Well, in general, I guess the easiest way to think about it is how much information did we have, assuming that we knew the mean of means. If we know the mean of means, how much here is new information? Well, if you know the mean of the mean and you know two of these sample means, you can always figure out the third. If you know this one and this one, you can figure out that one. If you know that one and that one, you can figure out that one. And that's because this is the mean of these means over here. So in general, if you have m groups or if you have m means, there are m minus 1 degrees of freedom here.