I consider someone a big winner at a school is someone who stays at that school for a number of years and has great success (conference/national championships).
Looking back at the last 20-25 years guys that I consider the most successful coaches all did very well within their first 3 years:
Bob Stoops: National Championship in 2nd year
Urban Meyer: National Championship in 2nd year at Florida, 3rd year at Ohio State
Mack Brown: Division title in 2nd year at Texas, Conference title in 4th year at Texas
Nick Saban: Conference title in 2nd year at LSU, National Championship in 4th year at LSU
Dabo Swinney: Conference title in 3rd full year at Clemson
Jimbo Fisher: Conference title in 3rd year (division title his 1st year) at Florida State
Jim Tressel: National championship in 2nd year at Ohio State
Now, the above list only shows national championship coaches, but it shows how they changed things pretty quickly.