A 2015 St. Louis Fed report referenced data from the energy information administration which found the following:
The EIA estimates that as much as two-thirds of the price of gasoline is due to crude oil and refinery costs. Crude oil is sold by the barrel. If nothing else changes, a $1 change in the price of a barrel of crude oil will result in approximately a 2.4-cent change in the price of a gallon of gasoline.
Even without these facts, one might reasonably guess there is clear and direct relationship between crude oil and gasoline. This report detailed just how much and in fact showed oil as the most significant factor affecting gasoline prices. The image below visualizes the breakdown of crude oil and gasoline prices (at the pump).
source: https://www.stlouisfed.org/publications/inside-the-vault/spring-2015/behind-the-signs
If we were to plot the spot prices of oil (WTI) versus gasoline (Gulf Coast), we would see this relationship is indeed correlated and holds quite well. The first chart shows the relationship over the past 30 years and the second chart shows the last 12 months.
Note: the charts below were created using Python and data sourced from the EIA
Crude VS Gasoline (Last 30 years)
Crude VS Gasoline (Last 12 months)
The last 12 months of data included Hurricane Harvey. Interestingly spot gasoline prices (more sensitive than futures prices) spiked during the hurricane (noted by the red line above) but quickly reverted back near the values preceding the hurricane. The unaccompanied rise of gasoline during the hurricane without crude oil following provided an opportunity to unload inventories of gasoline. This opportunity assumes of course that refineries were not damaged significantly enough to warrant the added input cost from oil to gasoline. Admittedly, this might be difficult given a lack of information during the storm but as the spread continued to move further apart, the probabilities of damage would have had to increase to warrant the extreme widening. If one could conclude the probabilities of a certain damage level were in fact not warranted, then a profit opportunity existed.
Another interesting observation from the 12 month chart is the following: as gasoline prices rose nearly 30%, crude prices dropped over this same period. Why? Were refineries "offline" and unwilling buyers? Perhaps. Or were traders of the crack spread who thought they were selling gasoline and buying oil at "good" levels, (perhaps over-weighting standard deviation risk measures and under-weighting the circumstances) pushed beyond their limits and forced to liquidate as the spread continued against them and thus perpetuating the move even further.
The previous charts showed spot prices which are more sensitive (volatile) and perhaps showed an opportunity which existed in the physical market but could not have been replicated with futures. To check, and show that the move was similar in the futures market as well, a front month oil-gasoline chart is shown below.
source: http://www.paragoninvestments.com/research/charts/custom-charts
To sum up, crude oil has been highly correlated to gasoline for the past 30 years (and in reality of course, even longer). Further, there are trading opportunities to be had from divergence in the spread price. And whether spread price extremes are caused by short term fundamental issues or by arbitrageurs getting squeezed beyond their pain threshold does not alter the fact that opportunities exist.
Finally one might want to model gasoline prices to predict the future without concern for the oil-gasoline spread. For this, a multiple regression model could be used utilizing crude oil, refining costs, geopolitical risks, weather, number cars on the road, fuel efficiency, etc. Once weights are found, predictive models of the inputs could be fed into the model and used to predict longer term trends (eg the effect of fuel economy on gasoline prices over the next 15 years).
It could also be used when a divergence in the spread exists to a) highlight the inputs from which the divergence is occurring and b) give higher probabilities (and thus confidence) that a spread should or should not be so wide, a useful measurement in energy trading.