4Game

You can check yours by typing in console dota_game_account_client_debug | grep flags
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The written below is my personal understanding which I gathered from reading many sources about the matter.

Most sources say that 0 or 1 is you are great human being or new account. 3 is you are an average player in terms of griefing. 7+ is you are a griefer

Most people including wiki (which is not official source) say that it is responsible for the "hidden pool". So for example behavior score is showing your (relatively) recent attitude and flags (from my understanding) for the whole existence of your account. And when you queue your games players in your games are most likely following your behavior score and flags. To compare hidden pool (flags) and behavior score, at low behavior score you will get unstable players who are prone to grief, be toxic, abandon games and big amount of flags just generally tries to put you with same type of people who established themselves as ruiners even if they have 10k behavior score.
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I asked my friends what is their number. One person who is often griefing said they have 9. Other person who is often griefing said they have 11. I have 3 and I pretty much never grief. Another person said they got 3 (and they also never grief). Another one said they also got 3 (and they pretty much never grief). On one of my old accounts from a few years ago I have 17 and I often griefed and was toxic.
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Some links to the info if you are interested

https://steamcommunity.com/app/570/discussions/0/3035978213211869956/

https://steamcommunity.com/app/570/discussions/0/2747650363463175518/

https://dota2.fandom.com/wiki/Matchmaking#Behavior_Score_and_Account_Flags