The biggest simplifications were that I treated both toward DI and side DI to be the same and each DI category had the same break points for their followups. Break points in the percent ranges were hardly even a real thing, given the non-binary nature of the game, only suggestions for ease and simplicity. I felt that this was needed in order for players to be able to handle all the information, but after a lot of practice, I was able to recall more than I thought possible.
When you think about it, it doesn't make too much sense that the percent ranges listed under "no DI" would be the same as those under "side DI" when the followups were often different. It just happened to fit pretty well together that you could start doing soft uair->regrab on no DI at around the same percent where you should start doing tipper uair->Fsmash on side DIs, for example. For those starting out with doing percent-based combos, it made it really easy to break the combo into sections.
The same is true for the conflation of toward DI and away DI. Uthrow does not have a perfectly straight-up trajectory, so the full side DIs will have slightly different trajectories that slightly affect the followups. For the percent ranges given, everything still works regardless of the inaccuracies resulting from the simplifications, which only leave out things that do work instead of listing anything that doesn't work, but the difficulty of each cell varies, and the goal of ease of execution was sometimes sacrificed for memorizability.
Memorizing can be practiced as well as execution, so what does a truly optimal uthrow combo strategy look like?
Transitioning from the chaingrab into the juggle
The transition from repeated regrabs into doing uairs or utilts is one of the most important parts of the combo and where many make mistakes even if they are chaingrab masters, including top players. The percent limits of the chaingrabs on Fox and Falco are affected by the differences between the different DIs. Instead of putting a hard limit on when to stop chaingrabbing for any DI, you should end the chaingrab once they approach the limit for the particular DI they've done. Against Fox, this means going for uair->regrab on away DI at about 50% but regrabbing if they do toward DI here, waiting until about 55% if they continue doing toward DI. The higher the percent at which you decide to uair, (up to a much later point, of course), the easier it will be to hit the uair, react to the DI and get your regrab. The trajectory for toward DI is slightly lower and further away at any given time, so you want to do your uairs at higher percents than you would for away DI. Again, the old table still works, but this is a slight optimization.
That's if you still plan on taking a purist no-utilting path that I strongly suggested in the past. Even if you avoid the difficulty of taking chaingrabs right to their limit, the uair->regrab transition from no-DI or slight toward DI is fairly difficult to pull off, requiring a pivot uair, as a SH back uair is weak to DI away. This occurs at 47%. The chaingrab limit on no DI is at 46% (away: 52, toward, 61 (58 is practical)). Taking this path then requires both a frame-tight regrab or two and a difficult pivot uair if the opponent is doing no DI or slight toward DI.
Here's how I would map out the difficulty of the relevant percent ranges:
31-43: very easy
44-52: very hard
Utilts at around this percent hit too hard if the opponent DIs in the direction of Marth's back, so the alternative given was a mixup between walk utilt (or middle-hit usmash) and turnaround utilt. However, this gives your opponent a chance to escape.
But, it's possible to skip this difficult part of the chaingrab if you utilt earlier, where you can still follow up on any DI. The percents where you can uthrow-(no DI)->utilt-(any DI)->regrab, 29-34, are a bit too low to make it past the hard range. 37-44 seems to be a good range to front-hit tipper utilt easily on side DIs (walk forward for away DI) while having a turnaround back hit utilt for no DI and slight DIs that won't give them a chance to escape. These utilts also hit hard enough on away DI and no DI that you'll be able to follow with an uair->regrab. Utilt->uair->regrab will put you right into medium or easy percents. Less ideal is if they DI toward on the utilt and you're forced to dash regrab, however "hard" or "medium" is better than "very hard."
The only stipulation is that these utilts may be susceptible to SDI. If you find that they are too far away to regrab, you can still mix up between a dash attack or dash SH tipper fair, both leading to a regrab at those percents. Dash attack loses to toward DI, while fair beats it. If you can't even get those, a tech chase should still be possible. You need to be able to react and adapt on the fly to strange DI scenarios, which brings me to the next section.
Note: this strategy doesn't work as well on Falco, since his utilt followup range on side DI is about the same, while his very hard range occurs later (53-59). This means that unless you can get an utilt->uair->regrab combo instead of just an utilt regrab, you won't skip the very hard range at all.
Uair regrabbing unreliable?
