Lewis Hamilton’s hopes of winning a fourth world championship took a major blow in Japan, leaving him 33 points behind Nico Rosberg.

A significant threshold was passed in Japan as Hamilton can no longer guarantee the title for himself by winning all the remaining races. Rosberg needs at minimum three seconds and a third to take the title regardless of what Hamilton does.

The good news for Hamilton is that other drivers have overcome greater deficits to win the championship in the past.

Which F1 drivers overturned the biggest points leads?

Formula One’s points systems have changed many times over the years which makes comparing different seasons problematic. However in almost all seasons the most points a driver can score in a race is by winning it. Therefore each driver’s lead or deficit has been converted to represent how many race wins it would take to overcome it. For example a one-win deficit today would be 25 points, whereas in 1991 it was ten.

We also need to consider how many races it took a driver to catch up. It’s easier to make up a deficit of 25 points in four races instead of one. So the number of races taken to catch up is also taken into account.

Based on that, every championship which was won by a driver who was not leading the points at one stage was analysed to find the point at which they were furthest behind in the standings. The results are below, with two caveats.

In early seasons drivers could also score a point for fastest lap, so this has been added to the maximum available points for winning a race. Furthermore in some seasons drivers were required to drop their lowest scoring results. Due to the negligible effect this rule has on the data before it hasn’t been taken into consideration.

How does Hamilton compare at the moment? He is 33 points behind Rosberg with 25 points available for a win and four races remaining. He therefore needs to catch Rosberg at the rate of 0.333 wins per race (i.e. just over eight points). As we will see if he can do that he will belong in this top ten.

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1974: Emerson Fittipaldi beat Clay Regazzoni

Gap overturned: 0.333 wins per race over three races

Having won the championship for Lotus in 1972 Emerson Fittipaldi missed out on the title the following year. Displeased with the manner in which he lost the crown – he would have stayed in the hunt had team mate Ronnie Peterson let him win at Monza – Fittipaldi switched to McLaren, whose new M23 chassis was shaping up nicely.

Ferrari were also enjoying a resurgence and at Tyrrell Jody Scheckter stepped in to replace outgoing champion Jackie Stewart. The result was a wide open championship. Fittipaldi won his second race for his new team but point-less races in Germany and Austria left him fourth in the standings.

He began to overturn that nine-point deficit – equivalent to a race victory at the time – by finishing second at Monza, coincidentally to Peterson once again. Crucially he led Clay Regazzoni home at Mosport, taking the championship lead from the Ferrari driver, and fourth place at Watkins Glen sealed his second title.

1982: Keke Rosberg beat Didier Pironi

Gap overturned: 0.355 wins per race over five races

When championship leader Didier Pironi suffered appalling leg injuries in a crash during qualifying for the 1982 German Grand Prix, it seemed inevitable his points lead would be overhauled before the end of the season. It was, but remarkably the unfortunate Ferrari driver still came second in the overall standings.

The only driver to out-score him was Keke Rosberg, in circumstances which owed more than a little to The Tortoise And The Hare. Rosberg’s Williams-Cosworth was nimble and reliable but hopelessly out-gunned by the monstrously powerful turbos. Or so it seemed.

Instead while the turbo cars repeatedly blasted away at the start of races, more often than not they weren’t running at the chequered flag. Rosberg, who had driven for backmarker teams until his surprise promotion to Williams, raised his game with consistent points finishes and a breakthrough victory at Dijon. It was the only victory of his unlikely championship campaign. Fifth place in Las Vegas secured the crown as emerging rival John Watson had to settle for second behind Michele Alboreto.

1999: Mika Hakkinen beat Eddie Irvine

Gap overturned: 0.4 wins per race over one race

Mika Hakkinen was briefly declared champion in the aftermath of the Malaysian Grand Prix, the penultimate race of 1999, after both Ferraris were disqualified. Eddie Irvine and Michael Schumacher had finished first and second, but their exclusion on technical grounds handed Hakkinen to first place and an unassailable points lead.

But with F1 set to enjoy a championship showdown at the final race if Ferrari lodged a successful protest, few doubted how events would unfold. Sure enough the FIA accepted Ferrari’s contention that a bargeboard had been measured incorrectly and annulled the ruling. That left Hakkinen four points behind Irvine heading into the finale.

Irvine put up a lacklustre fight in Japan. He crashed in qualifying and though Schumacher took pole position Hakkinen seized the lead at the start. From there the McLaren driver and was on his way to victory in the race and the championship.

