Points Systems Comparisons and Fairness of Each System

[rubbergoat]

Hey guys,

I have been busy blogging away looking at the different points systems that have been used since 1950, how the points were distributed and how fair each system was. This has been inspired by the change in the points system in 2010.

First, I looked at how points have been awarded since 1950. The original post is here but I will provide a summary for you guys: http://f1numbers.wordpress.com/2010/02/ ... 1950-2010/

The logic behind the new system is that by increasing the amount of points scored for a win and by increasing the gap in the amount of points for each position, overtaking would be increased as drivers have more incentive to fight for a win.

The new system, in case you did not know, is 25-18-15-12-10-8-6-4-2-1 from 1st down to 10th place.

But will it do this and what exactly is the gap between each position worth?

The first part of the question is speculative and my personal opinion is that it won’t – simply because the cars cannot overtake due to a heavy reliance on aero grip and a number of circuits being unsuitable for F1 cars (including some of the new ones). Increasing the incentive cannot and will not fix this…

However, the second part of the question is essentially a stats question and therefore one I can easily tackle in this post. Therefore what I will do is make a graph of each points system used in F1. I will then use these graphs to display each system separately and show in that particular points system how the points are scored in proportion to a win (100%)

Clearly a number of different systems have been used over the years, so it will be interesting to compare them to each other to see which systems reward drivers who go for wins and which systems reward consistency more. First, let’s have a look at the new system compared to the other systems in terms of amount of points scored:



What we see here is that until 2002 we had a nice system with about the same amount of points distributed through the field, and then in 2003 the ‘consistency formula’ meant that a lot more points were awarded. But 2010 is something else entirely and is two and a half times greater than the consistency formula! This means that the distribution of points is a lot more generous and also any records to do with most points scored will effectively become meaningless!

Let’s take another look at these systems and this time, focus at how the points are scored in proportion to the sum of all points available (from the previous slide):



Again, until 2002 the systems used were quite fair in awarding around a third of the available points to the winner, about a quarter of the points to second place and decreasing proportionally. The 2003 system instantly devalues a win by only awarding around a quarter of the points to the winner, and then a fifth to second place. The 2010 system does not change very much from this, which is interesting that considering one of the aims was to make a win more valuable. In fact, in the 2010 system a win is less valuable than in every other system!

But what about other possible systems? I have always had an idea of how to make a system that rewards winning, so I have decided to compare this to the 2010 system along with some other crazy ideas for points systems:



Are these good ideas or just silly? I mean, if we are prepared to throw out the records for points scoring, then why not use a system where loads of points are awarded for a win anyway?

In my next post, I’m going to look at how fair the points systems have been since 1950 up until 2010. Stay tuned for that, but in the meantime let me know what you think of the proposed systems, or if you have any better ideas

//RubberGoat
http://f1numbers.wordpress.com/

[rubbergoat]

In my next post, I’m going to look at how fair the points systems have been since 1950 up until 2010. Stay tuned for that, but in the meantime let me know what you think of the proposed systems, or if you have any better ideas

...And here it is!

In my previous post, we looked at various points systems used in the Formula 1 World Championship since 1950, along with some other possible systems that could be used. As promised, this is the second part of the post that aims to look at how ‘fair’ a points system is.

If you want to view the original post with a bit more detail, check here: http://f1numbers.wordpress.com/2010/02/ ... tems-been/

One of the reasons that the points system was changed was to give the new teams a chance of scoring points. Assuming 26 cars run this season (which is very much an assumption and not a certainty at this point!), the chances of any car being in a points scoring position is 10/26, or 1/26, which is about 38% (not taking into account any performance data of course). Under the 2003-2009 system, we had 8 points paying positions for a grid of 20 cars, which actually meant that at least 40% of the field could have finished in the points.

I am interested to see which systems were the fairest in terms of the most points paying positions in the field using this method, so I looked up some data on average field sizes and average number of cars that finished a race, with the help of Wikipedia, FORIX and Brian Lawrence from F1NGers (http://www.F1ngers.com) who had the stats available and helped compile them for me.

