This is where
Bayesian reasoning comes in.
My initial response to Rocket354's claim that Ameer will probably end up
much lower (780-820) began with:
Let me unpack that. That "Lower? Probably" wasn’t a hunch—it was a
Bayesian statement. Here's what that means, in plain English:
When a new player like Ameer enters the system and posts a 500-game rating of
849 with an estimated uncertainty of ±18, the question becomes:
How likely is it that his true long-term level is really that high?
We don’t answer that by pretending all ratings are equally likely. That would be what's called a flat prior, which misleads us.
Instead, we use what we already know: the
real-world distribution of established players. Among those with 400+ games, the FargoRate population is centered around
490 with a standard deviation of 101. That's our
prior.
Ameer's 849 with SD (
±) of 18 is our
observed data, or
likelihood
Bayesian reasoning combines the two:
• The prior says, “Players with skill 849 are vanishingly rare.”
• The observed data says, “But this guy’s results suggest he might be one of them.”
The result is a
posterior distribution, a balanced estimate that accounts both for the rarity of such high skill and the strength of the observed evidence. In this case, it gives us:
Posterior = 838 ± 17
Still elite, but a little more conservative than the raw 849. This softening is called
Bayesian shrinkage: the idea that noisy data gets gently pulled toward the typical range—unless the evidence is overwhelming.
So when Rocket354’s say:
That actually flips the reasoning on its head. It ignores the prior and implicitly assumes all ratings are equally likely--which we know isn't true. That’s the entire point of having a rating system in the first place.
So again, my
"Lower? Probably" comment was not a dodge--it was an acknowledgment that the observed 849 is more likely an overshoot than an undershoot. The interesting question isn't
whether but rather
by how much? Bayesian analysis gives us a principled answer.
Here's the visual for anyone curious:
View attachment 847446
—The orange curve is the prior distribution (real player population).
—The blue curve is the observed 849 ± 18.
—The green curve is the posterior: our best guess about Ameer’s true skill after combining both.
So yes—849 is more likely an overestimate than an underestimate. That’s not mere conjecture—that’s just applying what we know about statistics and the world.
