"Fixing" Running: Slower Running Speed Relative to Health

In a sudden moment of bathtub Eureka, I forged an idea that aims at solving the two golden plagues:  running and ranged weapons.  Everyone has fallen ill to uncatchable "running" play styles, usually reserved to those that will evade enemies while their health is depleted and aimed at regaining said health.  To counter this, I propose a new notion:

While at a lower health, players will be at a speed disadvantage.  This condition can take effect:

1.   Commensurate or proportional to the player's health.  For every red health dot or point they lack, they will move 5-10% slower when sprinting, sprint jumping, and/or walking and jumping.
2.   When the player's health is under a certain threshold, say 2-3 health points, the above effect takes place for about a 25-35% reduced speed.
3.   The above effect can take place when a player has a ranged weapon (they are heavier), for about a 10-20% reduced speed.

What is the justification of this effect?  Running players will not be able to outrun their pursuers when they are in need of health, and ranged players will not be as mobile as their melee competitors.  I will call the 2nd point the "injury" condition, which can also be inflicted in random, rare takings of damage.  The player should be notified in a pop up similar to the killstreak pop ups.  Another condition may include the "poison" condition from drinking random potions.

Further limits on injured players below the 2-3 health point threshold may include:

1.   Weaker damage, perhaps dealing half the damage they would usually.
2.   The inability to knock down pursuers (they are too weak to be able to).  A common tactic of runners is to kick or roll down pursuers and escape while the pursuers are rendered immobile.
3.   Drinking health potions and receiving health dots requires time to take effect, say 2 seconds for the health boost.
4.   Severely injured players (below 1 health point) may be unable to do certain functions, such as sprinting, using items, e.g.
5.   Faster stamina loss, perhaps 25% more, as well as not being able to use the 2nd stamina bar.

I assume the main effect of reduced speed should be easy enough to implement.  All Rez has to do is set the speed equal to itself minus the effect, correct?  I would like Rez to know that what we say are not demands, but rather ideas that you can take into consideration.  Thanks.

Leave some comments about the numbers.  Did you think the conditions part was a bit much?  My intention was not to implement every single one of these effects, I even disagree with some of them.  Tell me which you agree with, or tweak them down below.  Please expand on this main idea in further posts.