How Guitar Hero chart difficulty is scored

Back to the charts

Rendered at publish from Methodology.md in the fretwork engine repository, which is the reference for the formula and its calibration tables. The tables on this page are checked against the code that scored every chart here.

Where a number below differs from the code, the code is what scored the charts here; the document is the engine’s and its correction belongs there. At this publish:

GUITAR_REMAP_BINS tier 0 ends at 9.1 in Methodology.md but at 11.3 in fret_formula.py.
GUITAR_REMAP_BINS tier 1 ends at 13.6 in Methodology.md but at 16.6 in fret_formula.py.
GUITAR_REMAP_BINS tier 2 ends at 20.3 in Methodology.md but at 24.5 in fret_formula.py.
GUITAR_REMAP_BINS tier 3 ends at 28.0 in Methodology.md but at 33.5 in fret_formula.py.
GUITAR_REMAP_BINS tier 4 ends at 36.9 in Methodology.md but at 44.5 in fret_formula.py.
GUITAR_REMAP_BINS tier 5 ends at 53.5 in Methodology.md but at 65.6 in fret_formula.py.
CalcTier Drums is 9.0 / 0.2 in Methodology.md but drum_formula.py holds BASE_D 9 / LN_INC 0.196.

The Difficulty Formulas

5-Fret Definitions

Both families of metrics are derived from the song's chart or MIDI note events, each associated with a timestamp and a set of fret values, iterated over the duration of the song. Big thanks to TheNathannator for the extensive documentation on .ini, .chart, and .mid formats - would not have even started this project without that resource.

A sliding window of 1 second (1000ms) is swept over the note span in steps of 250ms. This deliberately includes silent intros and rests between sections, so that metrics reflect true density variations.

I am ignoring a lot of the data from the songs since this is mostly a proof of concept - see the Extensions section for ideas to include them.

NPS (Notes Per Second)

This is a pretty standard metric used on a lot of custom song sites. For each 1 second window, NPS is the count of note timestamps. This is counting notes the same way the games do - any frets played at the same time count as 1 note (whether chords or single frets).

VPS (Variability Per Second)

This is a unique metric (as far as I can tell). VPS calculates fret movement between notes by assigning a change value to each time stamp. This is computed by comparing each note's frets to the previous and returning the largest value of frets removed or added. The first note of a song is treated as a pure addition from an empty fretboard. VPS is the iteration of this calculation across the same windows used for NPS.

Variability Examples:
G to G - no frets added or removed so v = 0
G to Y - 1 fret removed, 1 fret added so v = 1
G to GYB - 2 frets added so v = 2
GYB back to G - 2 frets removed so v = 2
GR to YBO - 2 frets removed, 3 frets added so v = 3
If all of these happened within 1 second VPS would be 8

VPS adds value for calculating overall difficulty since it can differ so much from NPS. A fast picking section with an NPS of 12 could have low or almost no VPS if there aren't many fret changes, similarly, a complex solo with fast zigs and runs can have the same VPS & NPS. There are even rare cases where constant chord changes can push VPS over NPS. By using both NPS & VPS I think it's possible to get a better look into difficulty than either one alone.

5 Fret Math

Difficulty (D) is calculated by multiplying together N (using median, average, and peak NPS for a song), V (the same combination of VPS values), CoV (an interaction term that approximates how consistent through standard deviation, median, and average) and STAM (a gentle duration mod). The specific formula is described below.

D = N \cdot V \cdot CoV \cdot STAM

Median and standard deviation are computed over active windows only (windows containing at least one note). Including silent windows dragged the median toward 0 on any song with an intro or long rests, which underrated the active sections. Peak and average still run over every window, so rests continue to count against the average the way they should.

Epsilon terms

These are used during N & V calculations to prevent 0 medians from collapsing the entire D score, while being derived from the song's own average values for NPS & VPS.

ε_{N} = 0.05 a_{N}, ε_{V} = 0.05 a_{V}

N & V

Pseudo-geometric mean of the NPS & VPS metrics, they sit on similar scales and help to balance each other out. A slow/simple song with a tough solo will have a lower value than a fast/complex song with an unremarkable solo. Peak & average alone gave unsatisfactory results because peak can be an extreme single second, but instead of weighting values (endless tuning/optimization hell), adding modified median here as another way to account for the overall experience across the song's duration.

