Is LLM Pricing Converging?

PCI measures how tightly priced a quality tier of the AI model market is around its own median, in log10 dollar space. The headline value is the biweight midvariance of log blended prices for the 10 models in the rolling frontier tier. A PCI near 0 means prices are clustered into a narrow band; a PCI near 1 means prices span a full order of magnitude. We work in log space because token pricing varies across roughly four orders of magnitude (sub-cent per million to several hundred dollars per million), which makes any linear measure useless.

Sample standard deviation has 100 percent efficiency at the Gaussian but 0 percent breakdown - one extreme outlier completely controls the value. With only 10 models in the frontier tier, that is a fatal property for a metric we want to publish. Biweight midvariance retains 87 percent Gaussian efficiency while tolerating up to 50 percent contamination, so a single mispriced or experimentally-priced flagship cannot move the headline. We still publish the sample stdev alongside as the raw measure for readers who prefer the textbook formula.

The trend slope is estimated by OLS regression of log(PCI) on the week index, with an 80 percent CI from a moving block bootstrap. With only 20 weekly observations the CI on the slope is necessarily wide, and that is the correct, honest answer. We refuse to publish a tighter CI than the data supports, and we will not publish any long-run floor estimate until we have at least 20 weekly observations. The current slope is -0.0385 per week with an 80 percent CI of (-0.0160, +0.0161).

Rolling top-10 uses whichever 10 models hold the top spots on the live leaderboard each week, so the membership changes whenever a new flagship launches or an old one is overtaken. Composition-fixed uses the same 10 slugs across every week (the latest week's top 10), with no backfill - if a slug did not exist in an early week we simply drop it from that week's sample, and we report the smaller n. The two series tell you different things. Rolling answers "what does the current frontier cost". Composition-fixed answers "how have these specific 10 models repriced over time". The gap between them is the composition effect.

Two reasons. First, the long tail of premium endpoints (image generation video, reasoning specialist tiers above $500/M) is so far above the main commodity market in price that including them turns the dispersion into a measure of "is the long tail still long" rather than "is the commodity market converging". Second, those endpoints are typically priced as launch experiments and reprice on quarterly or annual cycles, contributing pure noise to a weekly metric. The commodity tier on this page additionally caps at $50/M to track the cloud-buyer surface specifically.