actually slardar doesn't really do that much dmg on his own, all his dmg is from amp dmg which helps the team. So if you mean in that sense then ok, but cent with double edge probably does more personal dmg.
I think running into a fight is just way more effective in pubs, compared to tactical focus with stun and amplify damage in pro play. There's more decision making with Slardar since you have to select the target you really want to fuck up and your team should follow up. With centaur it is more so just "welp, let's run at them and kill shit". Slardar can really fuck up low armor heroes, and nullify a whole AC or Shiva's worth of armor + 5.
I remember centaur being picked a bit back when Doom was popular, the idea was that unless you doom centaur (who won't die from it anyway) you will have a the target escape using cent's ult.
You can't just compare two heroes because they have ONE similar spell and happen to play the same role. They are nothing really close to each other and Slardar is popular right now because heroes like Lifestealer, Alchemist, DP are popular, who are all really weak to minus armor.
slardars significantly more mobile and because of sprint its possible for him to contribute without a blink. centaur, not so much. slardar doesnt even need 6 to leave his lane, which is good since his laning isnt amazing.
Centaur's biggest strength is his aghs upgrade which reduces the damage his entire team takes by 60% and gives his team free pathing (in addition to the stuff Stampede usually does). His ult is the only thing that makes him worth picking over slarder. Like you said, slardar has a superior stun, can initiate without a blink if needed and had a powerful damage amp spell. All centaur really brings to the table is an inferior stun, an aoe nuke that damages himself and has a small aoe and a passive which hurts enemies a bit if they hit him. Hes not even much tankier because he's hitting himself with 400 damage nukes all the time. The only time you pick him is if you really want mass haste for your team, and how often is that something you really want?
I feel they need to buff his stun a lot, make return scale up to 100% of strength and then give him some armour before he's even considered by pros. In pubs he has a high winrate because he lets his team run away from a bad fight, and he stops the enemy from escaping a good fight. Pros are usually much better at disengaging from bad fight with minimum losses so centaur is less needed.
As much as I love this hero, he needs several buffs before he's good. Also he needs lifestealer to go away because he will just eat centaur's 3.8 strength growth.
Another thing I just thought of is this: Stampede is a great ability for letting your team initiate before they get their blink daggers. Something like a Tidehunter charging into your team at Haste speed and Ravaging is terrifying. Unfortunately both Tide and Centaur are offlaners and fit the same role making running them on the same team awkward. Other heroes like Enigma can get the blink by the time Centaur has ult anyway and others like Void don't desperately need a blink at all. So Centaurs biggest problem is that he fills the same roll as the heroes he works best with. Most of the heroes who benefit most from Stampede are offlaners and so they cant really be run in the same line-up as Centaur.
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Pros love slardar and almost never run cent, but if we do a quick pros and cons of each is cent ever better? Both have stuns and fill a similar role but a bit differently.
For instance slardar has a low cd sprint for himself while cent has a medium cd ult that makes whole team sprint to initiate.
Slardar crush much lower cd, bigger radius, has lingering slow. Clear winner there over cents stomp.
Cent has a huge aoe nuke vs slardars bash effect. Slardars more control but rng based. Cent could be really good in a combo with like a magnus or dark seer to set it up. The abilities don't compare at all cus they're so differently.
Slardar ult makes taking rosh fast, greatly increases single target physical dps, cent has no comparison.
Cent has return dmg which idk helps him tank? No ones going to focus him in a fight if they can help it, meanwhile slardar dies faster if sprint is active.
I feel like cent is a lot tankier, has better str gain, does more dmg himself with his double edge and return, can be a true 3 position if he gets items and deal a lot of dmg. Slardar though has a lot more control, works as a 3 or 4, cus even if he doesn't get farm amps his teams dmg so much. I'm actually thinking cent could use a little buff to stomp after posting this. Slardar seems superior most of the time, but in pub play centaur's win rates are 3-4% higher. What gives?