A champion is considered a ball of stats when their kit has limited interaction between players aside from 'if I have more stats then you I win, otherwise I lose'.
A good example of this is warwick, hes either going to out sustain your damage while killing you and win the fight or he doesn't have the stats to do that and dies. He only has auto attacks and two point and click abilities to work with and so there's no real opportunity for either player to make any 'out plays' in a duel with warwick (barring qss or some other gimmicky way of self peeling from his ultimate).
Irelia is another example. She auto attacks you, has tenacity to lower cc duration, has a point and click conditional stun that people fighting against her have little control over if any, and you can't really dodge her ult at the range she uses it from in a fight. She will either sustain through your damage and cc and kill you with her targeted attacks, or she won't and it has little to do with the skill of anyone fighting her. Decision making maybe, gold lead yes, but not skill.
Ball of stats does not refer to champions who buy a lot of stats and then do a lot of damage to you. Zed is not a ball of stats because there's interaction with his shadows, his shuriken is a thin skillshot often used at non point blank range, his spin is melee and can therefor be dodged or avoided, and his ultimate is a window of time where you can go on the defensive or time cc to limit his damage - and that's without considering that you can qss or zhonia the ult to not take any damage from it whatsoever. He's filled with counterplay in that a duel or trade with him has a lot of opportunity to interact and put yourself at an advantage if done well.
Riven is also not a ball of stats for similar reasons. You have plenty of ways and opportunities to interact with her and the outcome of a duel or trade on equal gold champs can be heavily influenced by experience and mechanics as well as anticipation of what she'll do next and when. Her damaging skills are all non targeted which means that they can be missed, baited, or dodged, two of her basic spells are movement spells so getting snared means that not only can't she move but she can't use spells either (and her only defense is tied to movement so a snare might as well be a stun as far as setting her up to get blown up is concerned), her ult does not have an instant effect like warwick or malphite ult or something so if you can bait it out of her and back off it will go on cooldown without having it's full effect, she's squishy so she can be 100-0 unlike the type of champion that builds tank and sustain and out stats you (try catching a darius slightly out of position and blowing him up, he'll probably live long enough for his team to show), etc.
Akali is a ball of stats - her q and ult which constitute all of her damage are point and click and she heals up from bursting people. You can't run from her because of her ultimate, you have to fight her and then she either can tank your damage and kill you first or she can't and she dies.
Ahri is not a ball of stats. You can avoid everything in her kit in one way or another. There are many things you can do in a duel or trade against her that can allow you to win even if you have fewer stats than her (though it will be harder and she can probably live and escape before you can kill her if you are behind).
Garen is not a ball of stats. He has to hit you with his spin, preferably isolated and preferable with you being the villain, to get his damage off and his ultimate doesn't do any damage unless you are low hp already. His passive sustain can be kept in check just by interacting with him regularly, so it doesn't factor into whether he will win a fight other than him having more of his hp bar full at the start.
Darius is not a ball of stats. His hook and spin are telegraphed non targeted spells that put him at a disadvantage if missed that can be capitalized on. His ult requires him to stack his passive 5 times, and his q has a good and a bad hitbox even if it does hit. You can effect the outcome of a trade or duel with darius by playing around his abilities.
Those are just examples, I'm sure you get the idea at this point.
TLDR: "ball of stat" champions have little or no way for either player to effect the outcome of a fight through skill, it's just a numbers check. If there is potential for the champion or their enemies to take actions that effect the outcome, they aren't a ball of stats.