Points left to grab the championship - who and how?

[Manoah2u]

So, with Nico having a 33 point lead on Lewis, with just 4 races left,
there are 100 points to spread out the table.

313 points for nico
280 points for lewis

Theoretically, though a lot more difficult now, lewis can still be WDC.
if Lewis wins all next GP's - unlikely at this point i'm afraid to say - he'll have 380 points.
Nico then should not make more than 66 points in the next 4 races.
On average, that means Nico must not get over 16,5 points each race -
which really means if he finishes two times third and two times 2nd;
and Lewis MUST at all times win the race, then he grabs it by 2 points difference.

So concluding; what does Nico need to do to see this championship not slip out of his hands?

if Nico wins 1 GP, and comes in 2nd in 1 GP, he has won the championship.
if Nico wins 1 GP, and comes in 3rd in 1 GP, and comes in 9th in 1 GP, he has won the championship.
if Nico wins 1 GP, and comes in 6th in 2 GPs, and 10th in 1 GP, he has won the championship.
if Nico comes in 2nd in the next 4 races, he has won the championship.

what MUST Lewis do to still grab the championship this year?

Lewis must win all 4 GP's, and nico finish 3 races 2nd and 1 race 4th, then Lewis will be WDC.
Lewis must win 3 GPs, Nico win 1 GP, have 1 DNF, and 1 time 3rd, then Lewis will be WDC.
Lewis must win 2 GPs, have 2 GP's 2nd place, and Nico not make more than 43 points in those 4 GP's.

It's still possible, but i feel like Nico is too strong now, and Lewis is slipping.

Even if Nico gets a DNF and Lewis wins the next GP, he's still 7 points behind to make up. that means in 3 races,
he must get 2 races 2 points more and 1 race 3 points more in every single race. He'll have to be atleast 2nd 3 times
with Nico finishing behind him in that case.

[ChrisDanger]

Just for some perspective, at the end of last year the Mercedes 1-2 finishes were flourishing (see below, where we have the same locations this year for the conclusion of the season). Rosberg was dominant, although Hamilton had already won the title. But if this Mercedes form repeats itself, Rosberg will win.



The results this season from both the Mercedes team and each driver, is a little different though, compared to last last year. Here are the seasons side-by-side, leading up to the last 4 rounds.



In 2015 the were many more 1-2 finishes from Mercedes. The trend this year is a little different, so I think it's still wide open. Yes, the odds are in Rosberg's favour, but a DNF or a bit of bad luck for Rosberg could put Hamilton right back in the fight. It's never good to pin your hopes on the misfortune of your rival, but championships have been won this way.

It ain't over 'til the fat lady takes centre stage.

[Fulcrum]

Using the data available from 2014-2016 so far, I've generated a probabilistic model to find the state of the championship going into the last round, as well as after the final round.

The model takes into account the relative distributions of each drivers outcomes. I've modelled Hamilton as the prior, and Rosberg as the posterior event, as I feel Hamilton has the ability to affect Rosberg's outcomes more so than the other way around. It's an assumption, not necessarily correct.

Populating all possible Hamilton-Rosberg outcomes using their distributions, aggregating outcomes by net point differential, then repeating this for three races, I get the following:

Rosberg has a 45% chance of winning prior to Abu Dhabi.
Hamilton has a 0.70% chance of winning prior to Abu Dhabi.
This leaves a 54.30% of the championship being contested at the final race.

Outcomes decided at Abu Dhabi are split as follows:

Rosberg has a 32.3% chance of winning in Abu Dhabi. Or, if the title race is still undecided by this stage, Rosberg has an ~60% chance of winning.
Hamilton has a 22% chance of winning in Abu Dhabi. Or, if the title race is still undecided by this stage, Hamilton has an ~40% chance of winning.

Total probability favours Rosberg at this stage, obviously. Rounded to the nearest round number its approximately 75% Rosberg, 25% Hamilton. My 'exact' figures are 77.32% Rosberg, 22.68% Hamilton.

If I look at Sky Vegas, their current odds are 1:5 on Rosberg and 7:2 on Hamilton. If you reverse engineer these numbers to balance their book, you find Sky's implied probabilities of winning are 78.95% for Rosberg and 21.05% for Hamilton.

These mirror my own values, with some favouritism expressed for Rosberg - probably as a result of factoring in favourable recent performance.

I still feel that HE WHO DOES NOT DNF will likely win the Championship. With virtual certainty, one more for Hamilton and its over. One for Rosberg and it evens up dramatically. If I get some time I'll partition the model as a function of reliability issues.

[ChrisDanger]

These mirror my own values, with some favouritism expressed for Rosberg - probably as a result of factoring in favourable recent performance.

Does your model work on averages no matter where in time the results are placed, or does it account for trends, given that I noticed that this year there have been a lot less Mercedes 1-2s compared to last year?

