I think, hyperventilation after sprinting is not supposed to give you an advantage over the normal state because in such a case you already have more CO2 than usually, so intense breathing just helps you to normalize CO2 level then.
When hyperventilation is done in the normal relaxed state, you should be able to hold your breath for about 2 minutes without an urge to resume your breathe. The most intense urge will be perceived somewhere between 2 and 3 minutes of breath holding. Lightheadedness begins from approximately 3 minutes of breath holding, and passing out should happen somewhere between 3.5 and 5 minutes (most likely, close to 4 minutes) .