## Special SMOG Grading Revisited

By Nirmaldasan

In ‘Special SMOG Grading’ written in April 2010, I simplified Harry McLaughlin’s already simple readability formula of 1969. But the simplification had a limitation; it could predict years of schooling only from 5 to 12+.  Recently, I discovered a fresh simplification of McLaughlin’s formula for the higher grades 13 to 17+.

The average number of polysyllables per sentence (APS) is a useful metric. SMOG Grading = [square root of (30 x APS)] + 3. Here follow my simplifications:

If APS is less than 3, Special SMOG Grading (5 to 12+) = (3 x APS) + 5

If APS is 3 or more, Special SMOG Grading (13 to 17+) = APS + 10

Suppose APS is 2.6. Then, SMOG Grading = [square root of (30 x 2.6)] + 3 = 11.83; and Special SMOG Grading (5 to 12+) = (3 x 2.6) + 5 = 12+

Suppose APS is 5.3. Then, SMOG Grading = [square root of (30 x 5.3)] + 3 = 15.6; and Special SMOG Grading (13 to 17+) = 5.3 + 10 = 15.3.

For APS = 1 to 7, here are the corresponding scores of McLaughlin’s formula with those of my simplifications in brackets: 8.47 (8); 10.74 (11); 12.48 (13); 13.95 (14); 15.24 (15); 16.41 (16); 17.49 (17+). You can easily see how McLaughlin’s formula and my simplifications closely agree with each other.

An easy way to calculate the APS is to count P10, which is the number of polysyllables in 10 sentences. In which case, the simplifications assume these forms:

If APS is less than 3, Special SMOG Grading (5 to 12+) = 3 x (P10 / 10) + 5

If APS is 3 or more, Special SMOG Grading (13 to 17+) = (P10/10) + 10

However, my simplifications still have a limitation. While McLaughlin’s formula can predict years of schooling from 3 to 17+, mine can only predict from 5 to 17+.