I fully agree with your "HE WHO DOES NOT DNF will likely win the Championship", except while almost guaranteed if Hamilton DNFs, it would only make it less impossible (but still a challenge) for Hamilton to win if Rosberg DNFs.

[Fulcrum]

It takes the exact distribution of Hamilton and Rosberg's finishes across the 2014-2016 period, conditioned on Hamilton's finishing position. It does not account for local form in any way at all, nor does it factor in the finishing characteristics of the remaining tracks.

Factoring that into the model would in all likelihood slant the outcome more heavily in Rosberg's favour, given the data would show his win % has improved, especially this year, and the winner therefore inheriting a larger net benefit - given the next Mercedes is more likely to finish 3rd or lower than was the case in 2014/2015. Rosberg also has favourable outcomes in the remaining races, relative to the season as a whole.

By way of example within the interval 2014-2016, Hamilton has finished 1st 27 times from 55 races, and Rosberg has done so 20 times. The model accounts for the fact that, if Hamilton finishes 1st, Rosberg cannot, conditioning the potential outcomes correctly; hence Rosberg is referred to as the 'posterior' event. The only discrete event scenario where no such conditioning is necessary is retirements and/or finishes outside the top 10, where it is possible for both drivers to experience this outcome in a single race.

The model populates a tree of all possible finishing scenarios, using these probabilities, for the USA. The net point differential distribution is produced. Then, produce sub-trees for every unique point differential for the following race (Mexico); aggregate these again to get the unique point differential after race two; and so on.

All the fancy modelling is completely nullified by DNFs though, which is why I'd be interested to see what it says if we condition on, for example:

1 DNF for Rosberg
1 DNF for Hamilton
1 DNF for both.

DNFs in this era are never expected, so I highly doubt either driver, or both, will suffer more than one.

[Roman]

I do not think that a calculation based on 2014-2016 can correctly reflect the chances of winning or loosing the WDC. A correct calculation would be (IMHO) to calculate the different outcomes while assuming the 2 Merc drivers will always be within the top 3. As we saw in Malaysia and Japan, the Merc can come back to P3 from a bad start or even a spin in the first corner. This could give a realistic picture.

However, the OP (I didnt check the calculations) shows how slim LHs chances of winning the WDC have become. Bar any DNFs this one should go to NR. However, one DNF on his side with a LH win at the same time and it is all open again.

Edit: However, I (as a math genius ) am not sure the calculations in the OP are entirely correct. Lets take the "NR wins one race and comes second in one more" scenario: NR leads by 33 points at the moment with 4 races remaining. Assuming he wins the next race and LH comes second he will then lead by 40 points. The race after LH wins and NR comes in 2nd, the point difference will come back to 33 points. If NR doesnt finish the last two races and LH wins both of them LH will lead NR by 17 points.

Similar with the next scenario: Assuming NR finishes the next three races 1st, 3rd and 9th, while LH finishes 2nd, 1st and 1st: Points difference will be 33 (now) - 40 - 30 - 7 with one race to go. A NR DNF with a LH finish at least on 6th position will have LH win the WDC by 1 point.

Or am I making a mistake?

[Fulcrum]

You're perfectly entitled to an opinion. I don't necessarily agree with you though.

Firstly, I've used all of the data from 2014-2016, because using less would leave that subset of data prone to whatever peculiarities persist in that data. Confine it to 2016, and the model will suggest Hamilton is far more prone to failure than is likely the case. It will also suggest Rosberg is more likely to win than is reasonable - these events depend on each other to some extent; Hamilton DNFing, or simply having an issue, automatically results in Rosberg having a far greater likelihood of winning.

The effect of more data, while potentially masking local trends, removes local variance too. It also yields a more 'optimistic' result of Hamilton winning than would be the case were I to use 2016 data only. I think this is fair, as I certainly think Hamilton's results this year don't necessarily reflect his underlying, long term potential as evidenced in Mercedes.

Assuming both drivers finishing in the top 3 is simply a subset of the total solution space my model describes; these events only constitute about 65% of the solution space over 2014-2016, and only 53% of events recorded this year. Making this assumption would not represent the solution space accurately.

Similarly for any assumptions made for reliability failures, finishing in position X, etc... You're conditioning on the event, but not attaching a probability to the event.

It's still interesting, because it addresses what will happen IF someone DNFs (or some other conditions occur), but it doesn't say anything about the likelihood of those circumstances.

[Manoah2u]

I do not think that a calculation based on 2014-2016 can correctly reflect the chances of winning or loosing the WDC. A correct calculation would be (IMHO) to calculate the different outcomes while assuming the 2 Merc drivers will always be within the top 3. As we saw in Malaysia and Japan, the Merc can come back to P3 from a bad start or even a spin in the first corner. This could give a realistic picture.

However, the OP (I didnt check the calculations) shows how slim LHs chances of winning the WDC have become. Bar any DNFs this one should go to NR. However, one DNF on his side with a LH win at the same time and it is all open again.