N = {[({med}_{N} + ε_{N}) \cdot a_{N} \cdot p_{N}]}^{1 / 3}

V = {[({med}_{V} + ε_{V}) \cdot a_{V} \cdot p_{V}]}^{1 / 3}

Coefficients of variation

A modified version of coefficient of variation. Using standard deviation and mean alone was too sensitive, so adding median helped balance it out. While median can still be low on sparse songs, average is never 0 due to charts without notes being excluded from reaching the difficulty calculation step.

{CV}_{N} = \frac{σ_{N}}{a_{N} + {med}_{N}}, {CV}_{V} = \frac{σ_{V}}{a_{V} + {med}_{V}}

Interaction Term

CoV approximates how inconsistent the difficulty is and combines across NPS & VPS. CoV has a floor of 1 so worst case we get raw $N \cdot V$ for an extremely consistent song, while most songs will score above 1. In practice this mostly buffs songs that have a lot of rest between sections which tank the averages.

CoV = 1 + \sqrt{{CV}_{N} \cdot {CV}_{V}}

STAM (stamina)

A sub-linear duration modifier: short songs are discounted, long ones slowly build a bonus. The exponent is deliberately small, giving roughly 66% at 30 seconds, 75% at 1 minute, 1x at the 230s reference (a typical 3-4 minute song), 1.1x at ~6 minutes and 1.2x at ~9.5 minutes.

STAM = {(\frac{Duration}{t_{ref}})}^{s_{stam}}, t_{ref} = 230, s_{stam} = 0.20

Final D Formula

D = N \cdot V \cdot CoV \cdot STAM

Drum Definitions

Drums share the same windowing idea as the 5 Fret instruments (a 1-second window swept in 250ms steps, deliberately including rests), but hands and kick are tracked as separate streams.

HPS (Hands Per Second) is NPS for drums: For each window, the count of simultaneous lanes struck at each timestamp, summed (a 2-lane hit counts as 2, same as two separate hits). Roll-lane sections (charted rolls/alt crashes) are excluded from the literal count and instead capped at a flat rate, since a roll-lane marker represents "keep going fast," not a note-for-note performance.

KPS (Kicks Per Second) is a straight note rate (like NPS), computed separately for single (1x) and double (2x) kick pedal charting, with the same windows as HPS/TPS.

TPS (Travel Per Second) is the VPS equivalent, but two things are different from 5 Fret. Only lanes newly struck count, as there is no release equivalent for drums. Second, lane position matters: a hand moving from the hi-hat to a far crash cymbal is a bigger physical reach than a hand moving to the adjacent snare, so each newly-struck lane is scored by its distance to the nearest lane already being hit. That raw distance is compressed by a square root so one big cross-kit reach doesn't dominate a passage of many small movements the way an uncompressed distance would.

Travel Examples (lanes numbered 0-4 left to right):
Hat → Hat - same lane, nothing new struck, $t = 0$
Hat → Hat+Snare (lane 0 → {0,1}) - 1 new lane, distance 1, $t = 1^{0.5} = 1$
Hat → Crash (lane 0 → 4) - 1 new lane, distance 4, $t = 4^{0.5} = 2$
Silence → Hat+Snare - nothing struck immediately before, pure addition, $t = 2$ (no compression)

Drum Math

Difficulty (D) is calculated by adding together H (using median, average, and peak HPS for a song), T (the same combination of TPS values), and K (the same combination of KPS values), then multiplying by CoV (the same interaction term as 5 Fret, taken across hands & kick) and STAM (the same duration mod). Same rough shape as 5 Fret, with the axes added rather than multiplied. The specific formula is described below.

D = (H + T + K) \cdot CoV \cdot STAM

As with 5 Fret, median and standard deviation are computed over active windows only. HPS & TPS both gate on hand-hit activity, and KPS gates on kick activity. TPS is gated on hand-hit activity rather than its own values, since travel legitimately reads 0 on a repeated lane and gating on that would throw away real windows.

Epsilon terms

Same guard as 5 Fret, one per axis, derived from each axis's own average.

ε_{H} = 0.05 a_{H}, ε_{T} = 0.05 a_{T}, ε_{K} = 0.05 a_{K}

H (Hands), T (Travel), & K (Kicks)

The same pseudo-geometric mean 5 Fret's N & V use, applied to each raw metric (HPS, TPS, KPS).

H = {[({med}_{H} + ε_{H}) \cdot a_{H} \cdot p_{H}]}^{1 / 3}

T = {[({med}_{T} + ε_{T}) \cdot a_{T} \cdot p_{T}]}^{1 / 3}

K = {[({med}_{K} + ε_{K}) \cdot a_{K} \cdot p_{K}]}^{1 / 3}

$H$ (hit density) and $T$ (travel) are additive. A fast single-lane run and a slow wide-ranging one shouldn't collapse each other to zero the way a product would. Kick adds in the same way, for the same reason: a quiet kick under a busy hand part (or vice versa) shouldn't drag the whole song's difficulty toward zero.

