Bank savings rates are set and changed at a bank's discretion to encourage deposits, but broad trends in historical bank rates can be inferred from historical rates for U.S. Treasury Bonds and for certificates of deposit. Three excellent sources for understanding historical bank rates are the 100-year history of U.S. Treasury Bond rates, the 30-year history of U.S. CD rates, and the 30-year history of Bank of England bank rates offered online.
In the United States, bank savings rates hit historic lows after the 2008 recession. After the recession, the rates stayed at a very low level historically. A large contributor to the low bank savings rate was the low rate of return on U.S. Treasury Bonds set by the Federal Reserve. The Federal Reserve policy of setting low rates aims to encourage investment by lowering borrowing costs, and it has the side effect of discouraging savings by lowering bank rates. At the same time, the low rates on savings translate into lower mortgage rates from banks because the bank's costs to loan money decrease.
More specifically, bank savings rates are influenced by inflation rates and investment demand. Inflation tends to drive up savings rates because it erodes the value of money and indirectly raises the cost of saving for a depositor. Investment demand also contributes to bank savings rates. When investment demand is high, a bank has many opportunities to make money and has a strong desire for deposits. As a result, it offers a higher rate.