Sometimes they will go too high on your uairs. Maybe you did them too early, maybe your opponent ASDI'd up. What I have neglected to mention was that there is a middle height between uair->regrab and uair->tipper-Fsmash. It is usually possible to avoid this middle height by timing your uairs carefully, but sometimes things don't go as planned. It's very difficult to get the right timing to get uair->regrab at 60-64 as I suggested in the table, anyway. The solution of course is to do uair->uair (both tipper). At low uthrow->uair percents you might even need to do three tipper uairs.
You will just have to judge when you need to go for a second uair and when you can regrab in the percent ranges between early uair->regrab range and uair->Fsmash range. Remembering the percents from the table can give you a good gauge, though.
Soft Uair unreliable?
While we're talking about uair regrabs, the soft uair regrab loop was a major feature of the flowchart.
There are actually two soft uairs, a middle sword hit and weaker body hit. The percent range I gave for soft uair->regrab was 65-79, however, you can do it with the middle hit as early as 55. Body hit only causes Fox to enter tumble at 67. The thing is, it's really hard to hit the middle hit, and it's hard to tell that you've done it sometimes. The slight difference in knockback can mess you up at later percents where you have very little time to react to DI and so little time to differentiate between trajectories as well. So, you should honestly only be going for this past 67, up to about 75, since if you hit the middle hit there, they'll be hit too high.
The other issue with the move is its weakness to toward DI. The natural trajectory sends Fox slightly behind Marth, so toward DI sends them far away. The 80-94 range for soft uair->Fsmash is quite unreliable because you can't tell if you need to pivot or not. SDI makes this even more difficult. Half the time I settle for the soft Fsmash into an edgeguard, which isn't bad but it isn't ideal.
An alternate up to about 75 is to do a SH back tipper uair->Fsmash, but that has a weakness to DI away. Pivot uair into pivot Fsmash solves that issue, though it is difficult. 60-88 you can pivot Fsmash to either direction, and beyond that, up-B.
Just taking the Fsmash or up-B is especially advisable when you are not in center stage. An extra 10-13% damage tacked on before your Fsmash is not an improvement if it forces you to send them in a worse direction. That segues nicely into a discussion about stage position.
Hold your ground
If it's a good idea to use fair you have stage position, it's a good idea to use uair when you don't have it, since there's a chance they will DI toward and the position will reverse in your favor.
If you're off to a side of the stage, taking an Fsmash or an up-B is a strong option, especially when you don't have the option to fair, as is often the case when they do no-DI. I did recently learn that you can pivot fair, which results in a decent mixup with pivot Fsmash, but that will still only work up to 72 or so.
It's not always necessary to go for a mixup with fair. Instead you can take the edgeguard mixup from a low percentage Fsmash or a high percentage up-B. However, sometimes it is really obvious when your opponent is DIing toward you, you just have the read. Many players, even top players, can't resist holding toward, especially because DIing away against soft fair is also dangerous for them by the edge at high percents. The correct answer would be to do no DI, but players tend not to do that in fear of strong hits.
Fsmash and Up-B
So now you might be wondering when you can land these strong hits, really. In my table I said up to 95% is when you can dash pivot Fsmash. However, this is ridiculously difficult on away DI, and still very difficult on toward DI, and in fact you need to do a long dash-wavedash. Pivots for earlier percents still require practice. Being realistic, I say you should start trying it at 85% and when you're comfortable with that, up to 90%. It's also possible to land soft uair on side DIs, with it being more practical on away DI, at around these percents.
Charging Fsmash has a noticeable effect. For every three frames you charge, you get the equivalent of a 2% higher pre-hit percent Fsmash. You can pivot charge Fsmash against no DI if you're able, or you can do standing charge Fsmashes on side DIs (up to 69% on away DI, 72% on toward DI). This tends to make a bigger difference on smaller stages or when you're off to a side of the stage. On the other hand, charging telegraphs your Fsmash, letting the opponent execute optimal DI and SDI. If you decide to charge Fsmash, make sure it will kill outright or lead to a guaranteed edgeguard.
Some players say they are able to react to Fsmash no matter what, but that doesn't seem to always be the case. To exploit this, Fsmash can be used as part of a mixup with fair. Players tend to have some DI pattern, watch for it. Even trickier is to mix up what direction you Fsmash them in, with the use of dash dances and pivots when you uthrow them with no DI.
