Be aware of your surroundings (obstacles/map layout) and use it to your advantage. I think this is one of the most important factors in improving your gameplay.
A lot of people complain about how they are dying a lot to a particular gun like a shotgun or handcannon and then they immediately go and say that the gun type is broken before analyzing their own gameplay.
By using your surroundings you die less, can counter gun types properly, win more duels, and escape encounters you know you won't win. Of course your loadout will matter too as that will determine how you would use your surrounding.
If you are dueling and you see that you are losing, get back behind cover and don't challenge again. Find a different position to shoot from or just disengage entirely. People know this, but have a bad habit of not being consistent about it.
A lot of people constantly challenge even when their health is low. Yes you might want the kill and not want to lose the duel, but it's better to heal up and go to a different engagement than challenge with low health.
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Find gameplay of someone you admire in the crucible. My suggestion it (True Vanguard) but pick whoever your interested in. Also, live commentary helps you break down why the did what they did. Record your gameplay and watch it take note of every time you died and why. Compare what they do, to what you do. Then note why what they do works and why what you do does not work. Start adding these tactics to your gameplay. You’ll forget some to start with, but game by game you will forget less. Don’t worry so much about K/D rise or fall short term. When you feel like you have plateau’d find someone else to watch videos of. If you notice someone on your team dominating your opponents, watch them. The angles they use, did they crouch to break radar, did they lose line of sight then change angle to catch enemy off guard or after losing line of sight did they jump to take advantage of vertical space? Watching your last teammate standing in a survival match is great for this. Analyze their game play...why did they win or lose the round? Would you have won it and why? Practice just staying alive, the game mode Survival is great for this. If your getting shot before you know where they are, don’t waste time looking for them just get behind cover and look for an escape route just in case they decide to push you. If you are not the best one on your team, save as many lives for the person who is as you can. If you can stay alive and stop the enemy team from getting heavy your odds of winning just increased exponentially. If your not a 30 kill per game player, don’t try to be one. Run and gun, change angles until you get a pick or the killer on your team ends the round. Try to stop people from getting angles on your best player as well.