A great feel. Songs that feel great can get a lot of grace in the lyric department. If you can make people want to dance or move with the feel of your song, you might be onto a hit feel.
A memorable melody. If you write a melody that people can’t get out of their heads, you may have a hit on your hands. Hit melodies are generally easy to remember and they are infectious. Shoot for melodies like that to increase your chances of a cut!
A lyric that makes sense. You can write songs that feel awesome and make sense. If you pull off both, you’ve got a song that stands above most others. That should be your goal as a writer if you want to get cuts.
Put extra effort into those 5 areas, and you will find yourself writing better songs. And, as we always say – it all comes down to “writing better songs”.