If you can keep updated skill metrics on the players, then you are able to create a system that can peer people of similar skill.
Granted, this could lead to starvation (and by that I mean players unable to play because there is no match availed) and will not fly on couch gaming.
I believe this will not solve your particular case, so I will not elaborate any futher.
I would complain on any handicap system based on the skill of the players. I believe Bálint expressed the issue better than I could. With that said, handicaps in either direction are viable if they are on player volition.
That is, if the players go to a menu where they select what handicap they want and they are all conscious of that choice, then it can work. This is in particular useful in couch gaming with family or friends, because they would know each other and – given the motivation※ – they will find some setting that makes the game fun for everybody.
※: That is, if what they want is to win instead of have a good play session, then it will go wrong.
As I said, handicaps - as long as placed by player own volition - will work in both directions. That is, either making things harder for the "good" player, or making them easier for the "bad" player. However, I would side on making things easier for the "bad" player because...
Catch up mechanics
You can give boosts to the player that is behind (regardless of skill score) in order to help that player get back to the front of the race. After all, it is when players are nearby in the racetrack that the game play is more interesting.
A traditional example will be Mario Kart. In the game, players that are behind will receive better power ups which will allow them to catch up to the players that are at the front.
You might be interested in the concept of rubber banding. Which is how we call the idea of adapting events to fit player performance. Read more about The approaches to Dynamic game difficulty balancing at Wikipedia.
Address the issue
They all have cerebral palsy and is therefore heavily affected by their spasms when using the joystick
Perhaps the solution is simply to smooth the input. You can:
- If the joystick moves too abruptly, ignore that.
- Let the joystick input be a target angle, but limit the angular velocity at which the direction can change.
- Modern cars in real life already adjust the sensitivity of the input as a function of the current speed of the car, you can do that too.
Mario Chase from Nintendo Land is an excellent example of asymmetric gaming.
I would also start with the handicap approach. However not by giving some advantage or disadvantage to players, but by offering a different input mechanic※, and make it optional.
※: That does not imply to create or use a different input device - however, I admit that would be useful, I also recognize that might not be possible. When I say input mechanic I mean the way the game interprets user input.
For a first person shooter, consider the effects of auto aiming... it allows a player that has struggle with fine motion to enjoy the game. However, it does not offer means to improve the motor skill. Instead, I would suggest the following:
- The player aims in the general direction they want
- Then the game changes to an aiming mode where they can fine-tune the direction. The aiming mode may help the player by having:
- Less sensitivity
- Snapping to important targets
- The player shoots (or aborts out of the aim mode).
I suggest doing something like that for your car game. Let the person choose the general direction and then fine tune and apply the change. This means that for a turn, they will change mode ahead of time in the general direction of the turn, and then when they reach the curve they fine tune and apply. In fact, you could let the game gradually apply the turn as appropriate, after all, the result of applying the turn should not be to put the car into a circular path.
I have a vague memory of hearing of a game that had such mode, I have been unable to find it.
The good thing of this approach is that it is a difference in kind, however I admit this is just a rought sketch and I cannot guarantee it will work. If you take this idea, or any other similar one, you will have to take feedback from your players and iterate over it.
Did you consider making a different kind of game instead of a racing game? I think your objective is help these people, perhaps a different kind of game will lend itself easier to the kind of balance mechanics you need. May I suggest a “shoot’em up”? - I strongly belive that a cooperative game will suit you better.
You may also be interested in Incomparables, Perfect Imbalance, Co-pilot mode, Assit Mode and The Curb Cut Effect.