Nurse's range addons are unhealthy and broken

This is not going to be a rant thread, because I actually did some maths and therefore I'm bringing some quality data to support my thesis, so brace yourselves because this is going to be a long thread, with numbers too. A lot of stuff will be repeated and/or redundant, partly to understand what numbers I'm using (so you can scroll back and see how I calculated them), partly for myself since I wrote this in pieces.

First of all, we will need some data. More specifically, power times and movement speeds, that can be gathered here https://deadbydaylight.fandom.com/wiki/Sally_Smithson#Power_Trivia and here https://deadbydaylight.fandom.com/wiki/Movement_Speeds#The_Nurse

I will expose the assumptions I'm making:

1. we are taking into consideration raw distances. This to avoid discussions like "yes but break line of sight and double back" or stuff like that, which has no value whatsoever in the points I'm going to make;
2. the nurse 'example' we are using will have no 'dead times': therefore, we are looking at the optimal use of movement blink charging times (no seconds wasted between the moment the blinks are ready and the moment the nurse starts charging them, no overcharging of the first blink: everything will be immediate), while always holding W (always moving forward) towards the survivor;
3. we are assuming range addons are working as intended. More specifically, as stated in the pwoer trivia, a blink maximum time is 1.5 seconds. The addons descriptions only mention that the charge time is increased (maintaining the normal charge time / meters ratio) but not the blink time, which is capped at 1.5 seconds. Therefore I assume that for blinks longer than 20 meters, the cap will always be 1.5 seconds per blink -> changes the blink movement speed to compensate;
4. the second blink is assumed to last 1 second and to cover the full distance of 12 meters;
5. last assumption: I'm taking into consideration the "worst case scenario" for the nurse, which is having to catch up after blinking twice and lunging, giving her the longest fatigue + full recovery of both blinks.

So let's start with the numbers. At first I will analyze the distances covered while using no addons, dark cinture alone, fragile wheeze alone, and both the addons together. Then we will compare the results with range addons. The formula used is simple:

Total distance = Fatigue duration × Fatigue movement speed + Walking time × Walking movement speed + Blink charge time × Blink charge movement speed + Blink range (max) + Chain blink time × Chain blink movement speed + Second blink range (max)

The fatigue for the aforementioned scenario lasts 3.5 seconds, at which the nurse moves at 0.96 m/s. The distance covered is 3.36 m (constant).

Charging the first full blink takes 2 seconds, at which the nurse moves at 2.89 m/s. Space covered = 5.78 m.

The first blink lasts 1.5 seconds and covers 20 meters. The second blink is assumed to last around 1 second and cover 12 meters (^assumption). To charge it, the nurse will use 1.2 seconds at which she moves at 1.16 m/s. Distance covered: 1.392 m.

Total fixed distance: 42.532 m; total fixed time: 9.2s

The only variable in this case is the time that the nurse consumes walking normally after fatigue, which is affected by the addons. Therefore, I will calculate the single cases and add up the fixed values to each one of them:

1. no addons: walks for 2.5 seconds at normal movement speed of 3.85 m/s. Distance covered: 9.625 m. Total distance covered: 52.157 m. Total time: 11.7 s. Avg speed: 4.46 m/s
2. dark cincture: walks for 1.7 s. Distance covered: 6.545 m. Total distance covered: 49.077 m. Total time: 10.9 s. Avg speed: 4.50 m/s.
3. fragile wheeze: walks for 1.3 s. Distance covered: 5.005 m. Total distance covered: 47.537 m. Total time: 10.5 s. Avg speed: 4.53 m/s.
4. both addons: walks for 0.5 s. Distance covered: 1.925 m. Total distance covered: 44.457 m. Total time: 9.7 s. Avg speed: 4.58 m/s.

Now lets compare this data with a survivor's data, namely the survivor that has just been M1ed and is running in a straight line away from the nurse. The survivor's data is obviously easier to calculate. They will have a fixed 6 m/s speed boost for 2 seconds (fixed 12 meters), then run at 4 m/s for the remaining time. I'm not considering any decelarion aspect (is there even any?): the transition between the 6 m/s and the 4 m/s is instant.

1. no addons: 12 + (11.7 - 2) × 4 = 50.8 m. Distance difference: 1.357 m.
2. dark cincture: 12 + (10.9 - 2) × 4 = 47.6 m. Distance difference: 1.477 m.
3. fragile wheeze: 12 + (10.5 - 2) × 4 = 46 m. Distance difference: 1.537 m.
4. both addons: 12 + (9.7 - 2) × 4 = 42.8 m. Distance difference: 1.657 m.

This means that the better addon you use, the more distance the nurse covers, giving a smaller window of reaction to the survivor. Bear in mind that we're not taking into account the lunge too, as it would happen instantly after the data provided. But anyway, as you can see, the actual difference between using and not using addons is merely 30 cms. The 'actual' difference is that everything is sped up as it takes place in a smaller window of time. However, this is not what this thread is looking into. This data is used as a source of comparison with the actual point of the thread, which I'm going to explain now.

