Puzzling out Points
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Let’s have a bit of a short and funny one today, as it were.
As Lewis Hamilton steamrollers towards another drivers’ title, I was wondering to myself:
‘What, hypothetically, is the earliest a driver can win the championship?’
- Obviously I mean, what’s the earliest race
in the year for which is becomes mathematically impossible anyone to overhaul the leader’s
points tally? So, first things first: obviously, we have
to get at least half way through the season. If, say, Hamilton wins the first ten races
of 2019, there are still eleven races to go so more than enough points left to pick up
and beat Hamilton. In fact, if we stick with the 2019 season
for now, the maximum points available for any one driver per race is 26 points - 25
for a win and a bonus 1 for fastes t lap. With 21 races on the calendar, after race
one there are 26 points x 20 races left so 520 points available for any one driver.
As each race is completed, the number of points left up for grabs in the season decreases.
So, for the sake of argument, let’s use Hamilton as our dominant driver and say that
he progresses through the season by winning every race and grabbing the fastest lap point.
The initial instinct may be that as soon as he does this 11 times he’ll instantly be
champion because he’s got 26 x 11 = 286 points and there are only 26 x 10 = 260 points
left up for grabs. But of course, other drivers are accumulating
points as well. It’s impossible for all drivers to be on zero points by the 11th race
unless there is some suspiciously disastrous reliability issues so let’s assume that
each race, ten drivers get points. [Cum graph] Now, if Hamilton’s nearest rival
- let’s say Bottas - comes second in every single race then the gap between Hamilton
and Bottas only widens by 8 points every race. Let’s plot this a slightly different way.
Let’s go race by race and assume Hamilton scores 26 points each race and Bottas 18 points
for second place. Let’s plot the gap between Bottas and the championship leader over time.
It looks like this: a straight line going up by 8 points every race.
Meanwhile, the available points left after each race drops by 26 points every race. Bottas
can still grab 520 points after race one, 494 points after race two, 468 points after
race three, etc. Only once these lines cross and Bottas’s distance from Hamilton is wider
than the points he has left is Bottas out of the championship hunt.
So if Hamilton wins every race while scoring the fastest lap, he’s guaranteed to win
the championship by round 17 - with 4 races left to go. No matter what anyone else does,
if Hamilton does this 17 times, he’s unstoppable. So that’s the latest title clinch a driver
can get with a perfect run in 2019. What’s the earliest a driver can wrap up the championship?
Well, to figure that out we have to try and work out: what is the lowest possible point
score that the second placed driver in the championship can be on at any given race?
For race one, this is easy. The second placed driver - let’s say Bottas - has to have
scored 18 points for second place. So they’re 8 points behind Hamilton.
In fact, the top ten points positions need to be filled so let’s just whack them out
down to Ricciardo in this particular list. In race two, Hamilton gets 26 points again
but in order to keep his rivals from closing up, we give the remaining nine points positions
to people still on zero points. So Hamilton is up to 52 points and no one else is higher
than 18. Race three, then. This is when we start to
apply an algorithm - a way to keep applying the higher points scores to the lowest standing
drivers. So Russel has zero points, so he gets to come
second and have the full 18. Now who’s in last place? Ricciardo on one point - so he
comes third. Kubica also has 1 point so he comes 4th. Now Norris is last so he comes
5th. Now Giovinazzi is last so we comes 6th. And so on and so on until all the points are
dealt out. Now we go to race four and give second place
to the lowest standing driver, third to the next lowest standing driver and so on and
so on, race by race. What we end up with - if we look at the points
chart - is a kind of plait of lines, with drivers circling around each other taking
turns to pick up the big points. It’s actually an incredible battle for second; as the gap
between 2nd and 20th never opens to wider than 18 points, everyone is always in with
a shot of 2nd place. But if we switch to our chart showing the
points gap to Hamilton, we see everybody is wiped out of the title battle by the end of
race twelve.No driver can catch Hamilton even if they win all 9 remaining races, score the
fastest lap and Lewis retires from each one. Does this seem surprisingly early? It did
to me. Out of interest, if we apply the 2003 points scheme, with a much smaller difference
between first and second, it still only takes 12 races for Hamilton to take the crown.
