Let $f(n)$ be the number of ways to do this with $n$ people with any size of the two (nonempty) teams. If we play the game if follows we must do at least $1+f(11)$. This is because if for the first team we pick any subset $S\subset\{1,...,11\}$, we can pick for the other players of this team to be those of $\{12,...,22\}-(11+S)$. It is clear that $f(n)=1+\min_{k=1,...,n}\max\{f(k),f(n-k)\}=1+f(\lceil \frac{n}{2}\rceil)$, since $f$ must be increasing. From this it can be shown that $f(n)=\lceil \log_2(n)\rceil$. Therefore the number we want is $1+\lceil \log_2(11)\rceil=1+4=5$