Mining pools form due to the transaction costs of decentralization. Better explained as a result of the mining protocol being winner takes all, and is granted

Mining pools form due to the transaction costs of decentralization. Better explained as a result of the mining protocol being winner takes all, and is granted write access authority (for guessing a increasingly larger random number), that by pooling everyone's lottery tickets together and paying the pool operator, the agree to take a small sum of each successful guess from the pool (assuming the pool fairly pays out participants). "decentralized" except not.