I Want to See this Stat on Football Penalties

In general, a team or player is never happy to receive a penalty. However, getting a penalty seems like only half the story. In some cases, the penalty may be a wash--if the offense was not committed, the result might have been the same. For instance, a 10-yard holding penalty that prevents a 10-yard loss on a sack is not a bad deal. In a few cases, the penalty may be a positive good--defensive pass interference that prevents a catch that could have been advanced for a touchdown.

I suppose those are still a minority of cases. But what bugs me is when the announcers make a big deal of a big play being called back because of a penalty, most often holding. In my view, in most of these cases, without the hold, the play would have gone nowhere.

Then there is the subtler analysis...even if a particular penalty is a bad deal, is it just the "price of doing business"? That is, for every 1 time caught holding, is the player getting away with it 4 times?