In short
Looking at the genetic code, it appears that most redundancy is on the third letter rather than on the first or the second letter of the codon. Why has it evolved this way?
Longer version
In order to compare the relative redundancy accounted by each letter of the codon, let's assume that that every codon occurs at equal frequency. It is probably wrong but useful for the sake of the calculations. Using observed frequencies of codon usage in a given population would change the following probabilities but the question of why some positions in the codon has more redundancy than some others still hold.
A substitution of the first letter of the codon has a probability of $\frac{1}{2048}≈0.00005$ (Stop codon) to be synonymous. A substitution of the second letter of the codon has a probability $\frac{3}{256}≈0.012$ (nucleobases U and G) to be synonymous. A substitution of the third letter has a probability of exactly $\frac{2}{3}$ to be synonymous.
Probability of a substitution to be synonymous given that it occurred on the...
- First letter: $\frac{1}{2048}≈0.00005$
- Second letter: $\frac{3}{256}≈0.012$
- Third letter: $\frac{2}{3}$
Why are there more redundancy on the third position than on the second (which has more redundancy than the first position) in the codon?