Why AI benchmarks are more uncertain than they look
AI leaderboards often ignore statistical noise. Learn how Anthropic’s new approach to error bars provides a more accurate way to rank model performance.
Best quote from Why AI benchmarks are more uncertain than they look
Statistics is the science of measurement in the presence of noise. AI evaluations are, by their nature, incredibly noisy; this isn't about making the noise go away—it’s about learning how to work with it honestly and precisely.
This audio lesson was created by a BeFreed community member
https://www.anthropic.com/research/statistical-approach-to-model-evals and https://arxiv.org/html/2411.00640v1
Frequently Asked Questions
The question universe is the theoretical sum of all possible questions that could represent a specific skill, such as physics, law, or coding. Current AI benchmarks like MMLU or MATH only use a small sample of these questions. Anthropic’s research suggests that a model's score should not be viewed as an absolute truth, but rather as an estimate of its performance across this entire unseen super-population. Without acknowledging this "universe," researchers may mistake a model's luck on a specific set of questions for actual underlying mastery of a subject.
Standard statistical math often assumes every question is an independent event, but many evaluations use "clustering," where multiple questions are tied to a single long passage. If a model misunderstands a specific passage, it will likely miss all related questions, meaning the questions are not independent draws. Ignoring this clustering can result in standard errors that are three times smaller than they should be, giving researchers a false sense of confidence in results that might actually be statistical noise.
Instead of forcing a model to pick a single answer (like "A" or "B"), researchers can look at the internal probability the model assigns to the correct token. For example, if a model assigns a 72% probability to the correct answer, it receives a score of 0.72. This method eliminates the randomness associated with token generation and "temperature" settings. It provides a more nuanced, continuous score that can reduce measurement variance by up to two-thirds compared to traditional pass/fail grading.
A paired-difference analysis compares two models by looking at how they performed on the exact same questions, rather than just comparing their final average scores. Since frontier models often struggle with or excel at the same specific questions, their results are highly correlated. By focusing on the "gap" per question, researchers can subtract out the noise caused by question difficulty. This makes the measurement of the difference between two models much more precise and can even reveal that a model with a lower average score is actually the statistically significant winner.
Power Analysis is a mathematical formula used to determine if an evaluation is sensitive enough to detect a real difference between models before the test is even run. It helps researchers calculate the necessary sample size—often requiring at least a thousand independent questions—to ensure a result isn't just a false positive. This prevents researchers from "weighing a diamond on a bathroom scale" by ensuring the test has enough statistical power to see small performance gains, such as a 2% or 3% improvement.
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From Columbia University alumni built in San Francisco
"Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."
"I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."
"Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."
"Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."
"Reading used to feel like a chore. Now it’s just part of my lifestyle."
"Feels effortless compared to reading. I’ve finished 6 books this month already."
"BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."
"BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."
"BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"
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"The themed book list podcasts help me connect ideas across authors—like a guided audio journey."
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"Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."
"I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."
"Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."
"Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."
"Reading used to feel like a chore. Now it’s just part of my lifestyle."
"Feels effortless compared to reading. I’ve finished 6 books this month already."
"BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."
"BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."
"BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"
"It is great for me to learn something from the book without reading it."
"The themed book list podcasts help me connect ideas across authors—like a guided audio journey."
"Makes me feel smarter every time before going to work"
"Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."
"I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."
"Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."
"Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."
"Reading used to feel like a chore. Now it’s just part of my lifestyle."
"Feels effortless compared to reading. I’ve finished 6 books this month already."
"BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."
"BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."
"BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"
"It is great for me to learn something from the book without reading it."
"The themed book list podcasts help me connect ideas across authors—like a guided audio journey."
"Makes me feel smarter every time before going to work"
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