I went looking to see if I could find precise information on reputation gains from the new quest givers in Path of Exile. No such luck. I did find some reasonable conclusions drawn by some guy and I did some testing with Sceadeau and I feel like I have a rough idea of how things work.
To start, you're going to need to earn a total of a little over 10 million reputation to hit max level with all 7 masters. This morning after about a sixth of the available time for the league to end I had a total of 570k reputation. That's 5.5% of the way to completion and there's no way I'll get done at the current pace. But could the pace be accelerating? Doing today's dailies (and a couple of extra quests found in random maps we ran afterwards) got me up to 640k reputation. 19 days got me 570k, 1 day got me 70k. That's definitely an improvement on the past, but even 70 more days at that pace will only get me halfway to the end goal.
Chances are since things have accelerated to this point that they'll keep accelerating from here on out, too. From the testing we did and what I've been reading it feels like each master has a hidden character level based on your reputation level with that character. This hidden level acts as a gate towards how much reputation you earn in a similar manner to the way character level acts as a gate for how much experience you can earn. For example, my Elreon level is currently at 6, and the quests he gives me in my hideout are somewhere around level 54 or so. Elaine's Elreon level is more like 3 and the quests he gives her are more like level 30. So when I tag along on her daily quest the game sees that I 'should' be level 54 and I'm doing a level 30 quest and it drastically reduces the amount of reputation I get from the quest. The same works the other way too, and she's only going to get credit (at best) for doing a level 30 quest when she comes to do my daily instead of the full value of a level 54 quest.
What does that mean? Well, it means people behind the curve want to tag along on as many dailies as possible because even though they're earning less than the other people they're still earning as much as they can be. People way ahead can tag along on low level stuff to help or for fun but the reputation gains are drastically reduced if you're too far ahead. This also means I can't just run through zones on normal mode to spawn as many quest givers as I can because those quests aren't worth anything to me, but if all my quest givers give quests around level 54 then I could actually be running through cruel levels and getting full reputation for doing so.
I don't know the actual factor for penalizing you for being under leveled. It's entirely possible I should still be running through high level zones to find quest givers because they give a little more than the cruel ones? But presumably that's both slower and more dangerous depending on gear levels.
One other thing we found out is you seem to earn a massive bonus for doing your own daily quest. Somewhere between 2 and 3 times as much?
So I do expect that as I level the masters up the rate of reputation gain will also increase. And quite possibly that increase will be very significant. When you're first starting out you're getting 200 reputation from a quest and now I can do quests worth 5k. The jump in experience needed from 6-7 and from 7-8 is around 3.5x as much. If the quests themselves are worth 2.5x as much (so it still takes more time to advance in the later levels but they also get to have huge numbers) then the level 7 quests will be worth 6 times as much as the level 5 quests I'm currently doing. And since I only need to double my current rate to get it done that could be ok.
I don't know that it will be a big boost, but I don't have any real outs if it isn't so I need to just assert it'll be a big boost and move on from there. Assuming it is actually feasible with my current playstyle, what is the optimal way to get all the way to the end as fast as possible?
Well, there's a big boost to reputation gain speed by getting one of the masters all the way to 8. This lets you bring a 4th master into your hideout giving you access to another daily quest. Daily quests are worth double rep for you and you don't need to hunt them down, so that's very good.
There's also a big drain on your reputation gain when you get a master to level 8. When you're at the cap you can't make use of any of those quests that spawn randomly while you're playing the game. You also can't get reputation from your friend's daily quests for that master. And if you get 4 of the 7 up to max level you can no longer make use of the 4 personal daily quests.
This makes me think that ideally you want to get one master to 8 as fast as possible and then you want to spread the rest of them out as much as you can. Since you're never choosing who you encounter randomly the only real way to influence things is by who you have in your hideout and who your friends have in their hideout. So probably the optimal line of play is to have everyone invite the same master as the one you all want to get to 8 first and then spread the rest of them out. Things get complicated a little since one of the masters gives a free high level map each day as her quest but she also requires 74% more reputation to max out as the lowest guys. Everyone wants the map lady, overall reputation efficiency be damned. Sometimes she even gives quests to do someone else's quest in a map so it could be argued that she's the best option anyway.
So really the ideal situation is probably to have everyone invite map lady and one of the two easiest masters as the first two. Then have people invite a mixture of other masters as their third and fourth options to spread things out.
Looking at my reputation levels right now I've earned the most with Zana but my highest level is with Elreon since he's one of the lowest required guys. My third highest reputation gained is with Tora, who happened to randomly be the master I invited as my 3rd quest giver after Zana and Elreon. Tom also started with Zana and Elreon so we've randomly stumbled into what is probably a good plan. His 3rd is Vorici and since he's different than Tora I think that makes me happy.
There's also the slight worry that some of the masters have quests that can be failed. Zana, Vorici, and Vagan have all been failed several times by my groups. I don't think I've seen any of the other four end in failure. So maybe you end up needing to do more of those three just because you don't get the rep every time?