Things like this may seem easy to analyze, but there’s actually quite a lot to it in terms of variables you have to consider.
Variables:
x = distance from ledge (measured in mu (Magus units / Melee units), rounded to one decimal place)
p = percent (Fox’s damage before unstale throw)
y = TDI (trajectory directional influence) input (+1 yields the highest flying curve apex, −1 the lowest; not accurate, only estimated values)
t = amount of frames spent in Turn before starting the dtilt (not completely independent because its optimal value can mostly be told from x, p and y by evaluating the dtilt and move results below)
Results:
dtilt = which hitbubble of your dtilt connects (3 = sweetspot, 0 = blade, 1&2 = sourspot, no = no collision)
move = how far you have to move after the dtilt for the grab to connect
Thus, we have four mostly independent variables. Because the computer vision tools available to me here are limited to three dimensions (x, y and color), it is not possible for me to map out 5+ dimensions (four variables and at least one output) and display them here. (I’m not even considering the amount of time it would take to test every single combination.)
In other words, this micro-situation is too complex to do a complete frame analysis about, so I will eliminate p by setting it equal to 0 and only look at the “optimal” amount of t for a given DI so that I can create a table that is still both easy to understand intuitively and informative.
Right now, the table is valid for NTSC Fox. Falco is vastly different due to his stupidly long techroll, so don’t assume these values are true for him as well.
x|p|y|t|dtilt|move|comment
11|0|+1|-|-|-|closest distance from ledge where Fox will still land on the stage for +1 TDI
17.6|0|0|-|-|-|closest distance from ledge where Fox will still land on the stage for 0 TDI
16.5|0|−1|-|-|-|closest distance from ledge where Fox will still land on the stage for −1 TDI
24.6|0|0|-|-|-|closest distance from ledge where Fox will not slide off before dtilt hits for 0 TDI
35.2|0|−1|-|-|-|closest distance from ledge where Fox will not slide off before dtilt hits for −1 TDI
Now before I add more information to this table, we can already see that Marth needs to stand very far from the ledge to prevent Fox from doing missed tech to slide off, which evades both dtilt range and grab (obviously). It is, however, possible to catch it with a tipper forward smash, but only for certain distances.
Additionally, fsmash only connects when done immediately (assuming Fox DI’s perfectly and attempts to fast fall to the ledge), so considering it as well downgrades the strategy as a whole from a purely flowchart / reaction thing to a guessing thing.
When we only look at the flowchart part of it, it’s completely beaten by Fox’s missed tech → slide off → fast fall option. In other words, it only works on opponents who don’t know their options. So putting in more work into the table only makes sense when we include the instant fsmash option and accept that Marth needs to predict and cannot rely exclusively on reaction / flowchart execution.