Ranks are partly a progression system. Riot uses it to keep folks playing. People aim for benchmarks. Riot also uses it to hid when some one sinks. Demotion is a massive value inside the bottom of a Tier. So you have pools of players in Division 4 with MMR several divisions lower pretty often... But Riot doesn't want any one feelings to be hurt by deranking and losing their shiny rank.
A Pure progression system is not about skill, its a time investment. X games X exp X hours. ETC. Like your summoner level, that's a progression system.
The Ranks are Tied loosely to A skill rating system. MMR. They don't use the exact value because then people see when they sink, or when they peaked and got stuck. This is pretty common with Modern Devs as a lot of players will quit when they cap or fall.
Blizzard, for example would give you a Raiting, but their Raitng given and their MMR raitings where different. The ones you see moved slower then their internal MM's MMR to get more games outta folks.
Anyhow back to Riot. Riot added a worst case rank for placements as a response to people Bitching placements. You now see a value over every game. The dramatic leaps per win early on serve as "motivation"... but the MMR can be found fairly easy looking at match averages.
So, Some one new will be like HELL YES IM AT GOLD LEVEL OF SKILL! because they played and won vs a team W gold players or won lane vs one. When the match average is around silver 2. That player will then think hey I can hit gold, I have played vs and done just fine. Set that as the benchmark, and play all year aiming for it.
Also, The worst case you see after 1 game also serves to deal with demotion protection. Some one who goes 0-10 would end up at B4, Then they have a huge window to prevent dropping to iron so they don't rage quit but they avoid being stuck in silver 4 should they be low bronze or Iron level skill. Meanwhile folks who already did a season with poor results? They drop to iron and wanna at least make it back to their old rank.
So until the progression system catches up to MMR some ones's Rank is useless as a skill indicator, and riots Division 4 will always be a bit fucky due to demotion protection range. The way they can tie the two systems is LP slant. You take your MMR values and break them into chuncks. Say 1200-1270 = silver 2. Players At that MMR with that rank see LP be more or less equal. Players higher rank see slant for worse LP gains and Higher LP losses. If your ranks below it you see higher LP gains and lower losses. Built so that if you hover at 50% long enough your Rank falls into the exact same MMR range set for it.
Now, as far as Riot and LP slant goes? That does seem to be the case pretty frequently, thou Duo can make for some weird impact.
For you specifically, Your playing in silver and so a win jet speeds you forward because your placement rank is "bronze" and its far lower then your MMR of silver.
Information is accurate far as I know and I tried to be clear when it was an opinion or observation. Elo/MMR is a topic I find nifty, I like the math and logic behind them. So let me know if your interested or have questions.