I don’t know a lot about football beyond being a fan, but I do know something about statistics. I read about the coaches trying to “stay on schedule” to get first downs, and this is why we often run on first down. However, it seems to me that trying to “stay on schedule” is a low probability game because there is a relatively small chance of stringing together successive first downs, even if you have a good probability of getting the first one.
Consider the probability of getting a new first down given each 1st and 10. I do not know the probability for the NCAA but I found a value of 66% for the NFL (http://archive.advancedfootballanalytics.com/2008/07/first-down-probability.html). The probability of getting a touchdown after successive first downs depends on the number of first downs you need to get to the end zone. At a 66% probability of getting a first down (or scoring) for each 1st and 10, the probability of getting a touchdown depends on the number of first downs needed to get there and these are (0.66 to the power of the number of first downs):
3 first downs: 29%
4 first downs: 19%
5 first downs: 13%
6 first downs: 8%
Thus, even if your chances of getting a first down are about 2 out of 3, if you have relatively small gains each time and need 5 first downs to score, you only have a 13% chance of scoring.
So it seems you need big plays to have a reasonable chance. Of course, any play you call could be a big play, but a downfield play has a much better chance of being a big play.
Consider the probability of getting a new first down given each 1st and 10. I do not know the probability for the NCAA but I found a value of 66% for the NFL (http://archive.advancedfootballanalytics.com/2008/07/first-down-probability.html). The probability of getting a touchdown after successive first downs depends on the number of first downs you need to get to the end zone. At a 66% probability of getting a first down (or scoring) for each 1st and 10, the probability of getting a touchdown depends on the number of first downs needed to get there and these are (0.66 to the power of the number of first downs):
3 first downs: 29%
4 first downs: 19%
5 first downs: 13%
6 first downs: 8%
Thus, even if your chances of getting a first down are about 2 out of 3, if you have relatively small gains each time and need 5 first downs to score, you only have a 13% chance of scoring.
So it seems you need big plays to have a reasonable chance. Of course, any play you call could be a big play, but a downfield play has a much better chance of being a big play.