Edit: However, I (as a math genius ) am not sure the calculations in the OP are entirely correct. Lets take the "NR wins one race and comes second in one more" scenario: NR leads by 33 points at the moment with 4 races remaining. Assuming he wins the next race and LH comes second he will then lead by 40 points. The race after LH wins and NR comes in 2nd, the point difference will come back to 33 points. If NR doesnt finish the last two races and LH wins both of them LH will lead NR by 17 points.

Similar with the next scenario: Assuming NR finishes the next three races 1st, 3rd and 9th, while LH finishes 2nd, 1st and 1st: Points difference will be 33 (now) - 40 - 30 - 7 with one race to go. A NR DNF with a LH finish at least on 6th position will have LH win the WDC by 1 point.

Or am I making a mistake?

thanks for pointing out my mistake.

If Nico wins the next race, he adds 25 points to his tally. come in 2nd afterwards, and he has another 18 added.
that's 25+18 = 43 points.

he has 313 points now, which will lead him into a total of 356 points.
Lewis has 280 points. to be able to surpass 356 points, he thus has to make 77 points. If he comes even, Nico will win on amount of wins, so he HAS to beat him by atleast 1 point.

that means lewis must win 3 races more, to add 75 points to his tally, which sets him short 2 points for the last race.

It seems i made a calculation error on 3 races instead of 4. big oops.

[Formula Wrong]

All these calculations are just making me even more nervous about the 4 remaining GPs

[ChrisDanger]

All these calculations are just making me even more nervous about the 4 remaining GPs

Stats mean nothing though. You never know when you're going to get an outlier, or otherwise buck the trend.

But yes, the tension is tangible now!

[Shrieker]

What's Rosberg's engines looking like now? Is he going to need an extra ? That could influence things a lot.

[rscsr]

What's Rosberg's engines looking like now? Is he going to need an extra ? That could influence things a lot.

He gets a new engine in the next race for the remaining races.

[Vasconia]

I think the only hope for Lewis is a DNF for Nico and some crazy races, with rain and all this stuff.

Under normal circunstances they end 1-2 all the races so this would be the perfect situation for Nico.

Brazil could be the most dangerous race for Nico if it rains.

[Phil]

Some great calculations here and those pretty much sum up the overall picture.

One interesting element is the "mental aspect". Nico might become more nervous, it being his first WDC that is within grasp, Lewis might move into a state on which he has nothing to lose. We've seen Nico supposedly play the "calculation game" in 2014 when he had a significant lead and in some distinct races didn't drive aggressive enough. Then to make matters worse, his luck also ran out with the Singapore DNF that narrowed the gap.

Having said that, I think Nico is a too consistent performer to be still influenced by this. As has been pointed out, a 33 point lead at this point can be considered significant. I also think he has an ace up his sleeve with Brazil where he has always performed extremely well, maybe even Mexico too. And Abu Dhabi, a track considered to be one of Lewis's best tracks and again, Nico beat him in qualifying in both 2014 and 2015. Considering this, I think Nico has a lot to be confident about.

As such, without any fancy math to back up my humble prediction; If Nico doesn't suffer a significant technical issue that impacts his performance on Sunday, his WDC is a done deal.

Having said that, CotA might be coming at just the right time and it might just be the right race to kick start Lewis for a very strong weekend. If Lewis wins it in flawless manner (no botched start) and Nico walks away lower than 3rd, the point gap will come down quite significantly that it might mess with his head and confidence a bit. If Nico, despite a Lewis win, comes in 2nd or 3rd, he will still have a significant gap to not let that mess with him for the remaining 3 races IMO. The big question at this point is how Lewis will perform. IMO he was strong in Japan, but his mindset in that press conference wasn't right and definitely isn't setting the right message to your opponent.

As for possible DNFs; I think it's far more likely that Lewis will suffer another one than Nico. Maybe I'm just being pessimistic, but I don't expect Nico to have one. As for race starts - IMO it is still a lottery and I still expect to see some botch starts. Which IMO is a pitty, as this year, we've never really had a race between the two WDC contenders, except for Austria when two alternate strategies brought them into a battle for the win.

[KeiKo403]

Need to remember too that in the case of a DNF where a PU goes kaput then that's points lost at 2 races as there'll likely be a grid penalty for additional PU parts the next round too (unless of course it happens in the last GP).

Also, for all the splenid math I can see (and it is good) I think F1 has too many variables. What if it's dry/wet in Brazil. What is Verstappen splits the mercs in Quali? What if a Merc doesn't win the next 4 races? Taking data of races from 2014-2016 is also a bit skewed as Merc we're far more dominant/bulletproof in '14 & '15 than we've seen this year. By dominant I mean 1-2's. So yes, good maths but this season is a bit different I think.

Would love if Hamilton could claw it back though. Or Rosberg leads by 1 point in the last race so just takes Hamilton out at the start...wonder what would happen then?