(Note, hope nobody minds that I'm still posting a separate thread on this.)
It begins immediately... or rather, it begins when you start to feel it's not worth it. But it turns out what we're looking at is a straightforward
y = 1/
x curve.
View attachment 117751
I've run six different 1000 ly routes for 23 different jump ranges, between 9.76 LY and 55.46 LY. The above is a plot of the number of jumps needed by jump range. The curve immediately begins to shallow out, so the returns are always diminishing, and it's up to you when it's not worth it anymore. Certainly, I'd say after a 50 LY jump range you're really not saving much time at all: 1-2 jumps in 1000 LY, a 10% saving at best.
The curve is really beautifully clear if you look at the inverse: that is, 1/Number of Jumps.
View attachment 117752
This is a pretty clear indication we're looking at a
N = L /
j relationship, where
N is the number of jumps you need to take,
L is the distance to the destination, and
j is your jump range. More specifically, the empirical equation is
N =
L / (1.009213
j - 3.042410). I'm not normally a fan of empirical equations, but without Stellar Forge's data on stellar density this is the best way to look at it.
Since this thread is about jump
efficiency, here's a chart of that:
View attachment 117753
though only take it as a rough guide. At 10 LY you'll only spend 60% of your time going in the right direction, up to 80% by 15 LY, 85% by 19 LY, 90% by around 25 LY and reaching a soft limit 95% by 40 LY. Note that this
doesn't mean you don't get there any faster beyond a 40 LY jump range... you do, but it's not because of plotting a straighter route anymore.
One last way to talk about it... let's say you're either travelling 250 LY (you're an in-bubble player) or 1000 LY (you're an explorer plotting maximum routes).
In-Bubble Player (250 LY journey)
If your jump range is 10 LY, your journey will take 36 jumps. +1 LY range will drop this to 32 jumps, +5 LY range will drop this to 21 jumps.
If your jump range is 15 LY, you're looking at 21 jumps as above. +1 LY on this will drop you a single jump, to 20 jumps. +5 LY instead would get you down to a 15 jump journey.
20 LY jump range, 15 jump journey. +1 LY will take this to 14 jumps, +5 LY to 12.
Beyond this, 30 LY jump is 10 jumps, 35 is 8 jumps, 40 is 7 jumps, 45 is 6, 50 is also 6, 55 and 60 get it down to 5.
For an in-bubble player, I'd say anything over 40 will disappoint you.
Explorer (1000 LY journey)
Here, it's a bit different. A 40 LY jump range will get you across the 1000 LY stretch in 27 jumps, but you'll probably notice that a 50 LY jump range will cut it to 22. 60, and you're looking at 18... maybe not that big a deal, but probably still noticeable on a long trek.
