Metric definition
Notation
For artist $a$ and track $i \in a$: $p_i$ = lifetime play count, $d_i$ = duration, clip cap $K=50$, $\hat{p}_i=\min(p_i,K)$. Per-artist signals: $\pi(a)=\sum_{i\in a}\hat{p}_i$, $\tau(a)=\sum_{i\in a}\hat{p}_i\cdot d_i$, $\nu(a)=\log(1+n_a)$.
Stage 1 — per-artist composite
$$\phi(a)=\frac{1}{3}\left(\frac{\pi(a)}{\displaystyle\max_{a'}\pi(a')}+\frac{\tau(a)}{\displaystyle\max_{a'}\tau(a')}+\frac{\nu(a)}{\displaystyle\max_{a'}\nu(a')}\right)$$
Stage 2 — genre score & ranking
$$\sigma(g)=\sum_{a\in g}\phi(a)$$
Stage 3 — cumulative snapshot $\mathcal{L}_t$
$$\mathcal{L}_t=\bigcup_{t'\leq t}\left\{\text{tracks added in year }t'\right\}$$
Why recent years look stable: because $\mathcal{L}_t\subset\mathcal{L}_{t+1}$, normalization denominators only grow — new additions are diluted against an ever-larger base. 74% of total $\tau$ weight comes from tracks added before 2021.
Notation
$\phi(a)$ and $\sigma(g)$ defined identically to LTD. Only the snapshot changes.
Stage 1 — per-artist composite
$$\phi(a)=\frac{1}{3}\left(\frac{\pi(a)}{\displaystyle\max_{a'}\pi(a')}+\frac{\tau(a)}{\displaystyle\max_{a'}\tau(a')}+\frac{\nu(a)}{\displaystyle\max_{a'}\nu(a')}\right)$$
Stage 2 — genre score
$$\sigma(g)=\sum_{a\in g}\phi(a)$$
Stage 3 — rolling window $\mathcal{W}_t$
$$\mathcal{W}_t=\bigcup_{t'=t-4}^{t}\left\{\text{tracks added in year }t'\right\}$$
Trade-off: noisier than LTD. $p_i$ is a lifetime total, so $\pi(a)$ and $\tau(a)$ reflect all-time plays for tracks added in the window, not plays within it.
Notation
$\phi(a)$ and $\sigma(g)$ defined identically to LTD. Only the snapshot changes.
Stage 1 — per-artist composite
$$\phi(a)=\frac{1}{3}\left(\frac{\pi(a)}{\displaystyle\max_{a'}\pi(a')}+\frac{\tau(a)}{\displaystyle\max_{a'}\tau(a')}+\frac{\nu(a)}{\displaystyle\max_{a'}\nu(a')}\right)$$
Stage 2 — genre score
$$\sigma(g)=\sum_{a\in g}\phi(a)$$
Stage 3 — single-year snapshot $\mathcal{S}_t$
$$\mathcal{S}_t=\left\{\text{tracks added in exactly year }t\right\}$$
Caveat: $p_i$ is a lifetime count, so $\pi(a)$/$\tau(a)$ include all plays through 2025. This reflects what you were adding each year, not what you were actively listening to.