Liner notes · methodology

What the numbers mean

Raw popularity mostly measures promotion. Singles get radio and playlist placement, and track one gets every casual listener who presses play and drifts off. Fans adopt album tracks in two different ways, and we measure them separately. Some tracks they replay: people who hear them keep coming back. Some tracks they spread: more people end up hearing them than hear the album’s own singles.

This is one person’s project, built in the open; the notes say how.

01Definitions

Most replayed non-single (replay). The album track, not a single, not a skit and over the listener floor, that its listeners play most: the highest plays per listener. Its listeners play it more times each than any other eligible non-single on the album. “Non-single” matters: on most albums a single is replayed more. On most albums it is a song nearly every listener reaches, so it usually sits in the album’s Anthems (below).

The deep cut (reach and replay together). The album track, not a single, not a skit and over the listener floor, with the most plays per listener among the tracks in the album’s Deep cuts group: fewer of the album’s listeners reach it than reach its typical track, and the ones who do come back more than to its typical track. It is a definition, not a verdict: it isn’t the album’s best song or a hidden gem, only the track that fits those two lines best. An album can have no deep cut, and then the page says so: “No deep cut: every track fans replay, they also reach.”

Adjusted pick. The track the model picks once reach, position and length are allowed for: the one replayed furthest beyond what it expects. It is a second measure, shown in each track’s panel with the model’s ratio, not on the album page. Sometimes it is the same track as the album’s deep cut, often not.

Sleeper hit (reach). An album track, not a single, not a skit and not the opener, that more people have played than at least one of the album’s official singles. Track one is left out because everyone who presses play hears it. An album with no official single can’t have one.

The album in four groups

Each album is split at its own typical track. The two lines are the median reach share and the median plays per listener of its placed tracks: every track that isn’t a skit and has a reach share, singles included. With an even number of tracks, a median is the mean of the middle two. A track exactly on a line counts as high. When two tracks tie on plays per listener, the earlier one on the tracklist is the most replayed non-single or the deep cut; on the charts, ties go to the earlier track, then alphabetically by artist and album.

reach line = median reach share of the placed tracks replay line = median plays per listener of the placed tracks

Deep cuts: Below the album’s typical reach, above its typical replay.
Anthems: Above the album’s typical reach and replay.
Passed through: Above its typical reach, below its typical replay.
The rest of the record: Below the album’s typical reach and replay.

How far from the line. A group says which side of each line a track falls on, not how far. A track’s sentence says that, from its two ratios to the album’s typical track, in six steps on each side: far below, below, just under, just over, above, far above. For reach, “just” means within 0.90× to 1.11× of the line and “far” means under 0.67× or 1.49× and over. For replay, “just” means 0.91× to 1.10× and “far” means under 0.80× or 1.25× and over. The chart shades the “just” strip around each line. A track in the shade is near the line, and a track a hair from the line on the other side lands in the other group. The groups themselves don’t change.

Singles on the grid. A non-single in Anthems is the fan single: reached and replayed like one, never released as one. A single in Deep cuts is the single fans kept. A single in Passed through is the radio single. A single below the reach line, in either low-reach group, is a single that missed.

No grid. An album gets no grid when it is still early (its replays mix first listens with real attachment), when Last.fm’s album count is below its typical track’s (so reach can’t be measured), or when it has fewer than six tracks to place. The album page says which.

The charts. Across albums, a deep cut is ranked by its plays per listener divided by its album’s typical track’s (“replayed 2.3× the album’s typical track”), never by raw plays per listener, so a small album’s deep cut can lead. Anthems that weren’t singles, radio singles and singles that missed are ranked the same way, by reach share divided by the album’s typical reach. These are descriptions; none carries a test.

These rules were fixed on 2026-09-24, after every album on the site had been seen, so on these albums the groups are exploratory. Albums from lists added later are the check.

02Formulas

Plays per listener. How many times the average listener has come back to the track.

ppl = plays / listeners

Expected plays per listener. A straight-line model fitted once across every album on the site. It predicts replays from how many people heard the track, its position on the album (first track 0, last track 1), whether it was a single, how long it is, and which album it is on.

log(ppl) ~ log(listeners) + position + is_single + log(length) + album

Replays vs expected. Actual over expected, so 1.8× means listeners come back 1.8 times as often as the model predicts.

ratio = ppl / expected_ppl

Where a track sits among all album tracks. We rank its ratio against every eligible album track in the same fit, on every album on the site: the launch albums, the year-end lists (Billboard, Pitchfork, Rolling Stone, AOTY, Metacritic, the Guardian and Stereogum) and the artist crates. Albums still in their first months are ranked but never used as the yardstick.

beats = share of reference album tracks with a lower ratio

Read the adjusted pick’s number beside its base rate. Every album has a track fans replay most beyond expectation, so the model’s pick usually ranks high among all album tracks. The best of eight randomly chosen tracks beats 95% of album tracks about a third of the time. So “beats 97% of album tracks” describes the track. It is not proof that the album has one special song.

