Ok, so this thread is going to be long and rough, but the thought exercise was interesting enough to share. A whole lot of credit goes to dannyshan for figuring out the formula for rubberbanding (so uhh…not sure if you wanted it to be public on the forum, but you’ve made it pretty public in the FB group…)
So everybody knows that to maximize rubberbanding, you need to wait until the last possible moment to do your missions, but which missions do you do first? The high point ones? The low point ones? Does it depend on your current modifier? It’s tough to tell. 99% of the time, it really doesn’t matter. The gains are AT BEST minimal. But, it could mean the difference between winning and losing.
What’s the rubberbanding formula?
It actually became fairly apparent what the rubberbanding formula was in The Hulk PvE event. We had always assumed that the rubberbanding multiplier was determined by your distance from the leader, but it was kind of a guess. As The Hulk went on (especially the last non sub-event missions), it became more obvious. With The Hulk, we always knew who the global leader was in the event since it wasn’t bracketed at the main level. While I don’t know exactly how dannyshan came to the formula, I’d guess he just assumed the multiplier was linearly determined from the difference of points between yourself and the leader and noticed that the max multiplier seemed to go away at around the 4000 point mark.
So, you can make a guess that the formula for the multiplier would look like:
( - )/400
Then with the added condition that the multiplier could not be below 1 or above 10.
So, if you are looking to do a mission with base points of 100, and you are 3500 points away from the leader, then your multiplier would be: (3500)/400 = 8.75. So the mission would be worth 875.
The formula was tested many times across different times and players to know that it was accurate in The Hulk.
Well, that’s for The Hulk. We don’t know who the global leader is for the other PvE events. How do you know it’s still true?
You’re right - from a single player’s perspective, they could never be truly sure it’s the same, there just aren’t enough data points, since we don’t know what the top scorer’s point total is. It’s, however, highly likely that whoever leads your bracket is pretty close to the leader (within a few hundred, unless the bracket is new or has pretty lazy people.) You could notice that the max modifier changes at ‘around’ 4000 away from your bracket leader, but it doesn’t actually prove it’s the same.
dannyshan apparently has multiple accounts all competing in the PvE events. So, he was able to capture two or three data points for at the exact same time, which means that the top score would be the same for all data points.
So, you could assume that the old formula is still in use, and then compare answers:
(X - <player 1 score>)/400 =
(X - <player 2 score>)/400 =
Since you know both player scores and both modifiers (if you knew the base amounts of the missions you were playing), you could show that the top player score is the same for both calculations.
So, you can conclude (or, probably…just make a super awesome guess), that the formula holds true.
Ok great, now that we know the formula, what could we actually do with it?
When the formula was presented in the FB group, that’s basically the response dannyshan got. Nobody seemed to care, which made me slightly sad. But, it provides the information necessary to come to what is likely the ‘optimal’ way of scoring points in the PvE events. Really…it’s probably completely unnecessary to do unless it’s the last refresh before rewards go out.
Get on with it, what’s the most optimal route?
Wait, but you haven’t seen the math yet!
There are a couple of different cases you need to consider:
- I just started the event during the last hour, and I’m 50000 points away from the leader. (Or something so far away it doesn’t matter.)
- I’m just barely over 4000 points from the leader, one or two missions will get me below that.
- I’m less than 4000 points away from the leader.
Let’s say we have to choose between three different missions, each worth different points:
A : 100
B : 75
C : 50
Case 1: I just started the event during the last hour, and I’m 50000 points away from the leader.
This is obviously the easiest case. It doesn’t matter which one you do first, since you’ll always get a 10X multiplier.
10 (100 + 75 + 50) = 2250
Case 2: I’m just barely over 4000 points from the leader, one or two missions will get me below that.
and
Case 3: I’m less than 4000 points away from the leader.
(Because it’s easier to show both at the same time.)
For this example, let’s say you are 4600 points away from the leader.
Here are the six different combinations you could have done:
ABC
A: 10x multiplier * 100 = 1000 points, 4600 - 1000 = 3600 points from leader
B: (3600/400) = 9x multiplier * 75 = 675 points, 3600 - 675 = 2925 points from leader
C: (2925/400) = 7.3125 * 50 = 366 points, 2925 - 366 = 2559
2041 points gained.
ACB
A: 10x multiplier * 100 = 1000 points, 4600 - 1000 = 3600 points from leader
C: (3600/400) = 9x multiplier * 50= 450 points, 3600 - 450= 3150 points from leader
B: (3150/400) = 7.875 * 75 = 591 points, 3150 - 591 = 2559
2041 points gained.
(Obviously, that doesn’t look impressive, you get to the same spot!.)
BAC
This exercise is left up to the reader.
BCA
This exercise is left up to the reader.
CAB
C: 10x multiplier * 50 = 500 points, 4600 - 500 = 4100 points from leader
A: 10x multiplier * 100= 1000 points, 4100 - 1000= 3100 points from leader
B: (3100/400) = 7.75 * 75 = 581 points, 3100 - 581 = 2519
2081 points gained.
CBA
C: 10x multiplier * 50 = 500 points, 4600 - 500 = 4100 points from leader
B: 10x multiplier * 75= 750 points, 4100 - 750= 3350 points from leader
A: (3350/400) = 8.375 * 100 = 838 points, 3350 - 838 = 2512
2088points gained.
So, you can see that CBA gives the highest point total of all of the combinations (trust me on BAC/BCA).
What can we conclude from this?
We can see that there is no difference between the points gained from ABC/ACB. Knowing the multiplier formula, we should have actually known that to be true, though, since it’s just linear (if I’m bored, I’ll write a proof). The conclusion from that is:
- After passing the 4000 point mark, it doesn’t matter which one you do first.
In CAB/CBA, a different conclusion can be made. In those two scenarios, doing the first mission doesn’t go past the 4000 point mark, so the second mission is the one that crosses the 4000 point threshold. The mission you choose for that is the last mission that is important.
- When crossing the 4000 point threshold, do it with the lowest point mission possible (well, the mission that you actually plan on doing)
You can basically extrapolate those two points to conclude that you should be trying to stay as far away from 4000 points for as long as possible (in terms of picking high point missions in a run, I don’t mean that you should never cross into the 4000 point threshold.)
- Save your high point missions for after you hit 4000 points away from leader.
This sounds SO unintuitive. We’ve already concluded that it doesn’t matter what happens when you’re within 4000 points, so why are we ‘wasting’ our high point missions at this point? Well, it’s true.
Ok, so that gives us these simple rules to follow:
- After passing the 4000 point mark, it doesn’t matter which one you do first.
- When crossing the 4000 point threshold, do it with the lowest point mission possible (well, the mission that you actually plan on doing)
- Save your high point missions for after you hit the 4000 points threshold
EDIT for those who might actually dig this thing up again:
It’s said later on in this thread, but after you cross over the 4000 point threshold (or whatever the threshold is for when you lose 10x multiplier), it is still best to save your high point missions for absolutely last. There are two reasons for this:
- While the multiplier is completely linear between 10x and 1x, it does floor out at 1x. So, when you are within 400 points (or, well, possibly the leader), 1x is actually HIGHER than what your multiplier would be if it were a true linear function. So, missions done at 1x are actually given more ‘weight’ than the ones before it.
- A lot of the conclusions above assume a constant point value for the leader. This is obviously not likely to be true. The leader’s points are highest right before the end of the event, so you’ll get a higher multiplier at that point.
