MOA is an arc measurement, and the best place it comes into play is in sight adjustment. Say your group is 3" high at 300 yards. Your sights say 1/4 Minute. What they mean is that each click is 1/4 " at 100 yards, 1/2" at 200 yards, 3/4" at 300 yards, etc. Four clicks on your sight will center your 300 yard group. That 1/4 Minute on your sight is 1/4 MOA.
Group measurement is usually center to center. Take the extreme spread and there is a 1/2 bullet diameter at each end, so that is why you subtract one caliber. It is important to state the distance the group was fired at. A .878" group at 50 yards is ok for .22LR, but starts getting really exciting at 200 yards, regardless of caliber.
You could express your group as an arc measurement but that clouds the issue. Just because you shot a one minute group at 100 yards does not mean you can expect to shoot a 5" group at 500 yards (another one MOA group). You can hope it, but the ammo loses velocity, is subject to wind drift, loses stability, etc, etc. Interestingly, there are some loads I've seen that are less accurate at 50 yards than the very same load at 100 yards. Obviously the load needed some distance to stabilize and fly right!
There there is the issue of statistical validity. Did you fire enough rounds in the group, and enough groups, so that you can say with certainity the group you are so proud of is truely representative of the groups the ammo/gun is routinely capable of, or was it just a fluke?
Just some things to consider...