This is a copy of a shared ChatGPT conversation
ChatGPT said:
Yes, for historical Dota 2 rankings, a top ~1% interpretation is actually quite plausible, and it's a better anchor than assuming a generic normal distribution with σ=300.
A few reasons:
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Early Dota 2 MMR was essentially an Elo-derived system with separate solo and party (team) MMR.
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Valve used hidden matchmaking ratings and calibrated players into a relatively broad distribution, but the distribution was not perfectly normal.
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The upper tail was quite stretched because highly skilled players continued to gain MMR instead of hitting a hard ceiling.
If we use your data:
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963 games,
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57.32% win rate,
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initial calibration around the median,
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assume an effective K about half of what we initially used,
we obtained
Rf≈2205.The absolute number (2205) isn't directly comparable to Dota 2's published MMR because the scale depends on the game's internal constants. However, the relative gain
ΔR≈705is the meaningful quantity.
If the median is around 1500, then
300705≈2.35standard deviations above the median, which corresponds to about the 99th percentile.
This aligns remarkably well with your recollection.
In fact, your recollection provides an independent sanity check: if you remember your rank being around the top 1%, then an inferred gain of roughly 700 Elo-equivalent points from a 57.3% win rate over nearly 1000 games is internally consistent.
The main caveat is that Dota 2's separate solo and party MMRs complicate the interpretation. If approximately half of your games were solo and half party:
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each rating evolved independently,
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each received only about 480 games,
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so neither ladder experienced the full 963-game progression.
That means a more faithful model would treat the two ladders separately. If your win rate was similar in both, each rating would gain roughly
481.5×10×(0.5732−0.5)≈352points rather than one ladder gaining 705 points. Whether that still corresponds to the top 1% depends on where each ladder started and on the calibration scale Valve used.
So there are two possible interpretations:
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Single combined rating throughout all games → gain ≈ 705 Elo-equivalent, which is consistent with roughly the 99th percentile.
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Separate solo and party ratings → each gains ≈ 350 Elo-equivalent if the games are split evenly.
Do you remember whether the 57.32% win rate is for all games combined, or specifically for solo matchmaking? That makes a significant difference to the inferred peak solo rating.