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Riot probably has changed many things behind the scenes, but I think the MMR system (which is behind the League/LP system) hasn't undergone too many changes.supposedly the drastic drops are because rito fucked up the reset timing and it isn't or at least always isn't counting your pre season rank ups. So if you were actually XX5 at season end and then went to XX1 during pre season that whole grind didn't actually count as far as their weighing system went.
That said, from my observations playing since end of Season 1, here's why you experience drastic drops (and honestly, Gold 3 to Silver 4 isn't that drastic during a soft reset).
Starting MMR for an unranked player who never played ranked before is 1200 (with some consideration given to what your Normal games MMR is). I don't know how that equates to the League system exactly, but most assumptions are 1200 MMR is Silver V, 0 LP.
During placement matches the system tries VERY aggressively to put you into your correct MMR tier, so each game is +/- about 50 MMR
This aggressiveness slowly decays until you only get +/- 11 to 14 MMR per game.
It takes about 25 to 30 games to get to that 11-14 per game range, which means even games after the first 10 have a big influence on how fast you rank up.
That said, your placements are super critical in that each game is worth about 2-4 Normal Ranked games.
For those that don't know how the soft reset works, first, estimate your end-of-season rating:
Not exact ranges but close:
Silver V = 1200
Gold V = 1500
Plat V = 1800
The generally accepted formula is (Your MMR+1200)/2
In my case, Plat 2 is suppose to be around 2100 (from things I've read).
(2100+1200)/2 = 1650
Just the soft reset alone puts me in Gold 3 range without playing any games.
Then, because I went 2-8 in placements, and with every game equating to about 2.5 Normal games, I realistically went 5-20 in placements which is 15 games below .500.
15*12= -180
1650-180 = 1470 MMR.
This would put me high Silver 1, but it's also very close to Gold V. Obviously there are lots of factors at play here, but close 'nuff.
Using Rod's example:
Gold 3 is about 1600 MMR
After soft reset he's at 1400 which is Silver 2-3 range.
4-6 in Placements is about 5 more losses than wins in Normal MMR ranked games.
5*12 = -60 MMR
1400-60 = 1340 MMR, which is Silver 3-4 Range.
Again, it's going to vary wildly by when your wins/losses took place in Placements and what your exact MMR was and also what the breakpoints for the Leagues are, but it comes out close (within 50 MMR).
Just remember Game 1 of Placements is about +/- 50 MMR and game 10 of Placements is about +/- 25 MMR then you have another 10-20 games until you are back to 11-14 MMR per game.