Gods are incredibly powerful entities that live in their own realm but frequently roam in ours in search of entertainment—which they often find in causing destruction and misery.
In order to ensure our survival, humanity has found a way to appease them: through the regular gift of a small amount of magic via worship. This gave the god an incentive to keep us, mortals, alive and make our society prosper, as well as imbued us with some power in the relationship—finally—by giving us the chance to refuse to worship certain gods—although if too many people do so, then we'll all lose our protection from that god...
The easiest way to give some magic to the god is through prayers. Those are simplified and codified rituals that we can easily do every day, rotating through different prayers and different gods according to the calendar.
The second method to give god magic is to carry out special rituals that use sacrifice to increase the magic output sent to the gods. The sacrifices are commonly something like a little amount of blood or our hair after we cut it. In those cases, the extra magic comes from us and doing the sacrifice will leave us exhausted for a while. An alternative is to sacrifice plants or animals to offer to the gods their magic instead of ours. We can also choose to conduct a long and complicated rituals to gather the magic from the environment and offer it instead. Because it requires more preparation and cost more, sacrificial magic is only carried out on special occasions when we have a request for a god or want to thank them.
The final way to send magic to the gods is by taking a special potion attuned to one god. The magic will then be passively sent to the god until the potion leaves our system. This is the most practical method for us, mortals, as we are not required to do anything beyond drinking it. It is also the method which gives the god the most magic outside of outright human sacrifices. Drinking such potions leaves us in a slightly second state, where we are more in tune with our magic and environment. The brain impairment is annoying, but I have to admit that the enhanced magic is absolutely amazing and certainly highly addictive. A bonus point for the gods, as it incites people to take it more often and so to feed the gods more often.
The potions only have a slight inconvenient: they cannot be taken too often or they are bad for our health. This means that we take them during festivals as a kind of special gifts to a god for their special day. No one can celebrate absolutely all festivals, but falling to celebrate those of the major patrons gods will be noticed, as they see the worship as their due for all the good they do to our country. They consider a failure to worship them as an insult, and we all know how this always ends...
A lot of people go to the other extremity and try to give more magic to the gods than strictly required in order to be noticed by them. In order to do so, you can take a variation of the potions to increase your magic output. However, standing out to the major patron gods is hard, as so many people are trying to do so, and so quite a few end up being reckless with the amount or frequency of potions that they take. As a result, deaths during festivals are not so infrequent... Worshipping minor gods is not mandatory, and so it is much easier to be noticed by one of them. Thus, almost everyone chooses at least one minor god to whom to offer their worship.
Each god has their own cult and festival days consecrated to them. The advantage of having to take the potions during festivals is that nobody is in a state to work and so those days are national holidays. In addition, we do not truly need to pray or sacrifice to them all day thanks to the potion and so we can have some fun instead. The water festivals in particular are highly appreciated as we are forced to swim and play in pools and rivers.
Taking potions during major patron gods' festivals is mandatory, and daily prayers are unavoidable distractions for anyone caring for their good health. All the rest is unnecessary and only those who have let themselves get brainwashed by the gods choose to pay more of their magic to those who hold us captive. Unfortunately, this means that the vast majority of the population does so...