LoL matchmaking works with a hidden system that rates us as players, aka our MMR (match making rating or something). Typically, matchmaking tries to match players in the same division of the same tier, but it depends on your MMR. If i am bronze but I play with golds and plats in my normal games it is not because riots match making is wrong. I must have a decent mmr in norms and/or those golds/plats have a lower normal mmr. This is also a result because normal mmr and ranked mmr is separate. On top of that in norms once you reach plat-diamond (or wherever, but i feel like it becomes noticable here) ppl play more to fool around and try new things rather than try-hard every game. Typically you'll face higher divisions and ranks in norms as a result. Now, in ranked, mmr and match making is more stable. This is because your mmr is associated with your rank to an extent. If i am silver but am playing with all golds that tells me my mmr is that of a gold player and that given enough games i will make it to gold. If i am a silver player and play with high bronzes that means I need to step up my game to stay in silver, etc.
I dont know officially if kda goes into matchmaking or lp gains/losses BUT i think it almost certainly does. I think it affects your mmr more than your LP. However, I think your MMR affects your LP gains and losses (almost factually). If i go on a winstreak and i check my history i can see i go from playing gold 5 enemies on average to gold 2 on average even though I am still in gold 5 for example. However if it knows i am already a gold 2 level (as in im ranked g2) and im playing against gold 5's I might get 10 LP for a win and 20 LP for a loss. But if i am gold 2 and i am playing plat 4's i might gain 20 LP and 10 LP for a loss. Essentially you gain more lp the less likely you are to win a match. I also think you gain more lp if your MMR is MUCH higher than your rank (i believe) because the system wants you to be playing against even opponents as quickly as possible. This is also how you can skip divisions if your mmr is much higher than your rank. Its why all the challenger smurfs skip the 4th and 2nd divisions in every tier and gain over 20LP for wins even though they are actually challenger (system doesnt know this so if they were on their main they might only gain 1 lp for these games if for some reason they were playing against plats in ranked).
KDA is a bit trickier to see if it affects anything directly because obiouslly if you win you will naturally have a higher kda and if you lose a lower kda. Also kda is affected by positon and champion type since a tank will probably die more than an adc for example. HOWEVER, the new system rito implemented with grades/scores seems to give the impression that these grades will influence your mmr in a more complicated riot mmr algorithm.
Hope this made sense.