It also takes 12 races for Hamilton to win the championship under the older 1991 - 2002
points system but, interestingly, he does manage to push half the field out of contention
one race earlier. This is because, with only 6 points paying
positions out of 20, Hamilton’s rivals are picking up points a lot less regularly than
in 2019 when half the field can get points every race.
If we did a very simple points system where everyone gets points from 1st to 20th in a
20 points down to 1 system (ignoring retirements), the super-dominant driver wouldn’t be able
to clinch the title until the 14th race, no matter how hard they tried.
Our points chart forms a lovely bow pattern as well as the positions from 2nd to 20th
simply flip every race so every other race, everyone ends up on equal points. Except Hamilton.
Having said that, we have completely changed the weighting of the points here. In the 2019
system a win is worth a lot more than a second and so on, so if we create an alternative
system where everyone gets points, but highers finishes carry more weight…
...and in this scenario, Hamilton can wrap it up in 13 races instead of the 12 races
it takes in the ‘real world’. So actually, everything about this comes down to points
distribution. If you allow a larger amount of drivers to pick up more a bigger slice
of the winner’s points then the dominant driver won’t be able to strangle the title
so easily. But in doing that, you devalue wins and podium
places. By making the wins more proportionally valuable you encourage drivers to push hard
to gain those extra places rather than settling for second or third. That’s the balance
in creating a competitive championship. OK, let’s have a look at another hypothetical.
Let’s imagine the top ten for each race is exactly the same. And let’s scrap the
fastest lap for the moment, too. As we saw previously, the cumulative points
graph fans out over time with the points difference between each driver spreading.
And if we go to the distance-from-leader chart, we see drivers toppling out of the championship
as time goes on, with Bottas clinging on until race 17. But, that’s not what I want to
talk about. I want to show you what happens if Bottas
and Hamilton are in a fierce rivalry - more like the Rosberg/Hamilton era.
So instead, let’s say that everything else stays the same except Hamilton and Bottas
alternate between coming 1st and second each race.
In this case, obviously Bottas stays in touch the whole season and could still win the championship
by the last race. But now, 3rd place driver Leclerc is able to cling on until race 17
and fourth place Vettel until race 16. Previously, they’d been knocked out in races 14 and
15. This shows the benefit (rightly or wrongly)
of focusing on one driver. As Hamilton and Bottas are allowed to squabble across the
season, neither of them is able to break away from the pack as quickly.
We can see this exaggerated further with a stronger Leclerc in a scenario where Hamilton
and Bottas trade in finishing first or third this time, with Leclerc always finishing second
as one Mercedes gets hurt each race by the alternate strategy.
Here, Ferrari are slightly weaker but have focussed on Leclerc to make sure he always
picks up as many points as possible. And, despite winning zero races, he’s still in
the title fight by the penultimate race due to Mercedes infighting.
What if: instead of focussing on Leclerc and taking advantage of Mercedes teammate rivalry,
Ferrari let their drivers squabble similarly? So while Mercedes are getting 1st and 3rd
alternately each race, Vettel and Leclerc are swapping 2nds and 4ths?
Well in this case they lose sight of the title two races earlier and neither of them can
gather momentum to stay in touch with the leading pair.
This video wasn’t particularly made to make a point (no pun intended) but it was more
of a freeform exploration of how the numbers play out, a little touch on how point systems
shape championships and how teams can strategise to maximise how to get the most out of the
system. In some teams - like Red Bull - they focus
on one driver, which is the best way to do things if you definitely have a dominant driver.
In other teams, they let them race each other and this can hurt them. Ferrari’s drivers
have been fairly evenly matched and so neither has been able to have as consistent a run
on Mercedes as they’d have liked. That’s why, with 5 races left to go in the
real world, only 5 drivers are left in contention - and Vettel left Russia only 2 points inside
the safe zone. But in answer to the question - what’s the
earliest a driver can win a 21 race season with the current points? Race 12. Or Hungary,
this year. So be glad that didn’t happen.
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