Before using the different levels you have to know what a PR does.
The PR is responsible for the marketing of your team. He has an influence on the prices and after a loss he will have some effect too.
Let's take an example arena. The prices are pretty high. A lv 1 PR won't have any effect. His marketing is bad and the fans/visitors are not ready to pay these prices. A lv 6 or 7 PR increases this readiness and more fans will come and pay the high prices.
The second effect is, that a high PR can decrease the punishment after a loss. With a lv 1 you will have a drop in visitor numbers. And if you have high prices it will hurt you even more. A high level PR decreases this drop and brings the fans faster back to your arena. So one stupid loss won't punish you for 2 or 3 weeks.
For teams which tank, a lv 1 PR is enough. They can save their money and just tank through the season.
But teams like mine, which came down from 2. to 3. div, have a huge disadvantage during the first half of the season (until ASG). I had to lower my prices but this won't change the fact, that my fans don't like the relegation. A high PR works against this punishment and helps me generating higher visitor numbers.
Also in a very balanced league, where you could lose almost every game, a higher PR will help you to keep a steady income. If your are a über-team and you win every game by 20+ difference, it makes no sense to have a high lv PR. Your fans will come because you don't lose.
Now the doctor:
The level of the doctor has an influence on the propability of an injury and the outcome of the injury.
Just an example (the % is only an example):
The propability of an injury with a lv 1 doctor is 5%.
As soon as the player is injured, there is a propability of 40% that he will be fit after the game. If he stays injured: 5% for 5 weeks injury, 15% for 4 weeks injury, 25% for 3 weeks injury, 30% for 2 weeks and 40% for 1 week.
With a lv 7 doctor it could be like this:
Propability of an injury is 0,1%.
If the player is injured during a game, 90% that he will be fit after the game.
If he stays injured after the game: 0,5% for 5 weeks, 5% for 4 weeks, 10% for 3 weeks, 25% for 2 weeks and 59,5% for 1 week.
Again, these numbers are wrong, but they show the logic behind the levels. And the third point is: a higher lv will increase the speed of the regeneration time during an injury. 2 weeks can mean between 7 and 20 days. A lv 1 will be closer to 20 days, a level 7 to the 7 days.
If we assume that your best player gets injured for 5 weeks, just because you have a lv 1 doc, what kind of impact will this have?
You lose more games. Because of this you lose money (less visitors). You will drop in the league. A playoff team can end up at 5th or 6th rank.
In season 17 I decided to switch to a lv 5 doc. Since then I never had anything lower. During this time, the longest injury any of my players had was 1 week. Most of them came back after the game was finished.
Before season 17 I played with lv 1 and lv 3 docs. I had almost every seasons injuries with a duration of 2-4 weeks.