This morning’s round-up got me thinking about the perfect* ranking system for F1.
It should award points to every finisher, so that even the battle for 17th vs 18th makes a difference. But ultimately, a win should still be worth more a lot more than any other finish; and coming 1st & 3rd should be better than coming 2nd twice.
(mathematicians have a snappy word for rankings where “coming 1st & 3rd is better than coming 2nd twice.” They’re called convex.)
At this point I started wondering, how much better? And is 1st & 4th better than two 2nd places?
Then I realised the fairest way of doing it. This season we had 24 starters each weekend (even if they didn’t all make the race). Thus the chance of winning was 24:1. The chance of coming in the top 2 is 24:2, or 12:1. The chance of coming in the top three is 24:3, or 8:1. And there are your points.
But! We wouldn’t just add these points up. You see the chance of winning two races in a row is 24:1 squared, or 576:1.
Actually, this is a bit of a problem: nobody wants to do long multiplication to find out people’s scores. And Vettel’s score this season would be over 18 billion trillion!
No problem – mathematicians have a trick for that too. They’re called logarithms. Make the score for nth place be -log(nth/24), and then we can just add the scores up at the end of the season.
Here’s the table I ended up with:
{Position}
{Points}
{Equivalent to}
{1}
{3.18}
{25}
{2}
{2.48}
{20}
{3}
{2.08}
{16}
{4}
{1.79}
{14}
{5}
{1.57}
{12}
{6}
{1.39}
{11}
{7}
{1.23}
{10}
{8}
{1.10}
{9}
{9}
{0.98}
{8}
{10}
{0.88}
{7}
{11}
{0.78}
{6}
{12}
{0.69}
{5}
{13}
{0.61}
{5}
{14}
{0.54}
{4}
{15}
{0.47}
{4}
{16}
{0.41}
{4}
{17}
{0.34}
{3}
{18}
{0.29}
{2}
{19}
{0.23}
{2}
{20}
{0.18}
{1}
{21}
{0.13}
{1}
{22}
{0.09}
{1}
{23}
{0.04}
{0}
{24}
{0}
{0}
{DNF}
{0}
{0}
{Position}
{Driver}
{Points}
{1}
{Sebastian Vettel}
{51}
{2}
{Jenson Button}
{38}
{3}
{Fernando Alonso}
{37}
{4}
{Mark Webber}
{37}
{5}
{Lewis Hamilton}
{33}
{6}
{Felipe Massa}
{22}
{7}
{Nico Rosberg}
{20}
{8}
{Michale Schumacher}
{16}
{9}
{Adrian Sutil}
{16}
{10}
{Paul di Resta}
{15}
{11}
{Vitaly Petrov}
{14}
{12}
{Kamui Kobayashi}
{13}
{13}
{Jaime Alguersuari}
{12}
{14}
{Sebastian Buemi}
{11}
{15}
{Sergio Perez}
{10}
{16}
{Rubens Barrichello}
{10}
{17}
{Nick Heidfeld}
{9}
{18}
{Pastor Maldonado}
{7}
{19}
{Heikki Kovalainen}
{6}
{20}
{Jarno Trulli}
{5}
{21}
{Jerome d’Ambrosio}
{5}
{22}
{Bruno Senna}
{5}
{23}
{Timo Glock}
{4}
{24}
{Viantonio Liuzzi}
{2}
{25}
{Daniel Ricciardo}
{2}
{26}
{Narain Karthikeyan}
{1}
{27}
{Pedro de la Rosa}
{1}
{28}
{Karun Chandhok}
{0}
So, what do you think? Do you think the rankings shown here are fairer than the ones we have at the moment? A lot of drivers have changed rankings, and I imagine so have the teams. Does this give a fairer picture of the performance of the back-markers?
*sadly, this isn’t it. It’s a little bit complicated.
