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Close. To use your analogy, and limit it to omni-directional antennas, a low gain antenna, say a 0db 1/4 wave, is like the sprayer in the middle of your yard the kids run through. Water sprays a short distance in every direction, including up, within a 180° hemisphere. A gain antenna is more like a quality lawn sprinkler head. The water only goes out sideways, not up. So, the same amount of water covers a larger circle. (BTW, unlike radio waves, water that goes up will, at least according to Isaac Newton, come back down. So, the analogy is imperfect. You have to imagine that the water going up from the sprayer evaporates before it can drop back to the lawn.) Now, to extend the analogy, imagine you ditch the sprinkler and sprayer and get a nozzle. Now you have a strong stream of water in one direction only. So, even though only one person will get wet, they will be drenched. And, that is a directional antenna. Pure and simple, the power out put from the radio is constant. All the antenna design does is focus the direction, including up or down, that the radio energy is radiated. Less energy radiated towards the sky means more radiated sideways... hopefully to another antenna.