That's such a clean and easy way to include the audience selection - I love it
It also means that your number is more accurate than mine #goteam
I've calculated my numbers again using 9,216 combinations (thanks!) and an Arithmetic Series, but this is based on a shaky interpretation of the 90% found in the FRC Blog.
An average event has 100 matches, and 90% of those have unique field combinations (90 matches).
Therefore Event 1 - 90/9216 = 0.98%
At Event 2, 90% of the field combinations have been used before (at Event 1) and 10% haven't. (I think..)
Therefore Event 2 - 0.98% + (0.98%*0.1) = 1.078%
Similarly, at Event 3, 90% of the field combinations have been used before (at Event 1 and 2) and 10% haven't.
Therefore Event 3 - 0.98% + (0.98%*0.1) + (0.98%*0.1) = 1.176%
From this, we can see a pattern is emerging. For each event, we add (0.98%*0.1), therefore we can create a generic formula to represent the projected percentage of defensive combinations used at any given event.
Therefore Defensive Combinations = 0.98% + (n-1)(0.98%*0.1)
This fits the generic form of an Arithmetic Progression, where Term n = a + (n-1)d, where a is our first term (0.98%), n is the event number, and d is the common difference (0.98%*0.1).
Using this, the 121st event would be term 121 (n=121).
Therefore, Defensive Combinations used by the 121st event would equal
0.98% + (121-1)(0.98%*0.1) = 0.98 + 120(0.098)
= 0.98 + 11.76
= 12.74%
So this means that after the 121st event, roughly 12.74% of the defensive combinations have been played. Does that make sense??? Happy to explain further. This is so much fun!!!