If you blow the shot and the guy does a split-s, he just wasted a ton of E. Split-S not a good E conserving maneuver. Immelman is tons better, however it takes 'longer' to perform the immelman cause you really slow down over the top. Try something like this, if it's vertical separation you want to minimize...
Guy split-s, he may roll while vertical, you don't know which way, so...
pull up 45 climb till you hit sustained turn speed..don't immel. Then, go into flat turn to bring bogey into your 3-9 line. What? Did he say 'flat-turn?'. Yes! Speed is constant, height is constant = NO E LOSS! Your turn rate will be better than if you tried to pull over in an immelman and you don't have to pull any power back and you keep vertical separation to a minimum while 'retaining' your own energy. It's kinda like that last 100 mph in a vertical zoom/hammerhead...complete waste of time..you can't do anything until you dive down again past 100 mph so you can maneuver, where your back where you started!