osu!taiko: Note Speed Mechanics

Also posted on the osu! forums: https://osu.ppy.sh/community/forums/topics/1851087

Here is a description of how scroll speed works in osu!taiko. I couldn’t find this information elsewhere online so I did my own research. If you spot anything wrong with this then let me know.

In case it matters: this research was done as of November 2023 on the “classic” osu! client.

Calculation

Here’s a reference image:

• The typical scroll speed is 245 pixels/beat. This is calculated as 175 * 1.4 from the beatmap’s slider velocity setting. Most maps have their slider velocity at the default 1.4, but a small number of songs have set it differently, e.g. Yoru Naku Usagi wa Yume o Miru which has a base slider velocity of 1.6 => 175 * 1.6 = 280 pixels/beat. ^[1]
• HR applies a 1.4 multiplier and scales by aspect ratio.
• EZ applies a 0.8 multiplier. This is not affected by aspect ratio.
• Finally BPM and inherited timing points affect scroll speed.
  • BPM is applied by multiplying by bpm/60, which converts from pixels/beat to pixels/second.
  • Inherited timing points apply their multiplier.

The receptor is 165 pixels from the left of the screen. That makes the total playfield length 600*r - 165 pixels where r is your aspect ratio.

To get the overall reaction time, divide the playfield size (pixels) by the scroll speed (pixels/second) to get the number of seconds between a note being visible and it arriving at the receptor.

Here’s some example code representing the calculations.

def playfield_width(aspect_ratio):
    return 600 * aspect_ratio - 165

def scroll_rate(aspect_ratio, mod):
    if mod == "HR":
        return 245 * 1.4 * aspect_ratio / (4/3)
    elif mod == "EZ":
        return 245 * 0.8
    else:
        return 245

def reaction_time(aspect_ratio, mod, bpm, base_sv=1.4, inherited_sv=1):
    return playfield_width(aspect_ratio) / (scroll_rate(aspect_ratio, mod) * bpm/60 * base_sv/1.4 * inherited_sv)

Written out as mathematical formulas, with R being the aspect ratio (4/3 for 4:3, 16/9 for 16:9), B being the BPM, and assuming the normal 1.4x base slider velocity and 1x inherited velocity:

• EZ: B/60 * (600*R-165) / 245 * 0.8
• NM: B/60 * (600*R-165) / 245
• HR: B/60 * (600*R-165) / (1029/4 * R)

Analysis

HR is easier on higher aspect ratios

What’s interesting is that higher aspect ratios on HR give slightly more reaction time. This is because the HUD is a fixed size, so the proportion of screen dedicated to the playfield also increases, an extra factor which isn’t accounted for in HR scaling.

• bpm advantage factor vs. 4:3: (160 * r - 44)/(127 * r) where r is aspect ratio ^[2]
• at 16:9 it’s 1.065x (about 10-15bpm)
• at 21:9 it’s 1.11x (about 20-25bpm)
• at 45:9 it’s 1.19x
• asymptote is at 160/127 = 1.25x

However I’ve tried it and changing resolution won’t instantly make you read faster, mainly because of having to read at a different note spacing.

You can visually verify this by taking screenshots at different aspect ratios: more notes are visible at higher aspect ratios.

[2] - wolfram link. Basically calculating the bpms at which the reaction times on 4:3 and aspect ratio r are equal.

Comparison with AR in osu!std

The formula for AR in seconds is (1200 - 750 * (ar-5)/5)/1000. Below are some tables comparing certain values of BPM and AR.

• 200bpm HR = AR9.29 (4:3), AR9.05 (16:9)
• 220bpm HR = AR9.63 (4:3), AR9.41 (16:9)
• 240bpm HR = AR9.91 (4:3), AR9.71 (16:9)
• at 4:3: AR9 = 259bpm or 185bpm HR, AR10 = 345bpm or 247bpm HR
• at 16:9: AR9 = 368bpm or 197bpm HR, AR10 = 491bpm or 262bpm HR

Here is a desmos where you can play with the calculations: link.