The correlation between the homicide rate and Brady score in all 51 jurisdictions is +.032 (on a scale of -1 to +1), which means that states with more gun restrictions on average have very slightly higher homicide rates, though the tendency is so small as to be essentially zero. (If you omit the fatal gun accident rates, then the correlation would be +.065, which would make the more gun-restricting states look slightly worse; but again, the correlation would be small enough to be essentially zero, given all the other possible sources of variation.) If we use the National Journal data (adding the columns for each state, counting 1 for each dark blue, which refers to broad restrictions, 0.5 for each light blue, which refers to medium restrictions, and 0 for each grey, which refers to no or light restrictions), the results are similar: +0.017 or +0.051 if one omits the fatal gun accident rates. You can also run the correlation yourself on my Excel spreadsheet.
Now of course this doesn’t prove that gun laws have no effect on total homicide rates. Correlation, especially between just two variables, doesn’t show causation.
Perhaps there are other confounding factors (such as demographics, economics, and so on). Perhaps even controlling for those factors, there will be other missing factors that are hard to control for — for instance, maybe as the crime rate increases, calls for gun controls increase, so high crime causes more gun restrictions, or maybe calls for more freedom to defend oneself increase, so high crime causes fewer gun restrictions (e.g., liberalized concealed-carry licensing rules). And of course when small changes in the model yield substantial changes in results (e.g., if you calculate the state gun scores differently, the results will likely be different), you know how little you should credit the output. Figuring out the actual effect of government actions, whether gun laws, changed policing rules, drug laws, or anything else, is devilishly difficult.
But since people have been talking about simple two-variable correlations between gun laws and crime, I thought it would be helpful to note this correlation — or, rather, absence of correlation.