Explanation for LP loss in 4th place, and 8th losing you more LP than 1st gains you

There have been countless threads complaining about losing LP when they get 4th, or that they lose more at 8th than they gain at 1st. I think there's a simple reason that most people don't recognize, and doesn't just explain it, but also show you a hidden bonus we all get regularly.

The reason is this: when you lose at very low LP, you will NOT be demoted. You will instead be taken down to 0 LP, and you have to lose at 0 LP in order to be demoted. Yet, when you are high LP and win, you are instantly promoted with the extra LP to boot. These two things mean that every time you would have lost lots of LP at low LP, you instead barely lose any, giving you an effective bonus of the difference (If I would have lost 60 LP, but only had 5 LP, I essentially gained 55 LP for free). On average this effect would stack up infinitely, and the entire amount of LP gained per game on average would be more than the LP lost on average. This would mean everyone would creep upward in rank over time, horribly skewing the curve, with terrible players in plat and everyone else in diamond+. This can't happen, so they have to offset this constant bonus by making 8th lose more than 1st gains. Sometimes this, combined with getting 4th when you had very high MMR compared to your peers that game, results in 4th giving you negative a couple LP.

So next time you lose more in 8th than you gain in first, think back to the last time you didn't get demoted when you should have. =)