Agree mostly, but there are some things I should point out along with the one's
luke_atyeo
mentioned;
Throwing an opponent as Fox won't yield a KO; they are supposed to put opponents in uncomfortable positions. U-throw is very good at doing this, but there are situations when it is better to throw the opponent offstage.
Fox's offstage game may be garbage, but his ledge game is phenomenal. What do I mean by ledge game? I mean punishing the opponent's option at the ledge. I am going to cover only the ledge-trump here;
Fox's Ledge-trump
Reflex's video on ledge-trumping;
https://youtu.be/VR37CS30NAE
"Characters are forced to hold on to the ledge for about 20 frames ... If you buffer a ledge jump, ledge attack, or ledge roll, it is impossible to be ledge trumped"
With this knowledge in mind, how then can Fox use it to his advantage? For this example, we will assume Fox has grabbed the ledge in an attempt to ledge trump by running off and immediately pushing back to grab the ledge (if you are unfamiliar with how to do this;
read here).
Note: this assumes that Fox did not allow ample time for the opponent to do a regular getup or ledge drop (20 frames + input). This is because these options CANNOT be buffered, meaning that the opponent is going to get trumped if you do a ledge trump perfectly before they even have the chance of doing a getup or ledge drop. This means that Fox waited a maximum of 20 total frames to do the ledge trump and the opponent inputted the option immediately or got trumped.
Scenario 1 - the opponent doesn't react and is trumped
You have two options;
1. Follow up with drop ledge -> rising B-air. If the opponent doesn't air-dodge, they get hit.
For reference; when you are ledge-trumped, you are forced into an animation of getting shoved off the ledge, which lasts about 30 frames. This is half-a-second that your opponent cannot do anything while they fly helplessly in the air. Fox's B-air comes out on frame 9, but we are forced to stay grabbing the ledge for 20 frames before letting go and using rising B-air. This means it would take about 33 frames to get a perfect ledge-trump b-air; 20 forced + about 4 additional frames dropping and rising with double jump + using the 9 frame B-air. Note that you have to input the b-air as you rise with it. Hence, the opponent will only have roughly 3 frames max to react, since they have been shoved off and have to wait out the animation of 30 frames.
If you grab the ledge as the opponent is forced to do their 20 waiting frames and they don't choose an option and get trumped, this will make ledge trump -> B-air virtually guaranteed.
I say 'virtually' because of course here are other factors that come into play; Characters with fast jumps, moves that allow some characters to quickly go back onstage or have invincible frames will be able to escape it. Examples include Yoshi's armored double jump, Sheik's bouncing fish, and so on.
2. Since the opponent has that small time to air-dodge, you can just do a normal getup onstage and bait out the air-dodge, or do a rising Bair towards onstage (thanks Luke for this!). If they air-dodge, they will be forced to grab the ledge again unless they have an additional jump or recovery option. Additionally, an opponent re-grabbing the ledge without being hit offstage loses invincibility but still has to wait 20 frames before choosing an action. If the opponent goes to grab ledge again due to lacking another option, you can punish them with a D-smash or the late part of F-smash.
Again, character attributes and abilities play a part here. Keep all the things in the previous point in mind when thinking about what option you'll choose.
Now I'm going to cover the options which Reflex showcases on his video; ledge-roll, ledge-jump, and ledge-attack. Ledge-roll and ledge-attack are almost the same, but ledge-attack varies slightly.
Scenario 2 - the opponent does a ledge roll
You can do ledge-drop > double jump > Fox Illusion back onstage to cover the roll and punish it. Ledge roll data;
http://kuroganehammer.com/Smash4/LedgeRoll
Note how every ledge roll can be cancelled after 50 frames, meaning the opponent will go through a minimum of 50 frames total before doing anything.
This is universal in Smash4.
Assuming the opponent read your trump and rolled, you have 20 frames before dropping, about 2 frames dropping the ledge, then you double jump to get above the lip of the stage in position (since Fox rises fast, this should only take about 4 frames minimum if done perfectly), and then use side-b (active on frame 21) onstage to hit the opponent; total is about 43-46 frames, while the opponent is just ending the last frames of their roll (50).
This means you will catch the opponent's ledge-roll if done perfectly. As most of you know, Illusion can confirm into a U-air or B-air if you hit near the middle of the move because of the angle it sends opponents at and if the % is right.
Scenario 3 - they ledge attack
You can also cover this with side-b, though you'll be sending them backwards if you hit them near the beginning of the move. Another option is to do a drop down -> f-air copter or rising U-air to hit them. The ledge attack lasts longer than the ledge roll, so you have plenty of time to cover it too.
Scenario 4 - opponent ledge jumps
Fox is unable to punish opponents in this scenario. For every characters not named Palutena, Duck Hunt, and Shulk, they have to wait at least 13 frames to fast-fall back down. Fox has to hang on to the ledge or at least 20 frames. Since you can't punish this, what do you do?
With Fox's regular get-up of 35 frames with the last two being vulnerable, you do 55 frames getting back up. Assuming you grabbed the ledge as the opponent buffered their ledge jump, your opponent will have at most 42 frames to get back on the ground (or close to you) and abuse the 2 frames of invulnerability before you can put shield up, roll, attack, etc. Ledge jump heights are significantly high in this game (about the top platform of BF), so this gives you more time than you think and little time for your opponent to punish your attempt back onstage. Most characters (everyone who falls slower than Sheik) will not land fast enough to grab you if they don't fast fall, and most characters who fall slower than Link/ROB won't be near you to hit you with an aerial.
Another option you can consider is to chase the opponent with a ledge-jump of your own, although this isn't risk-free either; your opponent can use an aerial to hit you as you rise, but it won't put you at risk if you predict your opponent will try to come back down to the ground fast-falling. Other options to consider as mixups; drop > jump > side-b is risky and almost the same as doing it when an opponent is waiting onstage for you. Watch where they are and choose it if you feel is correct. Drop > jump and simply landing onstage is faster than a get-up but without the invincibility.
Since Fox can't punish the ledge jump after grabbing the ledge to trump, why should the opponent be afraid of using this? This is where we expand out of ledge-trumping and cover more of Fox's options
Summary - Fox's Ledge-trump
You see now why it matters to send opponents offstage and how Fox can take advantage of the trump better than just any other character. Obviously you shouldn't be using the trump all the time, you can mix it up by faking one and jumping with N-air to cover a getup or a ledge jump (this is how you can cover it), you can use your ground speed to cover a roll and punish with U-smash or dash attack, you can also use jab to cover a ledge getup. Or you can use F-smash (a la Snow) or d-smash if your opponent takes too long to get back up onstage, pivot grab them if you think they'll do a normal getup, etc etc etc, you have so many options with Fox to trap opponents holding the ledge.
And of course, be careful of characters who also have good options from the ledge; Shiek, ZSS, Yoshi, Ness, etc. Be wary of air command grabs that go through shields, be wary of quick rising f-airs, and be wary of recoveries that poke through the stage (Ryu, Ike, Peach, etc).