by guaranteeing to pay the player for 4 years, a total of $1 million in my example. The school has no idea if the player will be any good at all at the collegiate level and hence is taking a risk.

The negotiated amount would naturally balance between the how much the player wants / is worth, And how much the school is willing to pay.

A player could, for example, demand a 1 yr contract at a higher amount for their first year. But then the player would own the risk of underperforming and getting a significantly lower value for the remaining years.