Correlation

Pearson as published; the rank correlation, Spearman on the ranks of the same two columns; Pearson recomputed across every endpoint outside the top 1% by calls; and Pearson across the 13,269 endpoints carrying both counters at the first snapshot and at this one, which is the same set of endpoints throughout and so cannot move because the index changed shape.

The last two columns are the two explanations that do not hold. The same 13,269 endpoints, measured at both ends, move from 0.111 to 0.448: the rise is not the index changing composition. Outside the top 1% by calls the figure holds near 0.56 throughout: the rise is not the index as a whole.

Removing the single largest endpoint by calls takes Pearson from 0.45 to 0.10. That endpoint is q verdict resource on www.ax1.vc, paying to 0x7284D4…2d299C. Between 2026-09-10 and 2026-09-15 its counters went from 3,147 calls and 246 payers to 64,125 calls and 2,161 payers, 15.6% of all calls counted. It is now the largest endpoint on both axes at once, which is the one arrangement that pulls a linear correlation up.

What makes it a single point rather than a trend is the endpoints ranked below it. At this snapshot they carry 198, 1 and 1 payers against 2,161.

Pearson’s r measures linear association between two quantities, and each observation enters it weighted by how far it sits from the mean of both. A point at the extreme of both axes therefore contributes more than thousands of ordinary ones. The rank correlation asks a different question, whether endpoints that rank high on calls also rank high on payers, and a single endpoint can move a rank by at most one place. Neither is wrong; they answer different questions, and on these two counters they currently give 0.45 and 0.68.

The consequence is general. 80.7% of all calls counted sit in 1% of endpoints (concentration). In a market shaped like that, a linear correlation across the whole index is hostage to whichever endpoint is currently largest, and it will move when that endpoint’s usage moves whether or not anything else has. An aggregate figure published about this market without a rank or trimmed figure beside it says less about the market than about its biggest participant. TOLL publishes Pearson because it published Pearson from the first snapshot and a published figure is never restated; the other three measurements are published beside it, and the sentence each page states is chosen from the value rather than written once.

A figure moving by more than 0.05 when one endpoint is removed is the threshold at which the pages say so. At this snapshot the move is 0.35.

Every counter on every endpoint at every snapshot is kept and never overwritten. That is what made the fourth column possible: the set of endpoints carrying both counters on 2026-09-10 could be reconstructed after the question was asked, and the correlation recomputed across only those endpoints at every snapshot in between. None of that was planned for; it fell out of keeping the rows.

A change log cannot answer this question. A log records that a value moved and when, which is enough to notice the rise and nothing more: the rows it would need to recompute a fixed cohort, or to trim the top 1%, or to remove one endpoint and try again, were never kept. The difference between recording that something changed and recording what every value was is the difference between seeing this and not (the comparison).

None yet. Anything submitted through the form below is published here with its outcome.