It is disgustingly simple (though not as simple as looking at average runs scored per game).
We want to look at what the average winning percentage in baseball during any single year (from 1901 to the present) when the team scores four runs or less.
The higher the aggregate WPCT, the lower the run scoring basis for the league is in that given year. The opposite applies as well: the higher the runs scoring, the lower the aggregate WPCT.
The "normal operating range" for this value is between 275 and .325, with occasional spikes of deadball-style performance (remember, it's an inverse relationship, so we're looking at above .325 WPCT years--with 1968 sticking out as the year of years...in case you're wondering, that's a .362 WPCT for games with 4- runs scored) and extra-lively performance (the 20s and 30s, the 90s and the 00s).
As the chart shows us, the recent reversal began in 2008, and the increase from 2009 to 2010 was actually about twice as much (.020) as the increase between 2010 and this year (thus far).
We'll look at the percentages of games in the 4- runs bucket and the 5+ runs bucket soon, but for now realize that in terms of effective run scoring, offense is simply getting back into line with the historical average (teams win just a shade under 30% of the time when they score four runs or less).