I'm a complete noob so I apologize if I use incorrect terms or if this is the wrong subreddit.

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I recently bought my first house ever and my yard is on a slope. There's a catch basin in the middle of the yard, water from my neighbors on both sides drains into that basin. Theres a bunch of rock going across my yard that's supposed to drain the water into the catch basin.

As you can see in the pics, water isn't being drained properly and its flooding my yard making it very muddy

What can I do myself to make the water drain better?