A special thanks must go to Brian who already had the stats collated and actually did the analysis for me – along with spending a good part of his Sunday conversing with me via email giving me some great advice and pointers to help me calculate the Fairness index. What a Legend!

So here are the graphs showing the fairness of a points system in any given year. Remember this is calculated by dividing the number of points scoring places by the number of entrants, qualifiers or finishers:



Notes: during the 1950’s and 1960’s it was not unknown to fill up grids with Formula 2 entries to make up the numbers. These cars were not eligible for points, however most databases have included these entries without distinction. Therefore I have chosen to include them for simplicity’s sake. However, the Indy 500 races that were a part of the World Championship have not been included as they were not regularly attended by the majority of the F1 grids. Finally, I will assume reliability levels in 2010 to be similar to 2009 due to the rules being similar and that 26 cars will make the grid (as this was the amount of cars the system was designed for).

This first graph compares Entry Fairness (No. of Grand Prix Entrants divided by No. of Points Scoring Positions).

To sum up Finishing Fairness, the value of the curve gets higher if the number of points scoring places gets higher or (more likely) the reliability of the cars decreases. It also seems that long periods of stability in the technical regulations makes the system more unfair.

Entry Fairness calculates the probability that if a car was entered into a Grand Prix, that it would qualify, finish the race and be in the points. The average for this is just over a quarter (28%), and you can also see from the curve which years had many more teams than others – for example 1989, where pre-qualifying was mandatory and it was not unheard of to see 35 cars on the entry list!

The average over the decades is just over 50%, so about half the cars stood a chance of finishing in the points. Again, note that when the points paying positions increased from 6 to 8, both graphs spiked indicating the system became fairer.



The second graph compares Qualifying Fairness (No. of Grand Prix Starters divided by No. of Points Scoring Positions). This really compares Grid Size with the number of points paying positions. So in the 1950’s, with grid numbers and reliability low, you tend to get values above the average (about 28%). Then, from the 1970’s until the 1990’s, grid sizes increase so that it becomes harder to finish in the points. Finally, post-2002 with grid sizes decreasing and more points positions, we see an upward spike in fairness followed by a drop after the engine freeze regulations. 2009 gives a small increase due to a fundamental rule change.

So which system is best? Which system awards winning by giving the biggest proportion of points? Conversely, which system has the smallest proportion and therefore rewards consistency more?

If we look carefully at the numbers, the system used in the 1950’s was quite fair, but the one used between 1961-1990 was only really fair during the 1960’s. From 1970 onwards, with larger grids and improving reliability, the system starts to become unfair.

The points system starts to become very unfair right before it changes to the 8-points paying position system in 2003. But the system is hampered by the reliability of the cars after the engine freeze. In fact, under the newest system, because there are more teams on the grid with what we assume have a similar level of reliability then the newest system is less fair than that in 2009!

Finally, if we extrapolate the graphs to include 2010 with it’s new points system, making the assumptions that 26 cars make the grid and reliability stays the same, we see that the new system is a little bit more unfair than the old system and is below the average for all years since 1950.

So I guess under those circumstances the newest system does address the fairness issue but does not go far enough (as it is still below the average). In addition, as shown in my previous post, the new system actually makes a win less valuable than before.

Thoughts? Questions? Any other ideas on how to make a fairer or better points system? I’d love to hear your point of view on the subject…


//RubberGoat
http://f1numbers.wordpress.com/

[Slife]

Great post Rubbergoat.

Personally I'm not sure if we should change the system so drastically, because it makes it harder to compare previous seasons.

But with that said, we probably couldn't really compare any two seasons that had different scoring methods, because the team and drivers in those seasons would have used strategies that tried to optimize their points for that system.

[Giblet]

Great post Great analysis, very concise and useful.

I have difficulty with the changing points system, as the last 3 years have been some of the most exciting in recent history.

It wasn't broke, but here it is getting fixed.