ESP does much more than stop wheel spin, actually. It has a yaw rate sensor (accelerometer package) and a steering angle sensor. Using those sensors along with vehicle speed, the ESP module knows how much turning G-Force to expect when you turn the wheel a certain amount, for instance.
So you hit a snowy corner at 20mph and turn the steering wheel 90 degrees to the right. The ESP watches the yaw rate sensor to see if the appropriate amount of turning G-Force happens. Obviously it doesn't because you have bald all-seasons and just took that turn WAY too fast. Your A4 is understeering like that's its JOB. You are careening toward certain death due to your careless driving. Nice work.
*Enter ESP*
ESP kicks in (yo!) to save your butt from going in the ditch (and dying). It quickly recognizes that [you are stupid and] you are blowing the turn and promptly applies the brakes to the INSIDE RIGHT wheel. This has the effect of turning your car like a TANK. You know...with the treads? Anyway, ESP is pretty awesome in this respect. It works to keep the car headed on the requested turning angle, even when the front tires lose grip. It also works in the opposite mode to kill oversteer. It will apply the brakes to individual front wheels in order to keep the back end behind you...where it belongs. In addition to applying the brakes, it will also adjust engine output power as necessary in order to keep the car on course. The important part is that ESP does things that you actually can't do. It can apply the brakes to a single wheel to make the car do something special. You only have one brake pedal, so no matter how good you are, you just can't do that.
I believe in North America, ESP became optional on the A4 in the 2001 model year. It is pretty rare.
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