The broadcasts are done with true HD cameras and sent to your TV as HD. If you have DirecTV or cable there is compression/decompression involved but it is still the same HD image size. Compression would only affect some of the fine details of the picture.
Over-the-Air broadcasts are not compressed; although it's possible that compression was involved between the network and the local broadcast station. Regardless it's still HD video in a 16:9 format.
1080p: 1920x1080
720p: 1280x720
SD (US); 640x480 interlaced
In the US, SD (NTSC) is 480i and in Europe SD (PAL) is 576i.
Unfortunately, OTA broadcasts are also heavily compressed. They showed Congress all the pretty pictures we'd get if they got their digital bandwidth then after they got it almost all affiliates decided to cram 2,3 or 5 subchannels on the same channel by starving the primary channel of its bandwidth.
Dish Network used to remove about a third of the resolution until they got busted for advertising 1080 channels but not actually supplying 1080. Now they still cut about a third but they only remove vertical lines so it's still 1080 - except instead of 1920 x 1080, it's 1280 x 1080 and then upconverted to HD.
Now that they are promoting 4K, once again they are putting their best foot forward. Once everyone has adopted it they'll butcher that just the same. Just take a look at a 4K TV with a 4K football game and and see how incredible it looks. Even if you are only 10ft from a 70" 4K display, you are too far away from distinguishing 1080 from 4K. That's the picture quality we should be getting (on CBS/NBC not FOX/ESPN). - but it's not even close from anybody .
We'd see them start to use more creative framing and shots that take advantage of HD, but they know HD isn't making it to the viewer, so they don't do much different than before.
. . In fact, if you've ever seen the standard definition signal that used to be delivered to the truck outside the stadium, you'd think that was HD compared to what you are seeing at home..