One track clearly ahead of the rest. A rare flag. We simulate 100,000 albums of the same size where nothing stands out and note how far ahead their top track sits. If this album’s adjusted pick is further ahead of its album-mates than in 95% of them, it gets the flag, shown with the most replayed non-single when the two are the same track. About 5% of albums show this by chance. It says one song dominates the album’s replays. It isn’t evidence of anything more, and most albums, including much-loved ones, have several strong tracks instead.

dcae = (log(ratio) − album mean) / album sd clearly ahead if chance-only albums reach this dcae ≤ 5% of the time

Reach share and depth need no model.

reach share = track listeners / album listeners depth = (non-singles’ share of the album’s plays) / (their share of its tracks)

03Every number, in one sentence

Listeners: The number of distinct Last.fm accounts that have played the track at least once.
Plays: The total number of times the track has been played (scrobbled) on Last.fm, across all those accounts.
Plays per listener: Plays divided by listeners: how many times the average listener has come back to the track. The most replayed non-single is the eligible non-single with the most.
Expected plays per listener: What the model predicts for this track from its listener count, its album position, its single status, its length and its album.
Replays vs expected: Actual plays per listener divided by expected, in each track’s panel.
Typical track: The album’s middle track on each measure: half its placed tracks have more listeners than it and half have more plays per listener, so it is the album’s own yardstick, not a real track.
Group: Which of the album’s four groups a track falls in: Deep cuts, Anthems, Passed through or the rest of the record.
Replay vs typical: A track’s plays per listener divided by its album’s median; the meter in the tracklist draws it from half (0.5×) to double (2×).
Beats: The share of album tracks in the reference set that fans replay less, relative to what each is expected to get.
Adjusted pick: The eligible non-single with the highest replays vs expected, shown in its track panel.
Clearly ahead of the rest: The adjusted pick is further ahead of its own album-mates than chance puts an album’s top track 95% of the time.
DCAE: How far a track’s ratio sits above or below the other tracks on the same album, in standard deviations.
Single: A track the label released as a single, from the album’s Wikipedia entry or the label’s own page; the source is kept with every single in the data files.
Sleeper hit: A non-single, other than the opener, with more listeners than at least one of the album’s official singles.
Reach share: Of everyone who scrobbled this album, the share who played this track.
Reached least: The eligible album track with the lowest reach share: the one fans reach least, which is not the same as the one they skip most.
Depth: How much of an album’s listening goes to its non-singles, against their share of the tracklist: 1 means their fair share, lower means the singles dominate.
Listener floor: A fifth of the album’s median listeners (at least 1,000), so a track heard only by completists can’t win on a handful of devoted plays.
Held out: A track not in the running for any pick: a skit, a track under the length floor, a track whose bigger Last.fm entry may be the same recording, or one Last.fm returns no count for; the tag says which.

04What is a description, and what would be a claim

Everything on this site describes listening. Nothing on it certifies a track.

Descriptions (what the site shows): each track’s plays per listener, its replays against expectation and where that ranks among album tracks; which of its album’s four groups it falls in; which non-singles out-reach a single; each track’s reach share; the track fans reach least; an album’s and an artist’s depth; the rare “clearly ahead of the rest” flag, with its base rate.
Claims (what it doesn’t say): that an album has one special song, that a track is its best, or that fans value one song over another. The first would need evidence that an album’s best track is more unusual than the best of its size by chance. The data doesn’t show that.
What changed the headline. Two validation sets of albums with a published fan favourite were scored with rules fixed before the results were read. In both, ranking by plays per listener put the favourite in an album’s top three at least as often as the model did (18 against 17 of 22 in the first set; 42 against 38 of 46 in the second). So the headline track is now the non-single with the most plays per listener, and the model’s ratio is shown beside it as the adjustment. Either way, the ranking stays a description.

05The model, as fitted

Loading the model summary…

06Where the data comes from

Listener and play counts come from the Last.fm API (track.getInfo for each track, track.search to find the same recording under other names). Tracklists are the standard edition of each album, taken from its published tracklist and cross-checked against Last.fm's own album page. Track names are matched so that variants like "(feat. …)" or "Remastered" count as one track, while remixes and live versions stay separate. Which tracks were singles comes from each album’s Wikipedia entry and MusicBrainz, with a source kept for every one.

