One of the benefits of the SpaceX Raptor full-flow staged combustion engine is the extra power generated by having all of the fuel and all of the oxidizer flow through the turbines to produce power to run the fuel and oxidizer pumps.
At first, I thought having two pre-combustion chambers and two turbo pumps would double the power compared to an RD-180 style oxygen-rich-only staged combustion engine. But then I did this calculation (see below) of fuel mass and concluded that the fuel has only 25% of the mass of the oxygen, and so would only add 25% to the total pump power available.
${CH_4 +2O_2 = CO_2 + 2H_2O}$
${CH_4}$molecular weight = 16
$2O_2$ molecular weight = 64Fuel to Oxidizer ratio is 1:4 (Assuming Stoichiometric for simplicity)
Conclusion: Using the fuel as well as the oxygen to drive the turbines adds 25% to the available pump power.
Is that the correct conclusion? If so, is it worth the extra effort to get this 25% extra power?