2016 standings under alternate points system

Spinodontosaurus

Points Scorer
The current F1 points system - like all historical F1 points systems - does not award points for all finishing positions. This can make it hard to separate drivers in back markers teams that rarely if ever score points. So I came up with an alternate system based on the existing one that awards points for every finishing position.



The points awarded to positions 11 downwards may seem somewhat arbitrary, but they aren't. 11th place gets 1st place points divided by 50 (25/50 = 0.5), 12th place gets 2nd place points divided by 50 (18/50 = 0.36) and so on. 21st and 22nd places get 11th and 12th place points divided by 50. This way I keep the relative % between positions the same, and the fractional points are very easy to work out so don't need to be memorised.

DNFs are not awarded any points, and I usually class non-finishers that were still classified (due to completing 90% of the winners race distance) as a "DNF" even if they aren't regarded that way officially. For instance Rosberg was officially classified 17th at Italy last year, but because his engine blew 3 laps from the finish I class that as a DNF (more specifically a non-driver related DNF, which I'll get onto later).

As of Britain, this is the 2016 points table under my alternate system:


The fractional points have a negligible effect on front runners, but has a big effect on the back markers and allows us to separate the 5 drivers who have yet to score under the real points system.

However, differing numbers of DNFs can still skew the standings and make team mate comparisons deceptive. For such comparisons I prefer to use Points Per Race as the metric instead. PPR is merely the points scored divided by number of 'counting races'. A counting race is any race where a driver finished or where they failed to finish due to a driver-related DNF (for example crashing, being disqualified for driver misconduct, or failing to qualify). I count all driver-related DNFs even if, for example, the driver was not at fault for the crash, because that introduces a degree of subjectivity that I don't want.
Using PPR minimises the impact non-driver DNFs have on team mate comparisons, although a driver could still be unlucky and suffer DNFs from higher positions than his team mate and therefore lose more potential points (as happened to Ricciardo in 2015, and Hamilton in 2012).

If I order the 2016 standings based on PPR, they look like this as of Britain. I separated Verstappen and Kvyat's ppr scores at STR and RBR into different entries.


This improves the situation a little for a few drivers, such as Palmer, and we also see Vettel and Ericsson move ahead of their team mates.

This now allows us to see who has really been performing good and who has been bad relative to their team mates.
The biggest under performers are surely Gutierrez and Kvyat. Kvyat's Red Bull performance is actually fairly respectable, but after being demoted to Toro Rosso his season has just imploded on itself. His scoring rate is miles off both of the other Toro Rosso drivers and is actually lower than Magnussen in the woefully uncompetitive Renault, and lower than all 3 McLaren drivers.
Gutierrez is even worse; his scoring rate is a dismal 8% of Grosjean's which is the biggest disparity of the whole grid. Whilst Grosjean is off mixing it with Force India, Toro Rosso and Alonso, Gutierrez is mired at the back barely ahead of the Manors, Saubers and Palmer. It has been an impressively awful performance even by his own standards.

By contrast Verstappen and predictably Alonso have been very strong, while Wehrlein's performance has also been very promising. Consider that F1Metrics' mathematical model rates Ericsson on about the same level as Massa, Perez and Hulkenberg, based on average perform across 2013-2015 - for Wehrlein to outscore Ericsson in what I am assuming is a similarly good/poor car is a very impressive rookie performance.
 

TR

Rookie
The downside of the way you construct the extended points table is that it copies the weird idiosyncrasies of the current point table. If you look at the current points table the points for first 6 or so positions are will fitted by an exponential decay (i.e. the relative point increase per position is almost constant) after that the decay becomes nearly linear. By copying that behaviour in essentially an exponential way (dividing the position 10 higher by 50), this weird behavior is copied. Consequently, there is a fairly drastic change in the points behavior around position 10 and 20.

The weird behavior of the current system is induced mostly by the desire to assign integer points. If you are going to switch to fractional points anyway, you might as well switch to a smoother distribution of points by extending the exponential decay of the first couple of positions.

If you further insist of having integer values for the first couple of positions you come to a fairly simple formula for the number of points for each postion

pts. = (125/4)*(4/5)^p
This way the number of points decrease by 20% for each position. Comparing this to the current pointscoring system and the system from the OP we get:

Position12345678910111213141516171819202122
Current pts.251815121086421000000000000
alt. pts2518151210864210.50.360.30.240.200.160.120.080.040.020.010.0072
alt. alt. pts25.0020.0016.0012.8010.248.196.555.244.193.362.682.151.721.371.100.880.700.560.450.360.290.23

The main effect is a substantial increase in the number of points for the higher positions.

Interestingly when we look at the current rankings with these points:
1Hamilton172.8
2Rosberg170.6
3Räikkönen113.5
4Ricciardo110.0
5Vettel109.0
6Verstappen99.8
7Bottas67.7
8Pérez59.6
9Massa48.6
10Sainz38.7
11Grosjean35.5
12Hülkenberg32.9
13Kvyat32.5
14Button27.9
15Alonso25.0
16Magnussen16.8
17Gutiérrez13.6
18Nasr10.6
19Wehrlein10.0
20Palmer9.6
21Ericsson9.5
22Haryanto4.7
23Vandoorne3.4
[tr][td]Pos.[/td] [td]Driver[/td][td]Alt. alt. pts[/td][/tr]

We see only minimal changes in the positions compared to the OP.
 
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