Crosswind - critical direction?
On a prop-powered craft, a bit of rudder (sometimes a LOT of rudder) is required to hold the runway centerline on takeoff - the old "torque" effect (rotating slipstream against the fin, I'm told).
For a craft here in the Colonies with a clockwise-turning prop, it's right rudder that's required. (You backwards folks can do it your own way!)
If it's a left crosswind of any strength, you may well run out of rudder authority unless power is applied with caution. A lovely old taildragger met an unkind fate near here due to this effect.
Thus reduced takeoff performance is due to the reduced / delayed power used.
However, an equal but opposite crosswind would pose no such problem.
Are you considering the direction of crosswind in this study?