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Some corporations have an R&D division. Agents in this division won't give missions like most agents. Instead, you can ask them to perform research for you if you meet their standing requirements and have sufficient levels of Research Project Management to manage multiple agents. The condition for meeting the Agents skill level in that field is no longer required
Calculating Research Point Rewards
Once the agents start doing your research, they accumulate a specific number of research points (RP) every day. Also, they will mail you with requests to do missions for them which, if you complete them, doubles your reward for that day. These missions usually require you to obtain some specific items, which you will have to buy off the market or otherwise obtain. Most pilots that use R&D agents choose not to run these missions, since it costs a lot of isk to do so.
The rewards depend on:
Your skill level in the research field clvl
The agents skills level in the research field alvl
The agents quality qlvl
The agents field multiplier m
(clvl + alvl)^2 x (1 + qlvl)/100 x m
(to be confirmed - based on memory)
The fact that the rewards are based on the square of the two skill levels combined means that there is a significant jump between each agent level and each character level reward.
For example an comparing a L4, q0 agent doing research for a character with skill level 4 vrs skill level 5.
(4 + 4)^2 = 64
(4 + 5)^2 = 81
Choosing a Field and Corp to grind
Before you start your research programme check the market to see which Datacores are commanding the best prices. These indicate good demand due to invention and should be the fields you aim for, regardless of whether you invent items yourself or not.
This should narrow down your options to a handful of fields from the 20 or so available.
Now check what research corps you have access to, either geographically or via existing standings or both. Use the agents info to check whether these corps offer the research potential you are after (say, 5 level 4 agents who can research laser physics). You may find you still have a choice over corps at this point.
Now look at the other agents available for that corp. You want a good progression of non-research agents that you can do missions for to get standings. Ideally you also want to be doing these missions in high sec as dodging pirates is unnecessary and avoidable. Combat missions improve standings the fastest but most of the corps you will be interested in are light on straight combat. Instead look for something like Administration which gives a few (easy) courier missions but a majority of combat.
So by the end of this process you should have identified a corp that has good agents in the fields you are interested in, good progression from level 1 to 4 agents and a safe location to base from.
Grinding for standings
This is the pretty tedious part, especially if you are used to doing level 4 mission in battleships. Aim for efficiency, in terms of speed of completion, over looting and killing everything. Your goal is to get your research agents rewarding you as fast as possible and then move on to more rewarding activities.
Consider switching to a battlecruiser class vessel. These can tank all level 3's with moderate skills, rarely have trouble killing anything except very small frigates and a single setup will see you right the way from level 1's to standings for level 4 research agents. Their better speed and ease of killing frigate and cruiser groups make them generally superiour to battleships for this purpose. A passive tanked Drake with heavy launchers is ideal and even a dirt cheap T1 versions is very viable.
Many missions require a simple single goal, such as destroying a structure. Don't waste time on the ships, simply hit it and report back to the agent.
While the lottery still exists, after the last remaining BPO's have gone there will be no more issued. The emphasis therefore is shifting towards producing Datacores for using in invention. To redeem your research points simply talk to your agent and they will transfer the points to datacores, currently at rate of 50 rp per data core (check this). If you have 5 agents working to bring in 100 rp each per day you are earning around 10 datacores per day. Save them for your own invention jobs or sell them on market for profit.