There have been a couple RPG's that have come out over the last few years that use Player Facing Defense. Mork Borg with its target number, and the Black Hack with its roll under mechanic.
When testing out these games my group had a ton of fun being in control of if their character got hit or not. They expressed that especially in an OSR style game where death is a lot more likely, having more control was really nice. "Ah damn, I would have made it out of the dungeon too if I hadn't rolled that 4 to defend against the orc."
So it was clear to me that Player Facing Defense was a rule I wanted to adopt, but I had to figure out how to adapt it to the system I was using. Both Mork Borg, and Black Hack also use a Armor is damage reduction system I didn't necessarily want to fit in as well.
The answer is actually pretty easy, and works with almost any D&D based games.
Your AC is 12 minus your Bonuses/Penalty. (In most games this is 10 +- your bonuses) [or 9 if BX]
When you get attacked you roll a d20 and subtract your AC from the roll. If that number is equal to or higher than the enemies attack bonus they successfully defend. The math works out just the same as if the monster was rolling to hit their AC, it is just in reverse.
What I mean by bonuses are: We are playing BX, Jim is wearing Leather (AC 7 or [+2] and a shield [+1] with a Dex mod of 0. So his bonuses are (2 + 1 + 0) = 3. Which means his AC 12-3= 9.
If we were playing 5e and Jane's AC was 17 then to convert you would do 12 - 7= 5.
Let's give an example of play:
DM- "Jim you are being attacked by the Orc Chieftan, roll to defend!"
Jim- "Alright I rolled a 14 minus my AC of 9. That's a 5 to defend."
*The Orc Chieftain has an attack bonus of 4 (THAC0 15)*
DM- "Success. You lift your shield up just in time to deflect the cheiftain's axe with your shield."
If Jim had rolled a 12 he would only have defended against a bonus of 3. The Chieftain would have hit him as his bonus is higher at 4.
The final thing using roll to defend does is shift the critical hits and fumbles from the monster to the player.
Use whatever makes most sense in your game, but I would recommend the following.
Natural 20 on the Defense roll: The player was ready for, and predicted the attack, they may roll to make a counter attack.
Natural 1 on the Defense roll: The player zigged when the should have zagged. Automaticly Hit (potentially extra damage)