The below could probably be applied to most things, though it's targeted to healing and PvE. My advice is general, because if you have the attitudes and habits of a great player, you'll find the specifics. Some might claim my advice is also targeted at newer healers; while this is true in a sense, having trouble with the issues below is common even amongst veterans.
1. No, you didn't have lag -- accept responsibility. Lag is to healing as dogs are to homework. Let's take a moment to be honest with ourselves: Most of your healing errors occurred because you messed up. Step up and admit to your group that you mistimed, misjudged, zoned, went AFK, etc. People appreciate others who take responsibility. "I'm sorry about that, everyone, it won't happen again," will earn you respect much more than, "I had lag -- don't look at me!" How will you progress as a healer if all your healing mistakes occur at the same time as "OMG LAG"?
2. Be critically positive. When I used to raid lead, I tried to foster an environment of taking responsibility. After one wipe, the other healer whispered me to list every mistake she made. Five minutes later, I got her calmed down and we won. Hooray, loot for ... oh no! Five more minutes ... Next boss ... We wiped ... Elune, please not again! Ten more minutes of said healer apologizing for every mistake. I considered what I could say to restore her confidence and make her more positively critical. Ahem: "Get over yourself. You will make mistakes."
3. Mistakes = Opportunities. The third thing that healers should realize is that mistakes are learning opportunities. The very first raid I ever healed, I was pathetic. I spammed Greater Heal for 30 seconds and spent the rest of the fight wanding. Afterward, I sat down determined to learn from my mistakes ... and eventually, I did. Every mistake is a chance to not make it again and get better, if you will pursue it as such.
4. Patience reaps rewards. To prevent burning out faster than a Roman candle, all healers need to understand that even if you play perfectly, the team can still fail. No, that doesn't make it a fail team that you should swear at, then drop group. There will be times where a group has to wait for you to learn. When another member of your team is learning, realize that he waited for you and that the best thing you can do for your team is to be patient.
6. Find your rhythm. A funny thing happened to me once; I happened to be raid healing while my wife played piano a few feet from me. When she finished, she turned and stared at my hands on the keyboard. "Are you sure you don't know how to play?" My epiphany: Good healers are constantly in motion, and when healing, their hands dance across the keyboard with a distinctive rhythm. To play a healer well, you need to be able to get in sync with how healing flows. To do this, practice healing, alter your UI setup, change your keyboard. An excellent healer's goal is fluidity, to make healing music.
7. Seek out senseis. There will always be someone better. Take time to learn about your class and keep up to date. You will never know all you need to about healing. Find the best healers and figure out how to become just as good. Being able to identify a great healer makes you a pretty good one, too.
9. Forgiveness is a virtue. I have noticed an antipathy between healers and DPS. Realize that DPS are not all running to stand in a fire to irritate you. They don't all blame you for their mistakes, and they're trying to get better too. As a healer, your place is to heal, not judge. Falling into seizures for having to heal the DPS, stupid or not, takes away from what a classy healer you are.
10. Tanking is a responsibility; healing is a job; DPS is a game. If you said, "Definitely!" -- you shouldn't be healing. Play a healer because you love healing. That love of healing will make you into an amazing healer. If you hate what you're doing, I doubt you will ever measure up.
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