You probably

Ballista is not so much about mana efficiency, but more so about durability.

It's a card that can take mana sinks, pressure Planeswalkers, and add mind games; you'll always get something out of it.

It eats 1 tuffness doods (there are so many) as Gimmic mentioned but also can remove PW's that come out swinging with a neg ability. Chandra torch of defiance for instance is dead to a 1/1 ballista the turn she is played if she burns a creature. It's a reactive card that can do many things.

Have you ever seen Ballista do it's thing in a landfall deck that plays Retreat to Hagra and Retreat to Kazandu?

Ballista is good.
I agree with most of what has been said, but its main selling point for me is its scalability. Its a 2/4/6/8/10... Drop, so whatever fase of the the game your in, its gonna have its uses. Just like myr, its also a pain in rear-end to remove, because its always gonna do some damage and even if you do cast it early, it has an in-built ability to grow... Without even going into synergies and the colorless cc.
So its utility over efficiency.

Well if the game stalls out and you have a mana sink while they don't, sure. But what if your mana sink is Ballista and theirs is something like Oviya - they're going to win (until you use your counters to shoot the Oviya, because it's a better mana sink). Tireless Tracker is another key mana sink in my experience. If you draw lands, then you're converting them into cards. If you don't draw lands, then you're drawing action. In either case it's also a better mana sink than Ballista. I'm sure there are other mana sinks as well.

Then there is the 1-toughness creatures. The problem with this is that you are at a substantial mana disadvantage to kill them. Say you use your 1/1 Ballista to kill a 3/1 Veteran Motorist. Is this a good idea, I'd typically say yes, because the Motorist is bigger than your Ballista and you are unlikely to have the mana to charge it. But then you're down one scry 2, and possibly one crew as well. This is even worse against Toolcraft Exemplar, simply because you're trading your 2-drop for their 1-drop. For this to be worth it, you need to have a 2/2 Ballista and they need to have two 1-toughness creatures. Even then you're probably not trading at mana parity. You get card advantage, at tempo disadvantage, which is still going to lose you the game against any deck playing Veteran Motorist and Toolcraft Exemplar.

Then there is killing planeswalkers. But what planeswalkers are you hoping to kill? Some examples would be:

Flip Nissa - if you're able to ping Nissa off the table, chances are she used her -2 mode, in which case you've traded card for card (your ballista for their Nissa) and they still have a 4/4.
Gideon - you need a 4/4 ballista because he's probably at 4 loyalty. Very mana intensive.
Chandra, Torch of Defiance - if she's used her -3 mode, chances are she killed something. So you trade your ballista + that something for Chandra, effectively a 2-for-1.
Ob Nixilis - takes a 2/2 ballista, and even then, if he's used his -3 mode he's killed something, so you are 2-for-1'ed.

And so on. Plus in most of these situations you could've achieved the same result with a card like Shock (the same Shock trades at mana parity or better against Toolcraft Exemplar and Veteran Motorist, too).

Then there's the versatility of being able to serve as a 2-, 4-, 6- etc drop. But at each of these points it is seriously underpowered. A 2-mana 1/1 can't profitably attack or block against virtually everything. The same goes for 4-mana 2/2s, 6-mana 3/3s, and so on. Endless One also serves as a versatile drop depending on your curve and yet nobody runs that card.

So that just leaves things like triggering artifact synergies (how many cards are there that use this? Unlicensed Disintegration, Toolcraft Exemplar and improvise off the top of my head, any others?), +1/+1 decks (completely agree Ballista is to be considered there) and triggering revolt (but then you'd still have lost your ballista so you'd be trading at card parity). What are these decks (other than +1/+1 counter decks) that people put Ballista into? I'm genuinely curious, since every attempt I've made to use the card has fallen flat on its face, and a possible explanation is that I'm trying to use it in the wrong kind of deck.

Actually it was run a lot in Eldrazi winter, one of the better plays too.

Eldrazi winter yeah, but that's because Eye of Ugin and Eldrazi Temple enabled busted starts. I'm referring to Duels, where I haven't seen an Endless One in like, forever.

Endless One isn't in Duels...might be why.

LOL I'm a retard. I swear I remembered some X-costing Eldrazi card, turns out there are none in Duels. On a side note Endless One looks too much like Desolation Twin which may have contributed.

I wonder if Endless One would see play if it were in Duels. I'm skeptical, but idk.

Depends. Snek decks would likely at least test with it. Not sure if it would make the cut though. T2 Constrictor, T3 4/4 Endless One isn't the worst thing in the world.

The reason it saw modern play was the Eldrazi lands making them ridiculously big turns 2 and 3, so I can't imagine that play would suck in Duels with Snek.

The thing is even in snek.dec you're just getting an above curve body. Everything else in the deck does something apart from being a beat stick, whether it be gaining advantage/resources or just being able to get around bodies with trample. There is nothing I'd would cut for an Endless One that is just going to be chumped.

Yeah, Endless One would not see play I think. Compare him to WB in Snek, the only Endless has over Ballista is an extra counter, but he can't fling the Counters towards the opponents.

He would see play if there was such a thing as an Eldrazi tribal deck or we had access to cards such as Sanctum of Ugin (which saw play in Colossus decks). Other than that, meh.

Yeah, we don't get access to a T2 4/4 so it's a bit moot. Well, its all moot, we don't have the card.

Ballista can be a decent finisher: with 8 lands, you drop 4/4, next turn pump it to 6/6, deal 6 combat damage then burn 6 to face.

