rear suspention.

[Fazerider]

A floppy rear may not be the fault of the shock itself.
With the bike on the centre stand put your chest on the saddle, wrap your arms around and try pulling the rear wheel up. There is always a bit of free play in the shock linkages and the large amount of leverage means that translates to a couple of mm movement at the axle, but if the bearings in there have been neglected there could well be a lot more slop than that.
I'd check that before spending money on a replacement shock.