07Known limits

Last.fm users are not everyone. People who scrobble skew toward engaged, repeat listeners. That suits a measure of attachment, but it is not the general streaming population.
New releases are marked "early". In an album's first months, repeat plays mix first-listen curiosity with real attachment, so those picks are provisional and tracked live.
Name mismatches can split counts. If a track is scrobbled under a spelling the matching doesn't catch, its numbers are split. Where variants are merged, listener counts are summed, so someone who played both spellings is counted twice and plays per listener is slightly understated for that track. Stylised titles are the worst case: most of E•MO•TION’s listeners scrobble it as plain “Emotion”, which Last.fm’s search never returns, so we look up the plain spelling of every stylised track and album name directly.
Counts are all-time. A single released months before its album has a head start in listeners and plays. The model’s single term absorbs that only on average, not album by album.
A track can pass 100% reach. Last.fm counts a song’s listeners across every release it’s on, so they include people who heard the single, a compilation or a live album and never played this one. A reach share over 100% is normal for a single, and happens to other tracks too.
“Reached least” is not “most skipped”. A play is scrobbled only once the listener has heard a good part of the track, so a low listener count mixes people who skipped it early with people who never got that far. The data can’t separate the two.
Plays per listener isn’t adjusted for audience size. Within an album it compares tracks fairly. Across albums it rewards devoted fanbases: an album a few thousand people play over and over outranks one millions hear once. The charts rank it that way on purpose, and the adjustment sits beside it.
Adding albums moves the numbers. Every album shares one fit, so when new albums join, every track’s expected replays shift a little, and a close call on an album can change.
Singles come from each album’s Wikipedia entry and MusicBrainz, with a source kept for every one. Promo singles count as singles, so a track a label pushed can't be the most replayed non-single. Promo-only and radio-only releases are judgement calls. In hand-checked samples, about 1 album in 16 names as its most replayed non-single a track that a closer read of its singles would change.
Skits are excluded from the pick: tracks under 90 seconds or titled as skits, because short tracks get replayed as part of the album's flow, not on their own. Full-length songs with "Interlude" in the title, like "For Sale? (Interlude)", stay eligible.

08What people ask

The replies these findings get, each answered in one sentence, with the page that shows it.

So the model doesn’t matter?: It lost the test it was built for: in two validation sets scored with rules fixed before the results were read, plain plays per listener put the fan favourite in an album’s top three 18 times out of 22 and 42 out of 46 (the model: 17 and 38), so the most replayed non-single is the plain count and the model’s ratio stays beside it as the adjustment. What changed the headline
Last.fm isn’t Spotify.: True, and people who scrobble are keener, more repeat-minded listeners than streaming as a whole, which suits a measure of how often people come back. Known limits
That track was a single (in Japan, to radio, as a promo).: A track tagged Single, promos included, can’t be the most replayed non-single, and every album’s singles come from its published releases with a source, so its tracklist shows exactly what was counted. An album’s tracklist
It’s only because of TikTok.: A viral moment brings a track new listeners more than it brings them back, and plays per listener counts the coming back. Who plays each track, on DAMN.
You’re just measuring people who play the album straight through.: If everyone played albums front to back, every track would have the same plays per listener, so the differences between tracks are replays of one song over another. Reach against replay, on good kid, m.A.A.d city
Is the most replayed non-single usually the opener or the closer?: Not often: the most replayed non-single is the opener or the closer about as often as any one track would be by chance. Track positions, in DAMN.’s tracklist
Is it usually the song with the feature?: Not usually: a guest’s fans can add replays, but the most replayed non-single credits a guest about as often as an album’s tracks do. Each album’s card names the guest when there is one. The guest credit, on Certified Lover Boy
That’s not the best song on the album.: It isn’t meant to be: the most replayed non-single is the one its listeners play most often each, which says nothing about which song is best. Descriptions, not claims
The deluxe edition has a better track.: Only the standard edition’s tracklist is counted, so bonus tracks don’t compete. Vault tracks do where the standard edition carries them, as each Taylor’s Version re-recording does. Where the data comes from
Why is the chart all Taylor Swift?: It was, while the most-replayed chart ranked plays per listener: that counts a devoted fanbase once per album, and Taylor Swift held 7 of its top 30. It now ranks each track’s replays against what its reach, position and length predict (none of hers is in that top 30), with plays per listener beside it, and every chart names each artist once. The charts

09Attribution

Data from Last.fm, used under the Last.fm API terms for non-commercial use. Deep Cut Explorer is not affiliated with or endorsed by Last.fm.

Analytics. The site counts page views and a few clicks (which cards, share images and games are used), with PostHog, through this site’s own address. It sets no cookies and stores nothing on your device, keeps no personal data, and the count is only for the site’s own reporting.