H + T + K

Coefficients of variation

Same modified CV as 5 Fret, taken once per limb group. Travel doesn't get its own CV since it rides on the same hand windows as HPS.

{CV}_{H} = \frac{σ_{H}}{a_{H} + {med}_{H}}, {CV}_{K} = \frac{σ_{K}}{a_{K} + {med}_{K}}

Interaction Term

Same construction as 5 Fret's, taken across the two limb groups. A song has to be uneven in both hands and feet to earn the full bonus. Scale value of 2 to boost its impact.

CoV = 1 + c_{scale} \sqrt{{CV}_{H} \cdot {CV}_{K}}, c_{scale} = 2

STAM (stamina)

Identical to 5 Fret's stamina term - sub-linear discount for short songs and slow boost for long ones.

STAM = {(\frac{Duration}{t_{ref}})}^{s_{stam}}, t_{ref} = 230, s_{stam} = 0.20

Final D Formula

D = (H + T + K) \cdot CoV \cdot STAM

$D$ is computed once per kick reading - D_1x for single pedal, D_2x for double kick variants where they exist. RemapDiff & CalcTier anchor to D_1x, since 1x is the reading every chart has.

What's missing

Nothing here has any memory of what came before. Every axis is a per hit or per second rate, so a steady groove repeated for several minutes scores its last loop exactly like its first. Long, busy, repetitive songs are consistently overrated as a result. This is something that can't really be fixed without adding pattern recognition of some kind.

Vocal Definitions

Vocals use the same windowing idea (a 1-second window swept in 250ms steps, deliberately including rests), but there are no frets or lanes, and no EMHX levels - the games only ever have one lead vocal line (although some engines differ in strictness by level), so everything is treated as Expert. Only PART VOCALS from the .mid is read (.chart can't encode vocals, and harmonies aren't parsed).

The vocal track is split into three streams:

Sung notes - pitched notes, including slides (+) and placeholders (+$)
Talkies - rap/spoken/screamed segments. Two authoring conventions were uncovered: (RB-style) a pitched note paired with a lyric marked by # / ^ / *, & (GH-style) a lyric with no paired pitch
Percussion - kept for duration & render only, otherwise treated as rest time

Authored talkie lengths are ignored so RB & GH style talkies can be treated equivalently. Every talkie gets a fixed length (133ms, estimated from official data), clipped so it never overlaps the next onset. This length is only used for active window gating and song duration.

PPS (Pitch-travel Per Second)

Vocal's VPS equivalent. Each sung note is compared to the previous sung pitch, and the interval (in semitones) is its travel value. Like drum travel, the raw interval is compressed by a square root so one big leap doesn't dominate a passage of many small steps, and is capped at an octave (12 semitones). Travel is tracked across octaves as charted - the games accept octave shifts, but most people will try to hit the notes as recorded. Slides and placeholders are included since the pitch still has to move. Talkies aren't pitched, so they're skipped, but they don't break the chain. Unlike 5 Fret/Drums, the first note of a song has nothing to compare against, so it scores 0 rather than a pure addition.

Pitch Travel Examples (MIDI pitch, C4 = 60):
C4 → C4 - same pitch, $t = 0$
C4 → D4 (60 → 62) - 2 semitones, $t = 2^{0.5} \approx 1.41$
C4 → G4 (60 → 67) - 7 semitones, $t = 7^{0.5} \approx 2.65$
C4 → C5 (60 → 72) - 12 semitones, $t = 12^{0.5} \approx 3.46$
C4 → C6 (60 → 84) - 24 semitones, capped at 12, $t \approx 3.46$
C4 → talkie → E4 - talkie skipped, compares 60 → 64, $t = 2$

SPS (Syllables Per Second)

Vocal's NPS equivalent - a straight rate of new syllables per window. A syllable is any sung note that isn't a slide or placeholder, plus every talkie. Slides and placeholders continue a syllable rather than starting a new one, so they add pitch travel but no syllables. Sung notes + talkies also defines NoteCount. This is mainly a rescue for talkie-heavy/talkie only songs.

