As a runner and a coach, I see all kinds of extremes when it comes to recovery after races. Some people come back out for a workout two days after a hard race while others take months off, losing most of their fitness.
So, how much should you run, how often, and how hard after a race? We;;, of course the answer is "it depends" but I'll outline some important points to consider.
Why to Hold Back and Recover
First, let's explore why you want to hold back and recover after a hard race. For one, a race is a GREAT training stimulus, so if you are still training for races in the next month or two, races can be the best workouts you do. Unlike regular workouts, races can flood your system with hormones that create larger than normal adaptations. Psychologically, races strengthen the mind and prepare you to tolerate more and more discomfort as you run, resulting in faster races without actually getting "fitter."
So, after a race, you want to give your body time to absorb the race and produce a positive adaptation to it. If you go too hard too soon, then you might cancel that adaptation or you may exacerbate a weakness somewhere in your body and get injured. Races can be very stressful and too much stress too soon can cause recovery and performance issues down the road.
Why You Should Workout Soon After the Race
On the other hand, unless it is the end of your training cycle, you don't want to rest too much otherwise you will lose those fitness gains from the race. When your body is stressed (workout, mileage, long run, race) then you need to consistently "remind" your body to adapt to that initial stress. Otherwise your body will "forget" and stop getting stronger from that workout or race (or whatever stimuli). So, after a race if you're still training, you'll want to keep workout. But how much and how often?
Rules of thumb: 1 easy day for ever mile raced. This is a common rule of thumb that says if you race a 5k then you'll want three easy days after. 10k? 10 days. 1/2 marathon? 13 days. Etc..