Point distribution in reversed grid races

In motor racing, as in other similar competitions, it makes sense for the amount of points given to be a decreasing function of position at the finish line: for example, the current Formula 1 scoring system awards

25 18 15 12 10 8 6 4 2 1

points to positions 1-10. Same system is used in FIA Formula 2 and Formula 3 races held on Saturdays. However, their Sunday race has partially reversed grid: those who finished 1-2-…-8 on Saturday start 8-7-…-1 on Sunday, while 9-10-… start where they finished. Can this reversal make it profitable to give up a position on Saturday?

The Sunday payouts are smaller: only top 8 earn points, in the amounts

15 12 10 8 6 4 2 1

– that is, same as the Saturday sequence without the first two terms. If the Sunday race has no position changes (which is not out of question, considering F2 venues include Monaco and Budapest) the totals amounts earned by those in positions 1-10 on Saturday would be:

26 20 19 18 18 18 18 19 2 1

By this logic, finishing 8th on Saturday would be slightly better than finishing 7th. And of course, there is a huge difference between being 8th and 9th on Saturday. Let us see what happens in reality, when overtakes do occur.

2019 Formula 2 season

For each position 1-10 on Saturday, the table states the points earned on Saturday, average points earned on Sunday, and average Saturday-Sunday total. Bonus points for pole position and fastest lap are not included, in order to focus on the effect of the finish position alone.

Sat Pos Sat Pts Sun Pts Total
1 25 5.6 30.6
2 18 5.6 23.6
3 15 5.5 20.5
4 12 5.7 17.7
5 10 8.1 18.1
6 8 5.7 13.7
7 6 6.9 12.9
8 4 8.2 12.2
9 2 1.5 3.5
10 1 1.4 2.4

Finishing 5th on Saturday is on average more profitable than finishing 4th. The gambit here is that losing 2 points on Saturday, one gets on the second row of the starting grid on Sunday (while the 4th place on Saturday becomes 5th, hence the 3rd row, on Sunday). The second row start gives an opportunity to quickly overtake the potentially slower drivers on the front row (after all, they finished 7-8 on Saturday) and take the lead. And indeed, three of the Sunday races of the 2019 F2 season were won by the driver who finished 5th on Saturday. It was a different driver each time (de Vries in Barcelona, Sette Câmara in Spielberg, and Aitken in Silverstone), so it does not look like anyone is intentionally executing this gambit.

Finishing 8th on Saturday maximizes the expected Sunday payout; in particular, 4 of the Sunday races were won by the driver who finished 8th on Saturday: Hubert did it twice in Monte Carlo and Le Castellet, then Schumacher in Budapest, and Aitken in Sochi. But when Saturday points are included, finishing 8th becomes less profitable than higher positions, although it is nearly the same as 6th or 7th.

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