Static Features

A few per-song values that aren't windowed, all from sung notes only & used to build R (Register):

Pitches - count of distinct pitches used
maxPitch - highest sung pitch
ShortFrac - share of sung notes shorter than 120ms (quick runs/articulation)

Active windows & duration

Vocals gate windows differently from 5 Fret/Drums. Instead of counting onsets, a window is active if any note is active during the window, so a long held note still counts as active singing even with no new onsets. SPS gates on sung notes + talkies, PPS gates on sung notes only. Song duration runs from t=0 to the latest end across all three streams (incl percussion).

Vocals Math

Difficulty (D) is calculated by multiplying together P (using median, average, and peak PPS for a song), R (register - where the line sits), and A (articulation), adding S (the classic geomean combination of SPS values, down-weighted), then multiplying by CoV (the same interaction term, taken across pitch & syllables) and STAM (the same duration mod). Pitch movement is the main driver, with syllable rate as a secondary term. The specific formula is described below.

D = (P \cdot R \cdot A + S) \cdot CoV \cdot STAM

Vocals is sort of a hybrid of lessons from 5 Fret & Drums due to the pure insanity of vocals charting. Official tiering conventions are incredibly messy (officials don't agree on nearly anything, even comparing DLC vs main setlist), so this is the loosest fit to official difficulty of any instrument.

Epsilon terms

Same guard as 5 Fret/Drums.

ε_{P} = 0.05 a_{P}, ε_{S} = 0.05 a_{S}

P (Pitch-travel) & S (Syllables)

The same pseudo-geometric mean used everywhere else. S is scaled down by $w_{S} = 0.25$ so syllable rate differentiates rap/scream/spoken songs without overshadowing pitch work.

P = {[({med}_{P} + ε_{P}) \cdot a_{P} \cdot p_{P}]}^{1 / 3}

S = w_{S} {[({med}_{S} + ε_{S}) \cdot a_{S} \cdot p_{S}]}^{1 / 3}, w_{S} = 0.25

R (Register)

Where the vocal line tracks, not how fast it moves through it. Pitch vocabulary is square-root compressed, and the top of the line is squared for impact. Both are divided by a reference value (the pool medians - 12 distinct pitches, top pitch of 70) so R sits near 1.0 on a typical song and doesn't blow up the rest of the calc. R is 0 when a song has no sung notes.

R = {(\frac{Pitches}{12})}^{0.5} \cdot {(\frac{maxPitch}{70})}^{2}

A (Articulation)

A simple boost for quick runs, from the share of short (<120ms) sung notes. Ranges from 1 (no short notes) to 2 (all short notes).

A = 1 + ShortFrac

Combinig both Fret & Drum approaches, P, R, & A are multiplied, with S added on to rescue talkie-only songs from scoring 0 D across the board.

D = (P \cdot R \cdot A + S) \cdot CoV \cdot STAM

Coefficients of variation

Same modified CV as 5 Fret/Drums, taken across pitch travel & syllables.

{CV}_{P} = \frac{σ_{P}}{a_{P} + {med}_{P}}, {CV}_{S} = \frac{σ_{S}}{a_{S} + {med}_{S}}

Interaction Term

Similar to drums, with a scale value of 1.75. A song has to be uneven in both pitch movement and syllable rate to earn the full bonus.

CoV = 1 + c_{scale} \sqrt{{CV}_{P} \cdot {CV}_{S}}, c_{scale} = 1.75

STAM (stamina)

Identical to 5 Fret's stamina term - reused wholesale.

STAM = {(\frac{Duration}{t_{ref}})}^{s_{stam}}, t_{ref} = 230, s_{stam} = 0.20

Final D Formula

D = (P \cdot R \cdot A + S) \cdot CoV \cdot STAM

What's missing

A lot of what makes vocals hard is familiarity with the song, lyrical awkwardness, obscured or strange vocal processing, and other things that just can't be picked up from midi note data.

Binning Methodology

Reference for the calibration tables behind fret_formula.py, drum_formula.py, and vocal_formula.py.

RemapDiff (0-6) Calibration

RemapDiff buckets a song's calculated D into a 0-6 tiers, calibrated per instrument so that the distribution of remapped tiers roughly matches the distribution of that group's official diff_* tag values. Each row's D range is (lower, upper] against the Expert-level D.

