I have been fascinated, even inspired, by three readability formulae: SMOG Grading of Harry McLaughlin, Easy Listening Formula of Irving Fang and the FORCAST formula of FORd, CAylor and STicht. All these are single-factor formulae. Interestingly, none of them are based on sentence length, considered to be a key indicator of text difficulty.
To calculate SMOG (smoke-plus-fog as well as Simple Measure Of Gobbledygook), one needs a long sample of 30 sentences — the first 10 from the beginning of a text; the last 10 from the end; and the rest from the middle. If P is the number of polysyllabic words in the sample, then SMOG Grading = (square root of P) + 3.
The Easy Listening Formula (ELF) counts every syllable more than one per word in a sentence. That is, if W is the number of words and S the number of syllables in a sentence, then ELF = S – W.
The FORCAST formula needs a sample of 150 words. If N is the number of monosyllabic words in the sample, then grade level = 20 – (N/10).
Now, let us apply these formulae on a sentence from Martin Gardner’s ‘Mathematical Puzzles And Diversions’: “Flexagons are paper polygons, folded from straight or crooked strips of paper, which have the fascinating property of changing their faces when they are ‘flexed’.” Applying the ELF to this one-sentence sample is simple, but we need to suitably adapt the other two formulae that require a longer sample.
Since there are 4 polysyllabic words in this sentence, one may expect 4 * 30 = 120 long words in 30 sentences. Therefore, SMOG Grading = (square root of 120) + 3 = 10.95 + 3 = 13.95.
The sample contains 25 words and 40 syllables. Hence, ELF = 40 – 25 = 15.
For the FORCAST formula, let us consider only the first 15 words of the sample: “Flexagons are paper polygons, folded from straight or crooked strips of paper, which have the …” Since there are 9 monosyllabic words in a sample of 15 words, one may expect 9 * 10 = 90 monosyllabic words in a sample of 150 words. Therefore, grade level = 20 – (90/10) = 20 – 9 = 11. In short, if N is the number of monosyllabic words in a sample of 15 words, then grade level = 20 – N.
Our sample sentence has yielded different results: 13.95 (SMOG), 15 (ELF) and 11 (FORCAST). This cannot be helped because each of the formulae used a different indicator of text difficulty. Instead of asking which is right, we may simply calculate the average. This works out to 13.31. And that, we shall say, is the grade level of Gardner’s flexagonal sentence.