**It's the FSP-factor assuming you use all FSPs produced by sanctums to finish more sanctums. The Eco Sanctum on average produces 7/30 finish special production fragments. Basically you view yourself as only spending 30/30 - 7/30 = 23/30 of a collection when you collect it. So dividing by 23/30 is the same as multiplying by 30/23. This covers not only the immediate FSP (which could be viewed as only (37/30)) but also covers the fact that the finish you use also produces a fraction of a finish and then a fraction of a fraction of a finish, etc.**

**Hi there. 7/30 = 0.2333333...**

so to find all frags we just need to

multiply 30 with the

Sum of 0.23333333333333333^n for every integer n

( Σ (0.233333333)^n= 0.30434782608695652 according to

Therefore all the real frags for every collection
**are 30 x 0.30434782608695652 = 9.1304347826086956**

= 9.1304347826086956...

That's real average WON frags after each collection of Eco Sanctum, for infinite times.

Therefore for 1 full FSP , ones need approximately

30 / 9.1304347826086956.. = 3.2858 Eco Sanctums

These (on average) 7 produced FSP frags of each Eco Sanctum ,
**are in reality just bit over 9 real FSP Frags per Sanctum, **

so according to math, so you need just a bit over 3 Sanctums for each FSP.
Now, if we include BG-lvl91 collections to charge each Sanctum with a 2x chance,

then that 70% chance to double, is an average an extra factor of 1.7x

Because 100 % + 70 % = 170 % = 170/100 = 1.7 x

So, when using BG collections

** to gain 1 full FSP when charged with BG91**
**one needs**

3.2858 Eco Sanctums / 1.7 = 1.933 Eco Sanctums

Now the maximum BG level in Fandom info, is 75% chance at BG level 158 ( BG level 157 still has 74% chance)
Likewise, a 75% means a factor of 1.75x

**so with the Max known BG level of 158+**

3.2858 Eco Sanctums / 1.75 = about 1.87 Eco Sanctums needed for each FSP

But even a BG level 68 gives around 65% chance for doubling ( 1.65x)

which works out almost exactly like 2 Sanctums to gain 1 FSP , with BG68

( since 3.2858 Eco Sanctums / 1.65 = 2 Eco Sanctums approximately )