Robert Gunning’s Fog Index is the sum of sentence fog and word fog. Sentence fog is caused by long sentences and may be measured by the expression 0.4 x AWS (average number of words per sentence). To measure the word fog, the ratio of AHS (average number of hard words per sentence) and AWS is multiplied by 40. Hard words are polysyllables other than capitalized words, easy compound words and disyllabic verbs made trisyllabic by adding ‘-es’ or ‘-ed’.
Harry McLaughlin developed his SMOG (Simple Measure Of Gobbledygook) on the assumption that sentence length and word length must be multiplied instead of added. If we apply this valid principle to Gunning’s factors, then sentence fog x word fog = (0.4 x AWS) x (AHS/AWS) x 40 = 16 x AHS = H16 (number of hard words in 16 sentences).
This is a useful result as two variables are reduced to one. No need to calculate sentence fog or word fog. Just count the number of hard words in 16 sentences to get the predictive power of both the variables. This count H16 will help us easily match text with years of schooling from 1 to 17+.
If an average sentence has 6.54 polysyllables, then SMOG is 17+. Unlike Gunning, McLaughlin counted every polysyllable in a sample of 30 sentences. We will count only the hard words in 16 sentences and fairly assume that if the average sentence has three hard words or more, then the frequency of gobbledygook is 17+.
Based on this assumption, the Fog Estimate = (H16 / 3). If a text has 15 hard words in 16 sentences, then anyone with five years of schooling may read it with ease. But if it has 51, then the Fog Estimate is 17+. This new derivation from the Fog Index, I dedicate to Robert Gunning and Harry McLaughlin.