The LMC Price Convergence Index
A robust dispersion metric measuring how tightly priced the AI model market is around its own median, in log10 dollar space, across four quality tiers. Computed weekly using biweight midvariance with 80% BCa bootstrap confidence intervals.
The median output price of the world's top 10 coding models fell from $10.3 to $4.80 per million tokens over 6 weeks - a 53.5% drop.
That is a compound weekly rate of -12.0%. Over the same window, the robust PCI compressed from 0.969 to 0.773 (20.2% tighter).
The commodity tier median rose from $0.78 to $0.93 (19.8% increase).
The commodity tier includes every paid coding model with output price below $50 per million - the surface that cloud buyers actually feel. Current sample size n=276.
PCI biweight midvariance
same slugs throughout
paid coding, < $50/M out
Robust PCI = biweight midvariance of log10 blended price
| Week | Frontier PCI | CI80 | Frontier $/M |
|---|---|---|---|
| 02-16 | 0.969 | 0.863-1.159 | $10.3 |
| 02-23 | 0.504 | 0.063-1.049 | $9.66 |
| 03-02 | 0.957 | 0.843-1.135 | $9.66 |
| 03-09 | 0.824 | 0.609-1.041 | $7.56 |
| 03-16 | 0.773 | 0.592-1.028 | $4.80 |
| 03-23 | 0.773 | 0.590-1.034 | $4.80 |
| 03-30 | 0.773 | 0.578-1.005 | $4.80 |
Leave-one-provider-out (LOPO): the share of variance that disappears when this provider's frontier models are excluded. A negative share means the provider currently lowers variance (their prices are central).
Formal definition, tier specification, why log-space dispersion, estimator choice, a worked example with last week's actual numbers, what PCI is not, data lineage, changelog, and references.
ReadThe complete time series for all four tiers, including robust PCI, raw stdev, IQR(log10), median price, BCa 80% CIs, OLS slope, and per-provider LOPO contributions.
/api/pci/seriesPCI 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 7 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 -0.0011 per week with an 80 percent CI of (-0.0417, +0.0414).
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.
Mostly no, by construction. Biweight midvariance downweights any single observation more than three or four MADs away from the median by zero, so a single anomalous price has bounded influence on the headline. The per-provider variance contribution table on this page shows leave-one-provider-out shares so you can see directly which provider currently moves the metric the most. In the latest week, the largest single contributor is xAI at 18 percent of variance.