George W Bush wanted a distinguished statesman-type as his running mate in 2000 to compensate for his own relative youth, so he picked his father's defense secretary Dick Cheney.
What if George Bush had picked James Baker as his running mate? He'd have experience from being Chief of Staff to two presidents, Secretary of State, and Secretary of the Treasury, and Undersecretary of Commerce. The only prospective downside is they're both from Texas, but Baker's been a national figure so long that I'm not sure that'd be much of an issue.