You should consider using sheet protection to prevent inadvertent
deletions by other users. Without seeing your sheets it is hard to
explain to you how and where to use it, but you can look up Protection
in Help. Array formulas per se don't do anything to protect your work.
Because of their complexity and need for special confirmation, they
can be more sensitive to inexperienced meddling. Just ensure that all
your cells with formulas are locked (Format/Cells/Protection) or
rather, since cells are locked initially by default, unlock your data
entry cells, and then protect the sheets. You may want to choose to
allow row insertion with the protection, so that you can enter new
players using Copy/Insert Row and then change the entered data in the
duplicate row you get to that for the new player. You could also
supply a simple macro tied to a button that does this and clears the
cells without formulas to prepare them for new data.

You might also want to change the cells containing the consecutive
numbers in column A of the "Active Players" sheet to something like

=Row()-Row(HeaderRow)

so as to preserve the consecutive numbering if, by chance, you
Copy/Insert or Delete a row in that sheet. It is usually dangerous to
assume that consecutive numbers will survive row insertions or
deletions. Good formula design makes lists with formulas impervious to
row insertions and deletions.