Where the validator APR figure comes from

Two chain values per validator, every epoch

D is AlphaDividendsPerSubnet: the α the last epoch paid a validator hotkey's stake on one subnet. The chain writes it already net of the validator's take and of any child-key take, and it is the α part only — the share of dividends paid to root stakers goes to root, not into this subnet's α.

A is TotalHotkeyAlphaLastEpoch: the α staked to that hotkey on that subnet right after the payout. So A − D is the α the nominators held when the epoch paid. Both are chain storage, read directly; there is no third-party data provider in this path.

The formula, stated plainly

The epoch's return is r = D ÷ (A − D), and APR = r × epochs per year. At a tempo of 360 blocks that is 7,300 epochs: 7,200 blocks a day × 365 ÷ 360. A result too large to be plausible is discarded rather than displayed.

It is a simple rate: Taosis labels it APR (simple). Dividends are added to the stake every epoch, so they do compound, and the compounded yield over a year reads higher; Taosis shows it beside the APR as APY (compounded) = (1 + r)^E − 1, from the same r. Both are measured again at every epoch, so they move with every tempo. The difference between the two is its own explainer: APR vs APY on Bittensor.

Measured in α, not in τ

The APR says how fast the α staked to a validator grows. It says nothing about what that α is worth: your return in τ also depends on the subnet's α price, which can fall faster than the stake grows, or rise on top of it.

Validators paid through child keys are included. A parent hotkey with no UID of its own on a subnet still receives dividends there through its children, and its nominators are paid on the same formula.

Two windows, and which page uses which

On the screener, a subnet page and the portfolio, the figure is the latest epoch annualised. It is the freshest thing the chain will tell us.

In the validators directory the figure is the median of the last 24 hours of those epoch samples, on that delegate's main subnet — the one holding its largest α stake by τ value, and only when that stake is worth at least 500 τ. One roughly 72-minute epoch annualised is weather; a day of them is closer to yield. Epochs in which it paid nothing are left out of that median rather than dragging it to zero. Blank there means no subnet with meaningful stake paid dividends in the window, which is not a claim of 0%.

Root is measured differently, because root dividends do not arrive through an epoch's α dividends: the directory's Root APR (simple) and Root APY (compounded) come from the chain's root-return series, BasketTwr, over about 24 hours. The root explainer says how.

What it is not

Both are extrapolations — one epoch, or a day of epochs. Neither is a promise, an average of a long history, or a track record.

A track record is a different question — whether a validator has actually paid, consistently — and Taosis answers it separately, in its public API (/validators/reliability/{netuid}/{hotkey}, on the API page) rather than on a page, refusing to answer at all until the series is long enough.