# Sequential Pattern Mining – Statistically Relevant Patterns Among 25, 18, 15, 12, 10, 8, 6, 4, 2, 1

Here is the current Formula One World Championship points scoring systems
Currently in Formula 1, there is a lot of talk about this and whether it is adequate or if it should be changed.
$$\begin{matrix} {\it prix}\,{\it finishers} & {\it points}\,{for}\,{\it pos}\\ 1 & 25\\ 2 & 18\\ 3 & 15\\ 4 & 12\\ 5 & 10\\ 6 & 8\\ 7 & 6\\ 8 & 4\\ 9 & 2\\ 10 & 1\\ 11\!-\!{\it The}\,{\it Last} & 0\!,\!{\it Total}=101 \end{matrix}$$
The points system may not seem that important to some. But it can have a big impact on the tactics drivers and teams use in races, depending on the reward available to them.

Criterion. What should an ideal points system be able to provide ?—

· Reward for race winners.
· Motivation to overtake in the final third of a race & for front runners to keep pushing for the race win.
· Opportunities for points for midfield and back-of-the-grid teams.
· A system that can keep the championship close.
· A system where the best performing driver can win the title.
· The system has to be easy for fans to understand.
So how could this system be possible for a points system to provide those wishes all, then, what would be the statistically relevant patterns among $$25, 18, 15, 12, 10, 8, 6, 4, 2, 1, =101{\it ?}$$

• Reward for race winners

Give the race winner the most points.

• Motivation to overtake in the final third of a race and for front runners to keep pushing for the race win;

Create a dynamic with more variation. A good example is road cycling like Tour de France where various bonuses are granted on different aspects, climbing, sprinting. Also an extreme performance in a specific stage gives additional bonus because the actual time counts in the end classification, and not just the position.

To do this in Formula 1 would require not just a change in the points system (the final time could be included somehow) but also a change of the rules.

For instance, one could have a race that is composed of multiple sprints in which points are scored and the safetycar brings the field together in between. In this way points will be granted in the race earlier, which reduces the bad luck due to crashes or mechanical error. But don't worry if you like that risk component, the reduction will be balanced by teams and drivers being able to increase the risk that they take.

• Opportunities for points for midfield and back-of-the-grid teams;

As in the example before, this will provide more opportunities for smaller teams to obtain points early in the race and benefit from aggressive setups that try to reach a higher grid position.

Midfield teams actually have a lot of opportunities. They need to worry less about using an entire Mercedes engine in a single race, like Hamiltion did in Brazil last year. They could gamble and go for a few extra points in one race and then take the penalty in another race. For top teams, this is a bigger risk because the risk loosing points with the penalty (and the smaller teams don't worry about that).

• A system that can keep the championship close;

A straightforward example would be to penalize the better player. Or to have a progressive system where the points increase towards the end making opportunities to overtake after initial error more likely. But, these could be considered unfair.

Another easy way could be to strike a few of the worst results. This will reduce variations due to error. If you make a mistake in formula 1 you score zero points, the impact is big. In other sports, you just lose some time or miss a goal in a match. This type of points system will actually make the system fairer. While teams and drivers should be reliable and its is a component of the sport, it also occurs regularly that a car fails due to bad luck (e.g. some other driving crashing into you).

• A system where the best performing driver can win the title

Give all drivers the same materials. (but that is against the philosophy of the formula 1 which is a mechanical sport)

There are some systems that rank drivers based on how they performed compared to their teammates that have, in principle, the same material and team support. These systems combine results over the entire history and combine several years. But even then they are not perfect as we see all the time these type of comparisons but with a different driver that is at the top. For a single year it seems unfeasible to make a method of a fair ranking of drivers that have been driving with different teams in different cars. The drivers Formula 1 championship is like comparing apples and oranges. The fastest fruit wins with some help of the driver.