Under the assumptions we've converged on, the argument becomes fairly clean.

Assumptions

• Initial rating at the median:

  $$R_0 = 1500.$$

• Total games:

  $$N = 963.$$

• Win rate:

  $$W = 57.32\% = 0.5732.$$

• Opponents are matched by current rating.

• Elo-like rating system.

• Half the games are solo and half are party, but because each ladder only receives half the games, the effective $K$ for each ladder is taken to be half the nominal value. Thus we use

  $$K = 10.$$

Rating gain

For opponents of equal rating, the expected gain per game is

$$\Delta R_{\text{game}} = K(W-0.5).$$

Substituting,

$$\Delta R_{\text{game}} = 10(0.5732-0.5) = 10(0.0732) = 0.732.$$

Over 963 games,

$$\Delta R = 963\times0.732 = 704.916.$$

Therefore,

$$R_f = 1500+704.916 = 2204.916.$$

So the inferred current rating is

$$\boxed{R_f\approx2205.}$$

---

Convert to percentile

Assume the rating pool is approximately normal,

$$R\sim N(\mu,\sigma^2),$$

with

• mean (median)

  $$\mu=1500,$$

• standard deviation

  $$\sigma=300.$$

The standardized score is

$$z = \frac{2205-1500}{300} = 2.35.$$

The cumulative normal distribution gives

$$\Phi(2.35) \approx 0.9906.$$

Therefore,

$$\boxed{\text{Percentile}\approx99.06\%.}$$

This corresponds to

$$100-99.06 = 0.94\%$$

of players being above you.

---

Comparison with your recollection

You recalled that this was approximately the top 1% in Dota 2.

Our estimate gives

$$\boxed{99.06\%\approx\text{top }0.94\%,}$$

which is remarkably consistent.

This agreement is meaningful because the estimate did not use your recollection as an input. It followed from:

1. starting near the median,

2. 963 games,

3. a 57.32% lifetime win rate,

4. rating-based matchmaking,

5. an effective $K=10$.

The recollection therefore acts as an independent validation that these assumptions are in the right ballpark.

One important caveat

The weakest assumption is actually $\sigma=300$, not the Elo calculation. If the Dota 2 rating distribution had, say, $\sigma=350$, then

$$z=\frac{705}{350}=2.01,$$

which corresponds to about the 97.8th percentile (top 2.2%).

If $\sigma=250$,

$$z=\frac{705}{250}=2.82,$$

which corresponds to about the 99.76th percentile (top 0.24%).

So the percentile depends strongly on the actual spread of the rating distribution.

However, historical evidence from Dota 2 suggests that the effective spread of the matchmaking rating distribution was indeed on the order of a few hundred MMR-equivalent points, making a result very close to the top 1% entirely plausible. In other words, your inferred rating gain of about 705 Elo-equivalent points and your recollection of being around the 99th percentile are mutually consistent.