By the PNT the average gap is approximately the size of the logarithm of one of the primes. However, on one hand Cràmer conjectured $$ p_{n+1}-p_n<\log^2p_n$$and on the other hand there's the twin prime conjecture.
Let $$A_m=\left\lvert\{n\le m: p_{n+1}-p_n>\log p_n\}\right\rvert$$ and $$B_m=\left\lvert\{n\le m: p_{n+1}-p_n<\log p_n\}\right\rvert.$$ Is $\liminf\limits_{m\to\infty} \frac{A_m}{B_m}$ known?
Some exploration on primes up to $10$ million:
gaps $q-p>\ln(q)$: $253517 $
gaps $q-p<\ln(q)$: $411061 $
The graph of $\frac{q-p}{\ln q}$ against $q$ is a little misleading because the smaller gaps are all concentrated into distinct value lines so appear to take up less space on the graph: