Season 10, stage 1 qualifying simulation after round 19

I reran the simulation at the end of round 19, There are 5 more known results that don't have to be simulated. The full explanation of how the simulation is run can be found in my previous post.

Booot made a big step toward qualification. Its win combined with Chiron's loss mean that it is the leading candidate for the last spot in the top 8. Gull and Fire qualify with high probability, better than Booot which is currently leading them in the crosstable. The reason is that Fire and Gull have 3 easy games to play while Booot has none. Chiron also has 3 easy games, this is why it is not out of the race yet. The result of game 232 (Chiron-Booot) may be crucial. Also, Chiron has an advantage in SB score in case of a tie break with Booot, but this may change.

The remaining games

• Booot (12.5 pts) - 1 Hard, 0 Easy, 3 Within (Chiron, Jonny, Hannibal)
• Gull (12.5 pts) - 1 Hard, 3 Easy, 0 Within
• Fire (12 pts) - 1 Hard, 3 Easy, 0 Within 
• Chiron (11 pts) - 0 Hard, 3 Easy, 1 Within (Booot)
• Fizbo (10.5 pts) - 1 Hard, 3 Easy, 0 Within
• Hannibal (10 pts) - 1 Hard, 2 Easy, 1 Within (Booot)
• Jonny (10 pts) - 1 Hard, 2 Easy, 1 Within (Booot) 

Results of 10000 simulations
Average final scores, sorted:

1. Gull - 15.0449
2. Fire - 14.5279
3. Booot - 14.26945  
4. Chiron - 13.75535
5. Fizbo - 13.0356
6. Hannibal - 12.282
7. Jonny - 12.27295

Percent of simulations to qualify, including tie breaks:

(without tie break) + (need tie break)

1. Gull - 95% + 4%
2. Fire - 82% + 12%
3. Booot - 60% + 18%
4. Chiron - 28% + 21%
5. Fizbo - 1% + 8%  
6. Jonny - 0% + 1%
7. Hannibal - 0% + 1%

Score for 3rd place including tie breaks:

• 13 or less - less than 1%
• 13.5 - 11%
• 14 - 43%
• 14.5 - 37%
• 15 or more - 8%

Tie break combinations

27% of the simulations require a tie break, which could be at least 4 for first place, at least 3 for second, or at least 2 for third. There are many possible combinations of engines that require a tie break, the three most common ones are

1. Booot / Chiron - 7.5%
2. Fire / Chiron - 3.9%
3. Fire / Booot / Chiron - 2.5%

Score-qualification graphs 

A breakdown of qualification by score for Chiron, Booot and Fire:


 
Chiron needs 14 (3 of next 4) to have a real chance, 14.5 and it almost surely qualifies.

For Booot the score thresholds are the same, but it only needs 1.5 of next 4.


Fire needs 14.5 to be sure, 14 may need a tie break, and even in some cases 13.5 will be enough.