1950: Giuseppe Farina beat Juan Manuel Fangio

Gap overturned: 0.444 wins per race over one race

The first world championship came down to a three-way contest between Alfa Romeo’s Argentinean great Juan Manuel Fangio and his Italian team mates Luigi Fagioli and Giuseppe Farina.

Unsurprisingly, some insinuated that the Italian team would prefer Fagioli or Farina to take the title at the finale, which was held in Italy. But Fangio wouldn’t hear anything of such claims, even when his car broke down during the race. He took over the sister car of team mate Piero Taruffi but that too let him down, and Farina duly became F1’s first world champion.

“If I had paid attention to the rumours I would have felt as though I had marred my stablemate’s victory,” wrote Fangio in his 1961 autobiography. “If a driver could no longer trust the firm for which he races, that would be the end.”

1964: John Surtees beat Graham Hill

Gap overturned: 0.481 wins per race over three races

The 1964 championship was a humdinger. For much of the year it seemed either Jim Clark or Graham Hill would seize their second championship titles. But John Surtees, who had just ten points at mid-season, pinched it from beneath their noses at the final round.

Surtees, a Nurburgring master, scored his first win of the year at the German track. The next races on Austria’s bumpy Zeltweg course was a stalemate: none of the trio scored and Surtees apparently remainder an outsider. But victory on Ferrari’s home ground at Monza moved him decisively into calculation. He was back on the podium at Watkins Glen but victory for Hill gave him a handy five-point lead heading into the final race.

The title was decided in circumstances which would cause a social media meltdown today. Third-placed Hill was on course for the title until Surtees’ team mate Lorenzo Bandini punted him off. Leader Clark was now on course for the crown, but his Lotus split an oil line on the final lap. That put Hill back in the points lead – until Bandini waved Surtees through for a second place which clinched the title.

2010: Sebastian Vettel beat Fernando Alonso

Gap overturned: 0.5 wins per race over two races

With two races to go in 2010, Fernando Alonso took the lead of the championship by winning the inaugural Korean Grand Prix. Both Red Bull drivers had retired – Sebastian Vettel with an engine failure, Mark Webber crashing out – and though both still had a chance to be champion Webber was the clear favourite, 11 points behind Alonso and 15 ahead of his team mate.

The obvious thing for Red Bull to do was force Vettel to support Webber’s championship bid, particularly as Alonso had a subservient team mate in Felipe Massa who had already handed him a victory in Germany. But the team elected to let their drivers fight it out. In Brazil Vettel won followed by Webber, who was quietly nursing an injured shoulder, and Alonso. It seemed as though Vettel was inadvertently helping Alonso to the crown.

But the final race in Abu Dhabi delivered a stunning twist. While Vettel won as he pleased Alonso, preoccupied with Webber, pitted early to cover off the other Red Bull. He succeeded, but had allowed too many cars to separate him from Vettel. The first of these was the Renault of Vitaly Petrov, and Alonso toiled in vain for lap after lap trying to find a way past. He failed which meant Vettel, who had started the day third in the standings, snatched an improbable title.

1983: Nelson Piquet beat Alain Prost

Gap overturned: 0.518 wins per race over three races

A PR coup beckoned for Renault in 1983: Alain Prost was on the verge of becoming France’s first ever world champion in one of their cars. But Brabham’s Nelson Piquet was advancing.

Prost warned Renault of the growing threat posed by Brabham with Gordon Murray’s missile-like BT53, BMW’s potent four-cylinder turbocharged engine and its exotic fuel cocktail which unleashed the extreme levels of performance the turbo era was renowned for. But Renault were too slow to heed his words, particularly after a tangle between the two title contenders left Piquet 14 points down with only three races to make up the deficit.

The alarm bells rang at Monza where Prost’s turbo expired and Piquet motored to victory. Piquet won again at Brands Hatch, though Prost chased him home to limit the damage. But the Brabham driver was now just two points behind as they headed to Kyalami in South Africa for the showdown.

Once again Piquet scorched off into the lead while team mate Riccardo Patrese held second and Prost, third, was on course to lose the title. And then the Renault’s turbo packed up again. Piquet, wisely, turned the boost down and cruised home third to collect the championship. He had needed to score 21 points from the final three races; had he chosen to, he could have scored a maximum 27.

