To me, the term "overseed" refers to tossing a bunch of seed on a patch where there is currently not much grass. If we are talking about something that is a foot wide or more where there is no grass at all - then yeah, let's talk. But! If we're talking about spots where the grass is just thin, then let's talk about something other than overseeding.
Happy grass spreads by rhizomes (root-ish things under the ground). One sprig of grass can make a thick patch - when it is happy grass. Tossing a lot of seeds into an unhappy situation usually isn't gonna do much for you.
I would try to figure out why your grass is sad. And it almost always comes down to the soil. What does your soil look like? Feel like? Smell like? How deep is it? Have you had it tested in any way? Knowledge beats work any day.
Usually you can get away with damn near any effort by just adding organic matter. Most lawns people have asked me to look at that are sad got that way by years and years of taking away the grass when it is mowed too low.
If you are patient, you can mow high, fertilize a little in the spring and fall and leave the clippings there. In a couple of years the lawn with thicken up nicely. If you are willing to trade money for time, you can add an inch of
compost to your lawn AND fertilize (most composts contain wood chips or wood-product-waste that will suck the nitrogen out of the soil - you need your fertilizer to compensate for that).
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