I will contradict my previous post a bit for a minute by agreeing with this and noting that this is something that is often overlooked by the “take the points” crowd.
The risk/reward is not as simple there as a guaranteed 3 points versus a possible 6-8 points. If you forego the 3 guaranteed points and go for the 6-8 and fail, you still get a “consolation prize”, for lack of a better term, of 25 yards of field position versus position on the field if you take the 3 points.
Getting nerdy and analytical here for a moment, a drive starting from your own 5 yard line has an expected value of -1.3 points, versus +0.2 starting from your own 30. These are obviously just general estimates with no game context, but they give us some rudimentary idea of the value of field position.
So by taking the 3 points and losing the field position, you’re really only gaining +1.5 points in expected value.
Now obviously, there’s plenty of times and situations where that guaranteed 3 points is really needed, so situations can vary, but they give us more insight into what coaches are thinking about going for it down there.