^See, that actually illustrates why I think the card is so inferior. First, you used eight mana. Second, you assumed opponent has no blockers. In that case you could also play something like Gaea's Revenge and do 16 damage over the same two turns, and be immune to removal + counterspells to boot! The 6/6 ballista can also be chumped (sure you can shoot down the chump blocker, but then you'd do much less damage), and can still be removed (at least you shoot for 4 damage in this case) or countered (8 mana for 3 mana, oops).

I keep trying to play Ballista and I keep getting disappointed -_-;;

You aren't wrong.

The thing to consider though is that Ballista provides considerably more flexibility.

While Gaea's Revenge is definitely better in the above scenario where we are talking about spending that much mana, consider also that Ballista has value outside of being played with large mana investments or just being a big dumb beater.

Lets say we are talking about the same scenario, but the board is clogged. Neither Ballista or Gaea's Revenge can successfully connect with an attack. Ballista still has the option to convert that mana spent directly into burn to the face, which may be all you need to burn an opponent out through their clogged board.

That is the thing about Ballista. The point of the card isn't efficiency. If you compare it to cards that see high end play at each different point in the curve you will see that Ballista is usually not the best option. Pay 2 for a Ballista, well Sylvan Advocate would have been a more efficient use of mana (and would put the opponent on a faster clock). You can go all the way up the curve comparing it to cards like this and you will notice that Ballista is almost always the less efficient option.

Ballista isn't about efficiency though, it is about versatility. While it may not be the fastest, most efficient, or the most cost effective option, it fills a ton of different roles. It can help to cover gaps in your curve (either due to deck design, or just plain bad draws/mulls). It functions as a creature (attacking and blocking), removal, and reach in one card. It can make combat math hell. It can function as a mana sink. As a creature it isn't terrible against removal (since you can at least convert the lost creature into damage). While the cost to grow Ballista isn't efficient by any means, the fact it exists is still relevant, as self-contained snowballing creatures have always had their place in Control matchups. It works well with other cards that deal with +1/+1 counters (Snek decks and the like), as well as decks looking to trigger Revolt.

Being colorless means it can fit into literally any deck also, which helps even more with the whole "being versatile" thing. Especially since some colors don't normally get access to things like that (being able to ping an opponent while playing white weenie for example).

And that is outside of all the Artifact synergy we have going on currently because of the KLD block.

If you are just looking for pure efficiency, Ballista isn't it. If you are looking for a jack of all trades, Ballista is your guy.

Yes, that's the main advantage of Ballista. Gaea's is a dead card until you have seven mana, but you can conceivably play Ballista for 2, 4, 6, etc. It could even have some utility. But I'm somehow unable to find a deck to put it in.

Take for example my most recent deck, which is a B/R/C beatdown deck. Does this deck want Ballista? Well, if I'm looking to punch the opponent with Reality Smasher, I would also want powerful, mana-efficient threats. Cards that punish my opponent if they miss their curve or don't have removal. Cards that can attack through (smaller) blockers, or trample over for damage even if they can't. Cards like Thalia, Fleetwheel Cruiser, Forerunner of Slaughter. Ballista? I don't see it happening. It could conceivably win the game on a stalled board by burning down the last few life points, but then so can Fleetwheel Cruiser, and Fleetwheel Cruiser is just generally better otherwise (a 5/3 haste vs. 2/2 creature for the same 4-mana isn't a comparison).

Then take the example of the deck I was building before that, which was a G/C deck with mana dorks. The curve started at 2, and went as high as 10 for Ulamog and Kozilek (although most creatures were 6-mana or less). Does this deck want Ballista? It's inferior to Sylvan Advocate or a mana dork early. In the midgame, it's inferior to Tireless Tracker or Thought-Knot Seer. At 6 mana, it's inferior to Endbringer; at 10 mana, it's inferior to Ulamog. Would I take out any of these cards to include Ballista? I don't see it happening. Like, if I started losing a lot to aggro decks then I could conceivably take out Ulamog for a lower curve - but still probably not Ballista, since there are better cards for the role, e.g. Aethersphere Harvester or Reclamation Sage.

Then take the deck I worked on before that, which was an Orzhov control deck. This deck wanted to remove everything my opponent played, stabilize with sweepers, then win with either high-value creatures (Noxious Gearhulk, Avacyn, etc) or planeswalkers. Does this deck want Ballista? Probably not. It's worse than another removal spell early, and there are better win conditions later. I suppose Ballista could be useful if I desperately needed a threat (e.g. opponent has an active planeswalker but no creatures), but even if I ever ran into that situation there are better cards to use, like Gifted Aetherborn or Gisela or Kalitas. I suppose if a 2/2 Ballista gets bounced by opponent Jace, then I could shoot for one damage, making it better than these three cards. But even then the advantage is terribly small - losing a 2/2 Ballista to Jace is not a victory. And these three creatures are way, way better in almost every other situation.

tl; dr: I'm simply unable to find a deck in which I actually want Ballista, with the singular exception of +1/+1 counter decks (Winding Constrictor). It is inferior at every point. Seriously, what are these decks that people are putting Ballista into and it's pulled its weight?

The MtG historically had many cheap infinite colorless mana combos (even Duels had infinite mana bug not long ago).
Ballista is one of the best ways for instant win with infinite mana.

As an one of in delirium: adds 2 types and can be grabbed from the past for reach. something the deck is usually missing.