this is a math question. let's say i have 147 games with a spread of 1 and of those games 4 have pushed. this suggests a 2.7% push rate. how do i find the margin of error on the push rate?

i know that the margin of error is related to standard deviation and sample size. the sample size here seems to be 147 games. the confusing part is the standard deviation, or dispersion around the mean. generally a large STD means the margin of error is great but in this case i dont think that is true. for instance if all games finished off the line by 3 points this will yield a higher STD and higher margin of error than games off the line by 1 point, but clearly a game 1 point away from the spread is "dispersed farther" from the mean here. do you know how to do this problem here?