1976: James Hunt beat Niki Lauda

Gap overturned: 0.555 wins per race over seven races

Unquestionably the most famous championship comeback was the one 40 years ago which helped make Formula One the global spectacle it is today. The final showdown at Fuji might not have gone ahead had it not been for the pressures of live satellite television coverage, which was still a novelty at the time.

A season of drama had preceded the finale: Even Ron Howard’s excellent Hollywood recreation Rush couldn’t convey all its twists and turns. James Hunt’s pursuit of Niki Lauda had been dogged by controversial disqualifications at Jarama and Brands Hatch. But Lauda’s near-fatal crash at the Nurburgring gave Hunt the chance to eradicate his lead.

Even so the odds were stacked against Hunt: Halfway into the season he had only half of Lauda’s 52 points. And the Ferrari driver’s astonishing return, with terrible scarring from his burns, to take a heroic fourth at Monza, meant Hunt had to keep delivering wins.

They arrived at Fuji with Lauda just three points to the good. But to him racing in the Fuji rain was suicidal madness. He withdrew, spurning Ferrari’s offers to pretend a mechanical failure had forced him out. Hunt endured the conditions to take third which was one place better than he needed to become champion. Before the Nurburgring he’d been almost four wins behind with seven races remaining.

1986: Alain Prost beat Nigel Mansell

Gap overturned: 0.611 wins per race over two races

Ten years later, victory for Nigel Mansell in the Portuguese Grand Prix set him up to become Britain’s first world champion since Hunt. He was followed home by Prost, who lagged 11 points behind in the championship with 18 available over the final two races.

Prost’s situation was only marginally improved at the next race in Mexico, where Gerhard Berger and Benetton took a surprise victory thanks to the durability of their Pirelli tyres (yes, you read that right). Prost collected second while a disgruntled Mansell ruined his race with a poor start and finished a unhelpful fifth.

Even so third place for Mansell in Adelaide would guarantee him the title. He was running in that position on lap 64 when his left-rear tyre exploded without warning. Keke Rosberg had retired from the lead with a similar but less spectacular failure one lap earlier. Nelson Piquet, also in the championship hunt, was called in for a precautionary tyre change. Luckily for Prost he had already pitted due to a puncture, and not needing to make a further stop he took the win and the championship.

2007: Kimi Raikkonen beat Lewis Hamilton

Gap overturned: 0.85 wins per race over two races

Formula One has never had a rookie world champion, save for the obvious exception of its first season, but as the teams packed up at a sodden Fuji on September 30th, 2007, it seemed inevitable that would change. Lewis Hamilton had just won his fourth race of the season. Of his title rivals team mate Fernando Alonso had crashed out and Kimi Raikkonen only managed third after starting the race on the wrong tyres.

The Ferrari driver was 17 points behind with 20 available in the final races. To win the championship he almost certainly needed to win both races and also needed Hamilton to hit trouble. And that’s exactly what happened.

Hamilton should have clinched the title at Shanghai. He was pulling away from the field on a wet but drying track but he and McLaren made the strategic error of staying out far beyond the point at which his intermediate tyres could tolerate. When he finally came into the pits the McLaren failed to negotiated a simple left-hander and skidded to a pathetic halt in a tiny gravel bed from which it could not emerge under its own power.

Raikkonen won the race but second for Alonso left him as Hamilton’s closest threat at the finale in Brazil. The points leader made a nervy start, sliding wide while duelling with Alonso. Now running sixth, one place away from championship safety, his chances were finished for good when a gearbox fault caused a loss of power. He eventually reset the car and got going again, but had now fallen to 18th.

Hamilton fought his way back up to seventh by the end of the race, but with Massa waving Raikkonen through to a second victory the championship was lost. The most improbable Formula One championship comeback was complete.

Hill’s near-miss

One driver who very nearly occupied a place on this list is Damon Hill. In 1994 he came from 31 points behind Schumacher – needing 0.516 wins per race – to go into the final race just one point behind. A controversial collision between the pair decided the title in Schumacher’s favour.

Hill’s pursuit of his rival was aided by a string of disqualifications for the Benetton driver. Schumacher was stripped of victory in Belgium due to a technical infringement and barred from racing at Monza and Estoril after ignoring black flags during the British Grand Prix.

Over to you

Which F1 championship comebacks were the most impressive? How do you rate Hamilton’s chance of winning the title this year?

And which other series have seen drivers overcome huge deficits to become champion? Have your say in the comments.