Agree, I felt free of shackles once I had everything unlocked on my classes because I no longer dived on objectives for point I could dive on them if I needed to instead. Key stats such as KDR and SPM are good indications that player might be good but are not absolute because they can be skewed so easily. It's likely though not certain that players with high stats for one or both are good players to a degree, but it's not completely unlikely for a player with lower stats to still be as valuable a team member. Quite often one man capturing one flag can bring your team back in to the fight and on to a comeback, they might have died a tonne to get it but there action saves your entire team. It's sort of a quality/quantity argument, one quality action or play can outweigh numerous kills or easy objective grabs in a tight match. How many times has a guy managed to get away to an objective only to die after their squad has spawned on them and gets all the points?
I tend not to look at the scoreboard when I play for this reason if I can help it, so I play with my mind focused on what I can do now instead of what's happened so far. Stats are nice to have but once you stop thinking about them you'll have more fun and be a better player all at once. Measure yourself game by game, what did I do well? Where did I make mistakes? What can I do better next time?
One key characteristic is learning to avoid reflexes and replace them with reactions, I've spoke about this in the past about COD titles. A reflex is something you do instinctively, for example when players see an enemy they often get focused on killing that one guy and lose awareness of their surroundings. I regularly catch chasing jet pilots out by turning tightly around a large object like the massive tower on Caspian and they're so focused on chasing me they fly right in to it. Use this to your advantage, use peoples reflex actions to make your own reaction and checkmate them.
Example from COD (first clip, 2 perspectives enemy and myself):
From my perspective you can see the enemy up and to the right, I can see he's seen me but I know he's not got enough time to get me because of his position, he isn't threatened by me so he has no need to fire , you can see him get up predicting me to carry on as I've not displayed any action that I've noticed him (he think he's got an easy kill coming now, I've avoided forcing him in to a reflex to fire early as I have a worse position if he starts a firefight now). My immediate reflex would have been to immediately fire as soon as I saw him, but instead I've played dummy and then as soon as I break sightline you can see I turn my character and move back quickly so he's facing the wrong way with no time to react. Cold and calculated I turn his position of advantage in to an easy kill for me by not forcing him in to a reflex and calculating his reaction in a split second, he makes a relatively good decision but I make a better one. I've taken it a step even further by using his own reaction against him by keeping cool and not reflexing myself, had he been looking at me directly to take shots, I would have been forced to reflex but I've observed his body position and seen an opportunity to use his own mind against him. It's not a sure fire victory to repeat this, but it's the sort of thought processes that I constantly go through when I'm on form and playing well.
A BF3 example is when you see an enemy tank and you have a support guy you're talking with, as even a Recon player I will fire randomly and loudly so the driver and gunner focus on me in the hunt for points, they might kill me but by the time they do they've got a stack of C4 on them from my buddy. A clever tank team would not both become focused on my red arrow, but it's very hard to ignore when in the situation yourself unless you're with a trusted team-mate.
@Mike
I agree Mike, but those special skills are only applicable on the assumption they have the opportunity to use them. A great assault player isn't much use on Op Firestorm, a great heli pilot is no good on Metro or if some noob has his precious helicopter. Which brings me to my point, they are good players overall and nice to have on your side, but they're great if they always have a trick up their sleeve in any situation. Players should first focus on specializing in certain areas, engineer, assault and main battle tanks is a good start, and then later try out different things which are more specialized and of less general use.