Before I get started on the Why Fors: A control deck will never work if it only utilizes 1-for-1 removal. You will need some 2-for-1s or better somewhere in your deck or you will just run out of control cards. That's why not 0.

I dont really know the current Modern meta so this is all general info. It really depends on your meta. For example, last time I played standard I was running Steam-Kin RDW which puts down attackers down T1-4. In that kind of meta you need your 4 mana sweeper on T4 so white control decks were running 5 sweepers. Is there a deck like that RDW? Or are there any decks that can generate a large amount of non-haste tokens in one turn? Does green ramp quickly and then pump out big guys every turn? White weenies also play a part in sweeper determination.

Based on your description it sounds like there is not much of that going on, but maybe one or two creature decks to be concerned with. OR, the creatures in said decks are so potent they require immediate attention, and waiting for your opponent to build a board presence of two or three creatures is not viable.

You have an example decklist? Would probably be easier to work backwards

Assuming modern deck probably has a lot of filtering/tutoring so they probably run 1 maindeck and more in the sideboard because they can dig pretty deep for it if they need it in a pinch, snapcaster as well if the control has self mill

The first deck is proactive rather than reactive. The Chalices probably outperform any sweepers. Know what’s better than a sweeper? Keeping the cards from ever even leaving your opponent’s hand.

The next two are more reactive. I get why they’d do it. The existence of the first deck will make some aggressive players overcommit, which will run straight into the hands of the other two.

To get back to the original question. The correct amount of sweepers will depend the most on the likelihood of ever being able to two for one the opponent. If, for example, there are single creatures that can kill you all on their own (definitely the case in modern), sweepers stop looking so great. It’s hard to sit back and wait for the two (or better) for one when your opponent can never put another creature down, and still kill you before you can stabilize. And if you will never get the card advantage, spot removal will generally outperform.

Mostly this. Sweepers are fantastic catch-up mechanism, but only if decks go wide that you are need them in order to catch up. And sweepers also look bad if you have creatures yourself. Sometimes you still need to blow up everything when they have 4 bodies and you have one, but you're obviously losing something in the exchange as well. That's why decks like Grixis rarely run sweepers, except out of the sideboard, because they typically play to the board much more than classic Azorius Control. The tension in Modern is that just every deck usually plays to the board alittle bit.

Nah Verts a dumb dumb, listen to me instead who hasn't played a game in 2 years