Jab, cross vs. jab, pull, cross

I assume you are talking about to push with your left hand, and punch with your right hand at the same time.

When you punch, your opponent's body can

1. move back,
2. static,
3. move forward.

IMO, for your striking result,

1 < 2 < 3

MT guys like to pull their opponents into their knee strike. The head-on collision always cause more body injury.

A + B > A
That really depends on personal preference. From my perspective, you move back, when the opponent is ahead on timing/takes you by surprise. You stay static/either don't move or sidestep when both you and your opponent have the same timing, and you move forward when you're ahead on timing. I learned that initially with weapons, but feel it works perfectly with no weapons as well.

For the result you state, I think it depends on the situation. If they don't manage to dodge your attack, then your assumption of 1<2<3 is right. But if they manage to dodge, then 3 is probably the worst option. You never want them to dodge while coming in, if you punch. That results in their punching having the force of their punch + the force of your punch, which is not fun at all. Ideally, if I punch, whether or not their responding, I want them moving back as it allows me to chase for 1-2 more strikes before I back out and reset.
 
if I punch, whether or not their responding, I want them moving back as it allows me to chase for 1-2 more strikes before I back out and reset.
If your opponent can move back faster than your advance, your 2nd punch may not land. Your pulling just try to slow down your opponent's backward movement, or speed up your forward attack.
 
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I think the pushing vs. pulling depends on what type of fighter you are. As a striker, you want to 'push' with your strikes to get more power in them. As a thrower/grappler, you want to make sure your punch ends in a way you can pull, to move into your domain.

More what you are trying to do.

I would push to lift the elbow or pull to drop the hand.
 
If your opponent can move back faster than your advance, your 2nd punch may not land. Your pulling just try to slow down your opponent's backward movement, or speed up your forward attack.
I think that a fight where the other person can back up faster than you can go forwards is a rare enough occurrence I shouldn't plan around it.
 
I think that a fight where the other person can back up faster than you can go forwards is a rare enough occurrence I shouldn't plan around it.
If a person is attacking you then there is more probability that he or she is the one pressing the attack. I personally have never had to go chase people who wanted to hit me.
 
If a person is attacking you then there is more probability that he or she is the one pressing the attack. I personally have never had to go chase people who wanted to hit me.
I'm assuming here that we're talking about in a ring or sparring match. If not, then yeah I'm not chasing someone if they're scrambling to get away from me.
 
I'm assuming here that we're talking about in a ring or sparring match. If not, then yeah I'm not chasing someone if they're scrambling to get away from me.
I was only referring in general, that if I want to attack you, then I would need to come to you vs trying to escape. This gives you the opportunity to push me.
 
I was only referring in general, that if I want to attack you, then I would need to come to you vs trying to escape. This gives you the opportunity to push me.
I think John was referring to the second punch. So the idea that after your first punch lands, they would then start backing up.
 
I think John was referring to the second punch. So the idea that after your first punch lands, they would then start backing up.
Even then, if they plan on attacking you after your first punch then they will either stand their ground or push forward. If they escape at that speed then you will most likely not have the chance to pull them either.

For me, I don't think I've been in a fight where they moved back that fast. Usually the first punch stuns which is why people get hit with 1-2 combos all the time. Usually when they escape it's to avoid the first punch. Normally they don't see the second punch. The only thing with pushing is that it has to be in a way that makes them fall off balance and not assist there retreat. I hit someone and then wanted to push them, then I want them to hit the ground hard. So I'm looking to push them while they are off balance or in a bad standing structure.

For me this would be the same for pulling. I won't to pull my opponent off balance and not assist him with his forward counter attack. The probability of me being success is based on when I decide to push or pull and if I screw it up. I think I prefer pushing, but will probably pull off a slow jab.
 
I think John was referring to the second punch. So the idea that after your first punch lands, they would then start backing up.
When your opponent is in boxing guard, your punch can not punch through. If you use a fake punch to set up a pull, you can pull his boxing guard apart. You then punch through the opening.
 
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