This is something that has been neglected for quite a long time and was brought to my mind by another topic today. From what I've seen I think that most of the current active forum community will outright say that "this is not necessary", but all of it is important and necessary. The game is of course playable without, but playable is different than perfect.
Current audio/input syncing options:
Currently osu has a setting called 'Universal Audio Offset' which controls how early or late you need to hit on songs compared to the "zero point" of the audio track. Also each song has their own song offset which further adjusts the offset but for that song only. (Actually each beatmap has it's own offset so that multiple beatmaps in one song can have different offsets) All of this is very standard and has been through the history of rhythm games so most people don't have problems with this.
The only problem with the current setting is that the UAO actually works backwards to the song generic offset. If the song offset is negative then you need to hit earlier, but if the UAO is negative then you need to hit later. Although this is easy to notice it is confusing to new players so the UAO behavior should probably be changed.
Further input syncing options
Osu has the possibility of using different input methods to interact with the game, including mouse, tablet, keyboard and miscellaneous game controllers. Different controllers have different amounts of input lag depending on multiple factors. Even two different keyboards will usually have different input lag.
Most people only use one input method to do the hitting of notes so this doesn't usually cause problems. Some people might use two or more different input methods, but only one during a specific song. They might for example use the mouse on some songs and a tablet on other songs. In this case they can simply adjust the Universal Audio Offset setting to fix the sync when changing between input methods. There are however players who use multiple input methods during a single song. The most common cases are when a player mainly uses a mouse or tablet for playing, but also use the keyboard to hit certain special parts of the song (for example a mouse player might hit fast note stacks with the keyboard). Since the mouse clicks and the keyboard hits have a different input lag the player might need to hit too early or too late on the secondary input method since the game is synced to the primary input controller. There is currently no way to sync the two controllers separately from each other.
There are multiple ways to handle this issue. You could add a 'secondary input device offset' which is used to sync your secondary device separately from the primary input device, but then you also need to specify which controller is your primary device and which one the secondary. You could also just add a 'keyboard input offset' since keybaord is (as far as I know) the only input device used in cooperation with other input devices.
Hit sound sync
Osu has a hit sound system which plays a sound when you hit a note. The sound is played at the exact moment that the game receives the players input for the note. The aim of this system is to allow the player to hear his input and offer a possibility for him to adjust his sync with the help of the hit sound.
The players aim is to hit in beat with the music, so he clicks at the exact time he hears the beat of the music. From this actual moment of the click there is lag before the game receives the players input and plays the hit sound. This causes the hit sound to always be late compared to the music. There is no way of getting rid of this problem unless someone has a device that can foresee the future or guess very accurately when the player will hit next. Even though this is a problem with no solution, it doesn't usually disturb the player as the lag is so minimal. With some input devices however the lag is so huge that the hit sounds are far from being in sync with the song. The only solution to this is to actually turn off the hit sounds which is currently an option is osu so no further action is required.
There is also the possibility of adding an "automatic hitsound" which always plays the hit sound on correct time and is not affected by player input which allows the player to hear the correct rhythm no matter how much lag his input device has or how he plays. This is a feature that is present in some other rhythm games, but not all of them since it is sometimes seen as "cheating" due to players being able to listen to a hard part instead of having to play it over and over again to understand how that part needs to be played. Personally I think there is no reason to not add such a feature though.
Video sync
In addition to input device lag and the variation of the "empty space" in start of songs which both affect the audio sync the monitor that is used also can have lag. This lag affects the visual representation of the game. In osu this problem is not as big as in many other games since it is not so easy to say what is the "correct visual sync" as in where the approach circle should be when the player needs to hit. In games with a upwards or downwards scrolling note system the video sync should be so that the note overlaps the target area when the player needs to hit, but in osu there is no such specific spot. The video sync issue is still there, it's just not as noticable as in other rhythm games.
This system however brings another problem in addition to the sync actually being different on different monitor setups. Now different players might more easily have different preferences on where the approach circle should actually be when the player is required to hit. Some people might like the approach circle to be around the hit circle, some people might want it to be on top of it, etc.
