win, loss, draw chances model

Everyone knows the ELO point ratio model:

f = point ratio = 10^(ΔELO / 400)
g = point fraction = f / (1 + f)

Chess-com reports about 55% of points are won by black.  Plugging this into the equation yields a white ELO advantage of:
400 × log10(0.55 / 0.45) ≈ 35

So this adjusts to:
f = 10^(( white ELO + 35 - black ELO ) / 400)
g = f / (1 + f)

Fine -- this is all basic.   The trick is figuring out draws.  Obviously draws are most likely when players are evenly matched, and draws cannot result in more points than the ELO formula predicts.   So any formula for draws must leave room for wins by either player.

The following seems to work:
p(draw) = 2 g ( 1 - g )

then
p(win) = g - (1/2) 2 g ( 1 - g ) = g²
p(loss) = 1 - g² - 2 g ( 1 - g) = (1 - g)²

If g = 1/2 (players are evenly matched after adjusting for white advantage) then:

p(win) = 1/4
p(loss) = 1/4
p(draw) = 1/2

This would apply to classic games between top players, not bullet games or games between novice players.

Comments?

Here is a calculator by the mathematician François Labelle:

https://wismuth.com/elo/calculator.html

A 55% draw rate is claimed here:
https://en.wikipedia.org/wiki/Draw_(chess)
Since I assume 50% is the maximum chance for a draw, the average would be less than this, so my simple formula will slighly under-predict the chances of a draw. But as a crude model it's fairly close.
Additionally, studies have shown the exponential ELO formula tends to break down "in the tails" (when ELO difference reaches 150 or more). It's said you can tend to gain ELO if you play players rated +150 ELO. If the ELO formula was exact, playing players of any ELO would tend to retain your ELO. (there's other issues with ELO model, like whether games are correlated, and whether certain players at the same ELO are a better or worse match to your skills and style). There's also ELO "inertia" -- a player who has dramatically changed will play better or worse than their ELO until their score fully responds. So any ELO-based model is going to be limited.

@3

Draw rate depends on rating:
lower draw rate near 0% at lower ratings, higher draw rate near 100% at higher ratings

Interesting! The ELO per pawn plot is very interesting. I had come up with 120 ELO/pawn using a very crude approximation watching Hikaru play a "Botez Gambit Speedrun".
He'd trade a queen for a piece and positional compensation early. A queen is worth around 9.5 pawns, while pieces are worth around 3.5 pawns, so this goes down 6 pawns, but positional compensation is an additional pawn, perhaps, so it's a 5 pawn advantage. He was able to beat players most of the time rated 2100, so was playing at around a 2400 level, and was rated around 3100 or so, so that's 700 ELO / 5 pawns, so on order 140 ELO / pawn as an upper bound (he was playing distracted, so perhaps a bit lower, so I guessed around 120 ELO / pawn). The plot has the advantage at twice this. But that was playing blitz.
For draw chances, that model uses draw odds of 0.6 pawns. So the draw chance can be inferred from the difference of draw odds. My formula is simpler but doesn't account for the reduction in draw odds with ELO.