When we take into consideration range addons (Heavy Panting and Kavanagh's Last Breath), we intoduce another variable: charge time. However, most of the numbers used until now stay the same.

1. Heavy Panting only: we add 0.4 seconds to the first blink charge time with a speed of 2.89 m/s = 1.156 m, and 4 meters to the blink range. Since no addons are affecting the blink recharge time, we take the previous no addons data and simply add this. Final data is: 57.313 m in 12.1 s. Average movement speed: 4.74 m/s.
2. KLB only: we add 0.6 seconds to the first blink charge time with a speed of 2.89 m/s = 1.734 m, and add 6 meters to the total distance = 59.891 m in 12.3 s. Avg speed: 4.87 m/s.
3. Both addons: we add 1 second to charging time at 2.89 m/s = 2.89 m, and add 10 meters to the total range. Total distance covered: 65.047 m in 12.7 s. Avg speed: 5.12 m/s.
4. Heavy Panting + Dark Cincture: Total Distance = 49.077 + 1.156 + 4 = 54.233 m. Time = 10.9 + 0.4 = 11.3 s. Avg speed: 4.80 m/s
5. Heavy Panting + Fragile Wheeze: Total distance = 47.537 + 1.156 + 4 = 52.693 m. Time = 10.5 + 0.4 = 10.9 s. Avg speed: 4.83 m/s.
6. KLB + Dark Cincture: Total Distance = 49.077 + 1.734 + 6 = 56.811 m. Time = 10.9 + 0.6 = 11.5 s. Avg speed: 4.94 m/s
7. KLB + Fragile Wheeze: Total distance = 47.537 + 1.734 + 6 = 55.271 m. Time = 10.5 + 0.6 = 11.1 s. Avg speed: 4.98 m/s.

Looking at the average speed alone, you can already conclude how strong range addons have. But let's compare it in terms of 'closing the gap' with the survivor, by calculating the distance covered by them in the same fragment of time and then subtracting it to the distance covered by the nurse:

1. Heavy panting: 12 + (12.1 - 2) × 4 = 52.4 m. Distance difference: 4.913 m.
2. KLB: 12 + (12.3 - 2) × 4 = 53.2 m. Difference: 6.691 m.
3. Both addons: 12 + (12.7 - 2) × 4 = 54.8 m. Difference: 10.247 m.
4. HP + DC: 12 + (11.3 - 2) × 4 = 49.2 m. Difference: 5.033 m.
5. HP + FW: 12 + (10.9 - 2) × 4 = 47.6 m. Difference: 5.093 m.
6. KLB + DC: 12 + (11.5 - 2) × 4 = 50 m. Difference: 6.811 m.
7. KLB + FW: 12 + (11.1 - 2) × 4 = 48.4 m. Difference: 6.871 m.

Conclusion + personal comment:

As you can see, the distance covered when using range addons is a lot higher than that of the survivor. Not only that, but the use of Fragile wheeze only, in terms of raw distance, gives almost 300% more distance than using both recharge addons together. This renders almost any effort of making distance from the nurse useless, as she can immediately close the gap. I don't think this is healthy at all for the game, and the fact that those addons have no downside whatsoever is mindblowing for me.

As I said earlier, recharge addons almost have no impact on the difference of the raw distances covered, they just impact the speed at which the game is played, and I don't want to discuss the balance of that in this thread, as the numbers are very similar.

If we want to consider a more realistic scenario, the nurse will hit the survivor, and they will run somewhere where they can break line of sight. The nurse will be forced to walk for longer than the recharge time required. Then she will blink again to catch the survivor, who is probably trying to break LoS and build distance. If they 'win' the mindgame, they have a chance to actually make said distance, forcing the nurse to be a lot more precise in her next blink series. However, outplaying a nurse with range addons is basically useless, because she can close the gap immediately.

If we take an addonless spirit for example, in the situation where she M1s a survivor and has her phase ready to go, you will find out that the duration of the phase is just enough for her to be in lunge range, if she tracks the exact same pathing as the survivor, and provided that there are no pallets or windows in between (you can do the math). Nurse doesn't care about these. So I don't think it is healthy for her to keep having these addons, at least with no downside. Taking spirit as example again, it would be as if Yakuyoke Amulet was never nerfed, or if MDR showed scratchmarks).

Finally, even though in terms of raw numbers, double range addons combination is the strongest, I personally think that the 'best' is KLB + FW, as it helps cover the gap while also giving only 1.3 seconds of 'forced' walking time while the nurse can locate the survivor again.

Again, this is not a thread about nurse, but about her addons.

NB: I posted the average movement speeds as a normalization metric, as every case examined took into consideration different times and distances covered. However, this is not a discussion on the average speed of the nurse. Don't interpret it as "wow, she's actually faster than a standard 4.6!", because every killer has a way of closing the gap with survivors, and on average they will have an overall speed higher than 4.6 m/s too (blight, spirit, billy moving extremely fast almost as much as they want, clown and freddy slowing down survivors which could be seen as them speeding up, and so on).

NBB: I really hope the math is correct. Maybe I made some mistakes here and there, if someone had the time to double check this it would do me a great favor :)