Is there a formula that can be applied to this tool if implemented on a computer?

There is no mathematical formula to convert the score to weeks of gestation, since in the clinical arena, we are assessing the infant's achieved level of maturation, which is a continuum rather than a series of discrete data points. For this reason, we look at completed weeks of gestation, so that we do not make the mistake of artificially overestimating the infant's gestational age. 

Another way of arriving at the correct week would be to round DOWN and not up when using the grid to convert the numerical score to weeks of gestation.

 

The paper form doesn't allow for odd week results.  Why does the scoresheet only list the even weeks?

 

For bedside clinical and research purposes, we do use odd weeks by extrapolating between the five point increments in the score. In all cases, we record only completed weeks of gestation.

(As this is a clinical tool, trying to arrive at 1/2 weeks would be false accuracy.)

The score lists only even weeks for the sake of simplicity and brevity. 

To my knowledge there has not been a need for a complete list of ratings. Clinicians have extrapolated intermediate values similarly to the example given earlier, arriving at odd numbered weeks as shown.

 

An example of this extrapolation using scores between 15 and 20 would be as follows:

        Score             Weeks

           15                  30

           16                  30

           17                  30

           18                  31

           19                  31

           20                  32

This same pattern can be followed up to 50 = 44 weeks.

Dr. Ballard

References :
Ballard JL, Khoury JC, Wedig K, et al: New Ballard Score, expanded to include extremely premature
infants. J Pediatrics 1991; 119:417-423.

Neuromuscular Maturity

Physical Maturity