That said, I don't think good bullpens make a huge difference to 1-run result. A lot of my 1-run losses are games I was losing by 1 run after 6 innings, and then my bullpen threw 3 shutout innings, but I failed to score. If I had a worse bullpen, I might lose those games by 2 or 3, and have a better record in 1-run games.
I think the same thing happens in real life baseball. A good bullpen can preserve a 1-run lead, but also preserve a 1-run deficit, or a 2-run lead, and the effect of these things on records in 1-run games cancels out.