Minimum Number of Races to win the Formula 1 World Championship

Andre covered the guaranteed case no matter what. if you are asking for the best case scenario (i.e. if the results in the first races are ideal for you) the answer is 11.

After 10 there cannot be any winner no matter what The most a driver can have after 10 is 250.

The remaining drivers win on average 4 points per race (76 points for places 2-10, divided by 19 racers). This means that one average a driver will have 40 points after 10 races. As a racer can get another 225 points in the remaining 9 races, 250 are not enough.

After 11 there can be an winner under ideal circumstances If a driver wins the first 11 they have 275 points.

If every other driver has under 74 points, they can get at most 274 points.

As the average of the points obtained by the 19 remaining drivers for the first 11 races is 44, is very easy to distribute the places 2-10 in the first 11 races in such a way that no one has over 74 points. If you want an actual example, I can create such a list.

The list

  • Driver 1: 11 first place finishes, 275 points
  • Drivers 2-3: 4 second place finishes, no other point, 72 points.
  • Driver 4: 3 second place finishes, no other point, 54 points.
  • Drivers 5-6: 4 third place finishes, no other point, 60 points.
  • Driver 7: 3 third place finishes, no other point, 45 points.
  • Driver 8: 6 fourth place finishes, no other point, 72 points.
  • Driver 9: 5 fourth place finishes, no other point, 60 points.
  • Driver 10: 6 fifth place finishes, no other point, 60 points.
  • Driver 11: 5 fifth place finishes, no other point, 50 points.
  • Driver 12: 6 sixth place finishes, no other point, 48 points.
  • Driver 13: 5 sixth place finishes, no other point, 40 points.
  • Driver 14: 11 seventh place finishes, no other point, 66 points.
  • Driver 15: 11 eight place finishes, no other point, 44 points.
  • Driver 16: 11 ninth place finishes, no other point, 22 points.
  • Driver 17: 11 tenth place finishes, no other point, 11 points.

The list if far from ideal, if you want one ideal, you just move points from the last drivers to the ones at the top to make as many drivers as possible with 74 points.


I believe the earliest a season could ever be clinched is after 11 races.

11 wins gives the leader 275 pts. There are 836 remaining pts from those first 11 races to be distributed among the other 19 drivers, so there is a lower limit of 44 pts for the next best cumulative score. 8 more races do not provide enough pts for 44 to catch 275.

Similarly, 10 wins gives the leader 250 pts and the lower limit for next in line would be 40. 9 more races offers a maximum of 225 pts for the chaser, for a total of 265. Enough to pass the original leader if he or she was stuck on 250. So 10 races isn't enough to create an insurmountable lead.


If you win the first $15$, then you have $375$ points. The person in second place has at most $270$, and can get at most $100$ points in the last four races, so cannot catch up.

A similar calculation shows that winning the first $14$ is not enough to guarantee first place. For that produces $350$ points. The person in second place might have $252$, so could end with $377$.

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Permutations

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