A simple video sync slider will fix both problems.
Current audio/input syncing options:
Currently osu has a setting called 'Universal Audio Offset' which controls how early or late you need to hit on songs compared to the "zero point" of the audio track. Also each song has their own song offset which further adjusts the offset but for that song only. (Actually each beatmap has it's own offset so that multiple beatmaps in one song can have different offsets) All of this is very standard and has been through the history of rhythm games so most people don't have problems with this.
The only problem with the current setting is that the UAO actually works backwards to the song generic offset. If the song offset is negative then you need to hit earlier, but if the UAO is negative then you need to hit later. Although this is easy to notice it is confusing to new players so the UAO behavior should probably be changed.
Further input syncing options
Osu has the possibility of using different input methods to interact with the game, including mouse, tablet, keyboard and miscellaneous game controllers. Different controllers have different amounts of input lag depending on multiple factors. Even two different keyboards will usually have different input lag.
Most people only use one input method to do the hitting of notes so this doesn't usually cause problems. Some people might use two or more different input methods, but only one during a specific song. They might for example use the mouse on some songs and a tablet on other songs. In this case they can simply adjust the Universal Audio Offset setting to fix the sync when changing between input methods. There are however players who use multiple input methods during a single song. The most common cases are when a player mainly uses a mouse or tablet for playing, but also use the keyboard to hit certain special parts of the song (for example a mouse player might hit fast note stacks with the keyboard). Since the mouse clicks and the keyboard hits have a different input lag the player might need to hit too early or too late on the secondary input method since the game is synced to the primary input controller. There is currently no way to sync the two controllers separately from each other.
There are multiple ways to handle this issue. You could add a 'secondary input device offset' which is used to sync your secondary device separately from the primary input device, but then you also need to specify which controller is your primary device and which one the secondary. You could also just add a 'keyboard input offset' since keybaord is (as far as I know) the only input device used in cooperation with other input devices.
Hit sound sync
Osu has a hit sound system which plays a sound when you hit a note. The sound is played at the exact moment that the game receives the players input for the note. The aim of this system is to allow the player to hear his input and offer a possibility for him to adjust his sync with the help of the hit sound.
The players aim is to hit in beat with the music, so he clicks at the exact time he hears the beat of the music. From this actual moment of the click there is lag before the game receives the players input and plays the hit sound. This causes the hit sound to always be late compared to the music. There is no way of getting rid of this problem unless someone has a device that can foresee the future or guess very accurately when the player will hit next. Even though this is a problem with no solution, it doesn't usually disturb the player as the lag is so minimal. With some input devices however the lag is so huge that the hit sounds are far from being in sync with the song. The only solution to this is to actually turn off the hit sounds which is currently an option is osu so no further action is required.
There is also the possibility of adding an "automatic hitsound" which always plays the hit sound on correct time and is not affected by player input which allows the player to hear the correct rhythm no matter how much lag his input device has or how he plays. This is a feature that is present in some other rhythm games, but not all of them since it is sometimes seen as "cheating" due to players being able to listen to a hard part instead of having to play it over and over again to understand how that part needs to be played. Personally I think there is no reason to not add such a feature though.
Video sync
In addition to input device lag and the variation of the "empty space" in start of songs which both affect the audio sync the monitor that is used also can have lag. This lag affects the visual representation of the game. In osu this problem is not as big as in many other games since it is not so easy to say what is the "correct visual sync" as in where the approach circle should be when the player needs to hit. In games with a upwards or downwards scrolling note system the video sync should be so that the note overlaps the target area when the player needs to hit, but in osu there is no such specific spot. The video sync issue is still there, it's just not as noticable as in other rhythm games.
This system however brings another problem in addition to the sync actually being different on different monitor setups. Now different players might more easily have different preferences on where the approach circle should actually be when the player is required to hit. Some people might like the approach circle to be around the hit circle, some people might want it to be on top of it, etc.
A simple video sync slider will fix both problems.