Guitar (covers Co-op and Rhythm - `GUITAR_REMAP_BINS`)

Tier	D range	Official	Remap
0	(0, 9.1]	4.3%	4.3%
1	(9.1, 13.6]	10.6%	10.7%
2	(13.6, 20.3]	24.0%	23.9%
3	(20.3, 28.0]	25.1%	25.2%
4	(28.0, 36.9]	17.7%	17.7%
5	(36.9, 53.5]	12.0%	11.9%
6	(53.5, inf)	6.2%	6.3%

Bass (`BASS_REMAP_BINS`)

Tier	D range	Official	Remap
0	(0, 3.7]	6.7%	6.7%
1	(3.7, 10.0]	22.8%	23.0%
2	(10.0, 15.2]	27.6%	27.5%
3	(15.2, 22.0]	23.9%	23.5%
4	(22.0, 29.7]	10.9%	11.0%
5	(29.7, 41.2]	5.8%	5.8%
6	(41.2, inf)	2.4%	2.4%

Keys (`KEYS_REMAP_BINS`)

Tier	D range	Official	Remap
0	(0, 2.5]	8.7%	8.5%
1	(2.5, 7.8]	19.5%	19.7%
2	(7.8, 13.7]	18.3%	18.0%
3	(13.7, 21.5]	22.4%	22.4%
4	(21.5, 31.4]	14.9%	15.1%
5	(31.4, 42.4]	8.3%	8.1%
6	(42.4, inf)	7.9%	8.1%

Drums (`DRUM_REMAP_BINS`)

Tier	D range	Official	Remap
0	(0, 10.3]	4.0%	4.2%
1	(10.3, 12.3]	9.1%	8.9%
2	(12.3, 14.0]	15.6%	15.8%
3	(14.0, 16.2]	27.2%	27.5%
4	(16.2, 19.2]	27.5%	27.1%
5	(19.2, 22.8]	12.3%	12.2%
6	(22.8, inf)	4.3%	4.3%

Vocals (`VOCAL_REMAP_BINS`)

Tier	D range	Official	Remap
0	(0, 4.1]	6.5%	6.6%
1	(4.1, 6.0]	14.3%	13.9%
2	(6.0, 8.3]	26.9%	27.6%
3	(8.3, 11.4]	30.5%	30.3%
4	(11.4, 14.4]	14.1%	13.9%
5	(14.4, 17.6]	5.2%	5.3%
6	(17.6, inf)	2.4%	2.5%

CalcTier Calibration

CalcTier is an uncapped log-scaled tier, so very hard officials and many customs land at 7+.

BASE_D sets the tier 0 into tier 1 boundary. LN_INC sets the step size. This fit is developed using a minimum step size to try to keep the vast majority of songs under tier 7 for a comparable feel.

Group	BASE_D	LN_INC	D step per tier	Home
G/B/K	7.6	0.44	~55%	`fret_formula.py`
Drums	9.0	0.20	~22%	`drum_formula.py`
Vocals	4.4	0.32	~38%	`vocal_formula.py`

Guitar/Bass/Keys share both constants despite different D scales since they're mechanically similar.

Drums & Vocals need their own fits because their Ds are constructed differently. 5 Fret is multiplicative while drums is additive, so drum D spreads less far in log terms over a similar range of real difficulty. Vocals combines both addition and multiplication and has a much lower overall scale than either frets or drums.

How Guitar Hero chart difficulty is scored

The Difficulty Formulas

Index

5-Fret Definitions

NPS (Notes Per Second)

VPS (Variability Per Second)

5 Fret Math

Epsilon terms

N & V

Coefficients of variation

Interaction Term

STAM (stamina)

Final D Formula

Drum Definitions

Drum Math

Epsilon terms

H (Hands), T (Travel), & K (Kicks)

Coefficients of variation

Interaction Term

STAM (stamina)

Final D Formula

What's missing

Vocal Definitions

PPS (Pitch-travel Per Second)

SPS (Syllables Per Second)

Static Features

Active windows & duration

Vocals Math

Epsilon terms

P (Pitch-travel) & S (Syllables)

R (Register)

A (Articulation)

Coefficients of variation

Interaction Term

STAM (stamina)

Final D Formula

What's missing

Binning Methodology

RemapDiff (0-6) Calibration

Guitar (covers Co-op and Rhythm - GUITAR_REMAP_BINS)

Bass (BASS_REMAP_BINS)

Keys (KEYS_REMAP_BINS)

Drums (DRUM_REMAP_BINS)

Vocals (VOCAL_REMAP_BINS)

CalcTier Calibration

Guitar (covers Co-op and Rhythm - `GUITAR_REMAP_BINS`)

Bass (`BASS_REMAP_BINS`)

Keys (`KEYS_REMAP_BINS`)

Drums (`DRUM_REMAP_BINS`)

Vocals (`VOCAL_REMAP_BINS`)