for now it looks random with an effort to keep buybacks = to the amount of revenue they made that day
i am hopeful though that they will make this process more algorithmic, similar to how hyperliquid's AF has done it.
re: your question on short term buy pressure - you can track their wallets
here:
Pump Fun Buyback wallet: 3vkpy5YHqnqJTnA5doWTpcgKyZiYsaXYzYM9wm8s3WTi
(This wallet executes the market purchases of PUMP tokens.)Pump Fun Squads Multisig: G8CcfRffqZWHSAQJXLDfwbAkGE95SddUqVXnTrL4kqjm
(Where the consolidated PUMP tokens are sent after buying back.)
although i am skeptical that trying to front run or trade around their buys is a worthwhile strategy haha.