Think of it this way. There are 2 goals you can have when setting the length of the race.
1. Long enough to see who is playing better "that day".
2. Long enough to see which player is better overall.
If the race is so short someone can run out the set, that's no good.
Well.. it's ok if the odds of running out the set are like 1-in-a-million.
Pretty much all tournaments use #1 as their goal... trying to do #2 takes too long.
So to figure out a good race with goal #1 in mind, you can just use simple statistics.
Decide how many chances you think you want to give the player...
I personally like 3 chances. Like in baseball, 3 strikes.
Track how many racks a player runs, on average, when he steps up to break.
Let's say it's somewhere between 2 and 3 racks. So if you want to ensure 3 chances,
then race to 9 should be ok. Round up to 10 to be safe.
Goal #2 is different and much tougher to calculate.
You can have two APA 5's, who both play very very similar.
If they played 100 racks, it might end up with a score of 51 - 49 or something.
So for that specific pair of players you need a very long race.
If you suspect two players are extremely close, and you have goal #2 in mind,
Then you should race to the absolute maximum they will tolerate.
I think oldschool races to 100 in TAR follow this thinking.
The funny part is, pool is hugely psychological. Momentum is a real thing even
if you can't quantify it. Mindset, attitude, what people call "heart" can change from day-to-day.
So if Alex beat Shane in one race to 100, and then Shane wins the next race to 100,
does that mean 100 is not long enough?
Maybe. But probably the 'intangibles' affected the outcome.
They play close but not so close they need 500 racks to figure it out.