Up-B percent listings were just incorrect. I couldn't seem to land reverse up-B past the percents given. Using non-reverse up-B (yes, with the strong hit), I was able to get the following, including in real matches:
Away: up to 130
Neutral: up to 125
Toward: up to 120
Again, start lower and practice it until you can get these consistently, it's worth it. You can mostly disregard what other options I had at 95-120. Up-B is criminally underrated, just don't use it when they won't be sent far away enough off stage for you to fall to the ground and edgeguard.
It's also possible to up-B in either direction on uthrow no DI via pivot jumping in order to face the other direction before double jumping back. This sacrifices some of the percent range of possibility, depending on how fast you are, but it is very much worth it to be able to reverse positions with a strong hit if you're cornered.
Juggling out of uthrow (side DI)
So, later in the Fox table post I got into juggle options, but they were mostly not accurate, talking only about tipper fair, and the ranges tested were for no-DI, assuming that everything would still work the same way for toward DI and survival DI. In fact, these numbers still assume toward DI. Survival DI, the DI that's meant to survive Fsmash, will affect the numbers and followups a bit. Up-B is a good fallback when things go wrong, or you can use numbers further in these listings to continue with long juggles. You want to keep your juggles short, this is not a stylistic choice. The less mixups you have to do, the better. And if dair is possible and will kill, just do it, I won't always list it.
Here's how I now think the juggles should be done (t means tipper, s means soft):
A quick fair and a tight FF is required on the low end of this range, and a big delay on the fair is required on the later end. Alternatively, you can do a SHsFair or SH Uair to continue the juggle.
Like in soft uair combos, you don't have much time to react to properly align a tipper Fsmash. Soft Fsmash is still pretty good at this percent. I've found that charging Fsmash after landing and then releasing when it's time helps with reacting for the tipper. Alternatively, you can do a SHtFair or SH Uair to continue the juggle.
96-105 SHsFair->dair/fair only
You can dair most of the time in the other ranges, but that's all you can do at this point. If dair won't kill, use a fair to end it.
106-120 just Up-B
up to 100 or so
FH tipper fairs are okay, but SH fairs tend to give you more options. They do have the advantage over soft fairs for giving you more time to react, but soft fairs carry further. The way you hit the tipper fair on the way up can be varied greatly, being possible to hit with the bottom part of the fair.
As I later discovered, on uthrow side DI you can do soft uairs, which can be done at about 90-105 for away DI and 85-95 for toward DI. Reacting to DI a little bit easier at this high percent, and you can follow with a tipper Fsmash at 90-100 if they don't do toward DI.
SH tipper uairs in high percentage juggles (up to 105) are aiming for away DI into a dair. It's usually a dair because away-DI'd uairs will carry them across the stage. This makes SH tipper uair as good an option to beat away DI than up-B when you're off to one side of stage. They're equally effective at beating away DI, but toward DIs will reverse position in your favor if you uair, and up-B is slightly better against no DI here. Fairs have slightly less DI coverage in these situations.
Choose your aerials depending on how much room you have on stage left. Tipper uairs and soft fairs carry further, but you'll some room on stage to dash in order to follow up on them. Tipper fairs and soft uairs can be used when you're lacking room, or you can end it there with a strong hit or a dair that would only work if it isn't DI'd in as your option coverage for away DI.
At many points in the juggle, you can end it with up-B. This can come into play especially when they do no DI on your SHtUair at a fairly high percent, above uair-(no DI)>Fsmash range (80+) or fair-(no DI)->Fsmash range (75+). Or, when they just happen to go too high for Fsmash due to the opponent's DI or your mistake in timing the aerial and you need a strong hit or don't have a good juggle followup.
There are several other ways to continue juggles, such as with side-Bs or reverse fairs and bairs, but they rarely find usage right out of uthrow and are often not necessary or worth the risk. However, there are some situations at high percent, as part of extended juggles, where these options are viable, along with neutral B, generally when they are just out of reach above you or above their effective percent range for the usual options.
Further research needs to be done on juggles from uthrow no-DI. The juggles that I listed for 95-110 no DI are not that great, often if you're close enough to the edge where reverse aerial juggles are useful, you're also close enough for up-B into edgeguard to be a more consistent option. The side-B->uair->up-B combo is useful in theory at center stage, but I have yet to land it in a match.
That's enough for now
I probably could have broken this up into multiple posts, but the sections flowed so well together! Next time I'll go over any loose ends regarding uthrow combos on Falco on FD.