A theory that might connect with effective altruism may be that of leading organizational psychologist Adam Grant.

Tl;dr:

The most successful people are givers.

The least successful people are givers, too.

The difference is that successful givers also take themselves into account. In addition, they are also strategists; see Adam Grant's TED talk.
 

A few distinctions made by a co-author of Adam Grant, Red Rebele:

Some things a selfless giver would do: 

• Give to anyone.
• Anytime.
• In anyway.

Some things otherish givers would do: 

Ask themselves:

• How much is this going to take?
• Am I the right person?
• Can I introduce you to somebody else who would be a better and more efficient resource for you?
• And they say, where am I best able to apply my energy for maximal results without burning myself out?

So they contain those costs.

Otherish givers would also:

• Find 4-5 people who need help with the same thing and help them simultaneously instead of just taking each person one on one.
• Use value-extending strategies, taking the way that they will help one person (or, I would add, animals), and figuring out how to extend that value to multiple people, including themselves.
• For example:
• They would allow themselves to feel gratitude, pride, and other positive emotions when they do good for others because they know that that will recharge them.
• They would take time to say no (which, if to throw in another reference, is the ultimate productivity hack according to James Clear) at times when they are going to need to because that's going to give them more energy and more resources to be able to help more people down the line.

Professor Raj Raghunathan adds these:

• They would also increase the chances that they will actually see the impact of their generosity, making them feel competent and capable (my addition: I would not necessarily pick an organization based on that because countless important organizations are doing a great job without ever seeing their recipients but even a picture of a recipient, as shown by Adam Grant, would increase your productivity doing good).
• They would enjoy the act of being generous. Consistent with the value-enhancing strategy, in which they feel grateful or proud for being generous. Again, that would not be my 1st priority, but I am certain that the martyr complex does not help.

Additional links:

• To the quiz (it will not tell you what kind of giver you are, only if you are a giver, a matcher, or a taker).
• To explore further the differences between selfless givers and otherish givers.