Rainbow perfect-matching game threshold conjecture

Let $n$ be even. In the rainbow perfect matching game $\mathcal{RP}_n$, played on $n/2$ copies of $K_n$, Maker wins by claiming a rainbow perfect matching; let $b_{\mathcal{RP}_n}$ denote its threshold bias. Rainbow-perfect-matching threshold conjecture.

$$b_{\mathcal{RP}_n}=\left(\frac{1}{2}+o(1)\right)\frac{n^2}{\log(n)}.$$

This is posed as a conjectural threshold for a natural rainbow extension of the perfect-matching Maker–Breaker game; no supporting theorem or resolution is supplied in the source.