Lag displacement rolls convert excess lead pursuit into lag pursuit.
They can be used defensively or offensively.
On offense they are most often used when the bandit creates excess lead pursuit by turning. The classic example is when you are in lag pursuit and the bandit reverses his turn. Lag instantly becomes lead pursuit.
The training example I've used is the high yo yo that converts to a lag displacement roll when the bandit reverses.
Here is an old film demonstrating this.
Yo yo to lag roll filmOn defense the most common use is to create excess lead through proper use of a break turn. Done correctly you create an across the tail overshoot which is, by definition excess lead pursuit. Wings level then nose high followed by a lag displacement roll to bring yourself onto the bandit turn circle.
Here is a short film that demonstrates the technique on defense. You will see in the film that it successfully converts the bandit from offensive to neutral. There are some requirements before using the lag roll on defense. The first priority is the bandit has to have excess closure. In the example the closure rate is just adequate to convert him. If the bandit has no excess closure he can follow the maneuver and get an easy shot. The break turn is where you make your decision.
Don't do a panic break. Slowly build the G force. The rate you build the G force depends upon the bandit distance and closure. Your goal is to time the break so that you reach maximum angle just as he arrives at guns range. Practically this means pulling the bandit through the canopy so that he reaches the lift vector (an imaginary line running from your seat through the top of the canopy out into space) just as he reaches guns range. At that point you have to know his closure. If he has excess closure and will overshoot behind your tail, go wings level, bring the nose above the horizon and put the lift vector on the bandit by rolling the wings to him. Hold the lift vector on him until he squirts out ahead of you.
If the bandit doesn't have excess closure the lag roll will get you killed. Roll underneath for a split S if you have altitude or flat scissors if you don't.
defensive lag roll