Well, there was some recently published research that claimed to find that most of the effect attributed to CEO performance actually can be explained by random fluctuations. Make of that what you will.
X and Y are arbitrary
The PR version: http://today.tamu.edu/2015/10/15/ceo-effect-on-firm-performa...
But there could be an element of truth to it, which might warrant further research. If CEOs really do have a much more limited influence than they are given credit (or blame) for, then incentives perhaps ought to be adjusted, not just in the interest of fairness but also in the interest of finding better ways to actually improve performance.
Regardless of the firm's performance, it's a difficult role to fill -- especially for a large, multi national conglomerate.