What is the frequency of drop items at the end of each game?

Solution 1:

In Dota 2 there is an Item drop system:

The item drop system is a feature that allows players to obtain cosmetic items for free through playing the game.

Notes:

• After every matchmaking game, each player has a small chance to receive an item or set.
• All drops in Dota 2 are solely based on time played in Dota 2 via matchmaking.
• Winning, losing, or individual performance has no effect on item drop chance.

And also:

While spectating a tournament game with over 100 viewers, one or more Heroic items are randomly given out to viewers each time a memorable event occurs.

For more information about Item drop system read this.

Solution 2:

From my personal experience, I can say that there is no loot refresh system in Dota 2. The stuff is awarded randomly. Last week I've got like 2 pieces of different item sets and of different quality, but haven't got any items at all for like half a year or so.