• Missing a one-point conversions is an extremely rare event, which seems consistent with its one-point value.
• Two-point conversions are also rare and probably impose twice the risk if not difficulty.
• Safeties result from happenstance more than stratagems, so two points seems reasonable.
• Most scoring opportunities in football produce either 7 or 3 points.  Do these make sense?

Time out.  Whereas touchdowns are often scored in a sequence of offensive plays following a kickoff return, touchdowns can also result from a turn-over (pass-interception or fumble) anywhere on the field.  Field goals, on the other hand, can be scored only by the team in possession of the ball -- the offensive team -- and only from some limited distance from the goal line.  Let us embody these observations into assumptions...

It is evident that  X_TD = 100 - X_TP .

Assumption #2 That scoring a field goal requires an offensive advance from the point of taking over possession of the football at X_TP to within some distance X_FG  from the goal line. 

The requisite drive for a field goal would be given by 100 - X_TP - X_FG .

he two scoring options ought to be brought into balance, don't you think?  Football is kind of a metaphor for the "territorial imperative."  At four points, say, the typical field goal would cost 12 yards of offensive advance per point, about the same territory as a touchdown.  Just a suggestion.

Whereas touchdown points are easier to get than field-goal points, there is another possible outcome in every offensive drive -- the much dreaded fourth down, particularly with long yardage.  When that arises outside of field goal range, a punt is the most common play, which relinquishes control of the ball.  A fourth down inside field goal range produces a likely three-point score.  Using the present scoring units of football, it should be possible to make reasonable wagers on which type of score will be made at the next opportunity during a game.

If a sophisticated solver gets curious, he or she might test the sensitivity of his or her wagering decisions to various numerical values for those distances (X_TD and X_FG).  For now, let's just apply the ones we already have postulated.  Thus, it is reasonable to predict that, out of every three successful scoring opportunities, a team will make two touchdowns and one field goal. This prediction merely appropriates our foozling in formulas that balance scoring preferences with realities of the fourth-down.

We are also recognizing another reality -- that our analysis here does not warrant more than a digit of precision, as follows: 16.7 / (16.7+10.7) = 0.60 replaced by a nice round 2-out-of-3, and 10.7 / (16.7+10.7) = 0.39 with 1-out-of-3.

For an applications of these results, see The Next Superbowl.