against him and Ferrari and the strength of Hamilton and Mercedes, between a one-in-four and one-in-five chance almost seems a little generous.

He has turned the tables before (pictured below in 2010), and when you have a small run of races anything can happen. All most want is a great title fight, regardless of who wins, so we can but hope that Vettel's chances are increased over the next few races to ensure a dramatic denouement to a great '17 season.

After all, if anyone can, history tells us that Vettel is the man to fight his way out of this position. But with such a reduced chance of victory, it's clear he can't afford any more significant slips.