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Solutionme, the Yoshi players get a lot of hate from FG noobs. A LOT of hate. The boards get defaced once every couple weeks. But then Yoshi can't manage to break top 16 at a major tournament despite heavy representation in Japan, lots of theory crafting saying he's super good and general player interest. The conclusion among many Yoshi mains is that Yoshi is badly overrated. He lacks effective setups, has a nonexistent grab game and lacks any techniques he can really fall back on. The result is a very strong frustration among Yoshi players with the character and the response the community gives them in general. Your rubbing salt in wounds here.
Down-B is actually one of Yoshi's riskiest moves. It comes out quick, but has a long animation and a long punish window afterwards. If you space it right, I
believe it should be possible to stutter step Fsmash (though the spacing seems near perfect). By any means, counter will make him hurt. Aerial Down-B loses to a fresh shield (use the shield to take the stars and counter attack with Usmash OOS). If you want to prove you got guts, it also loses to Usmash (but not recommended). If you are slow to see it, space out a DB or something quick (like Nair). Grounded Down-B can actually be rolled out of if it hits shield. It's a high risk move for him so you shouldn't see it too frequently from good Yoshi's. YOU SHOULD NOT BE FINDING YOURSELF HIT BY THIS DURING A "COMBO." You should be either to the side (Fair, Nair or something) or should be watching his angle to try and maintain landing pressure. Don't expect him to come directly to you if you throw him upwards.
I can make a similar argument for Yoshi's Nair, it simply doesn't have the range to hit a Marth making full use of his range and ends up being a nice guarantee he won't try to airdodge that you can exploit by virtue of your sword.
I actually "main" both Yoshi and Marth and have done this MU many, many times--especially on the Marth side so let me weigh in on this. I'm not going to assign numbers--everything here is my experience and theory more than a set of numbers so take it with your own skepticism. I think this is a spacing/zoning MU and the question is if the range advantage or the speed advantage is more important. (And if you think it's speed, why aren't you playing Roy?). I will say the more experienced members of the Yoshi boards tend to think this is a losing MU for him. I'd listen to
Pugwest if he cares to share his thoughts. Raptor is considered among the best Yoshi players in NA.
Yoshi's eggs have deceptively long endlag (probably because he has control over where they go, think what happens when dancing blade goes sour). If he arcs high and far, he's vulnerable to having his eggs get run under. At the least, Marth can advance between eggs until he feels scared. If he throws them close dash->shield or walk->shield usually leaves him open. He wants to throw them because that's his counter-option to Marth's spacing. Figuring out how to get past his wall without doing something silly like rolling or air-dodging too close is a big part of the MU.
On stage, shielding is a good option because the best Yoshi's grab has all the risk of Link's (with just as much endlag and none of the range) and can't setup anything reliably nor will it kill reliably in sudden death. Egg lay is funny--I'll let you figure that out, but I will say it's not as rewarding as a traditional grab. Yoshi has practically nothing safe on shield, which is an exploitable weakness. He also has to close that extra half body length or so to land anything that's not an egg which means Marth gets the "first strike" so to speak and the disjoint usually wins trades. Exploit your spacing advantage, this isn't Falcon. Be aware most Yoshis will begin to feel pressure as you close and get antsy to try something. Also try and avoid letting him land. Force him offstage or look to land a hit as he lands (Yoshi really can't cover his landing).
Off stage, watch out for fair, but it has a pretty hefty windup and he probably won't get another chance if you get around him and get back. Fair swats him away and should be considered (but not used universally) as an option. If you have him offstage, watch out for eggs covering his return. You can be well assured Yoshi will try and return high, so you can also try and pressure as he gets close to stage. Don't let him get onstage for free. Double jump is his only real option and the armor wears off fast once he starts taking damage. Swat him away repeatedly for damage. Footstooling Yoshi's DJ offstage flat out kills at almost any percent (but I wouldn't recommend going for it).
Yoshi has a lot of flexibility to mess up due a high weight and natural ability to escape traps, but doesn't have an immediate way to really kill a careful Marth. Simultaneously, Marth can kill Yoshi, but it takes some work to work him up to the damage where stuff becomes semi-reliable. Don't blindly throw smashes, tilt tippers near the edge or rage-enhanced Uthrows can be sufficient. Leave the smashes for when you've found something exploitable--also, Usmash is terrible at picking Yoshi out of the sky so don't use it to contest Yoshi's aerials. Realize Yoshi
has to smash or edge guard to kill, so take advantage of this at high percent. Yoshi kills better off punishes, but Marth has more reliable secondary options.
Curiously, both characters have to play the other's game. Yoshi has to outspace/outzone Marth or he'll get shredded before he closes the gap. Marth has to play passive/aggressive footsies lest he throws an unsfafe attack and gets punished. Both sides just want to find the one weakness in the other player to exploit.
Be aware that the
only pattern universally recognized amongst the Yoshi boards is the FG Yoshi strategy, which is a good way to get knocked out in round 1 of a serious tourney. I can't tell you exactly what will happen in the MU (nor can most Yoshis, frankly), so you'll have to play it and get careful enough with Marth to win it. For what it's worth, there's been a pattern of players complaining about Yoshi on his boards and then learning the matchup and suddenly going quiet. I think Yoshi is a skill-gate character, figuring out how to beat him marks you as a player who knows how to seriously
play.