That's a question I've asked myself a few months back.
What is your trading style, what do you do ?
My main strategy is to do intraday trend-following and when I look at 40 years of data, trade my strategy every day, or trade it every day at the exception of days that are inventory days, I have the same results, roughly. So for my trading style, on average over a long period of time, inventory day is traded as business as usual.
I typically am very cautious on report days as any surprises can send prices skyrocketing or dropping like a rock.
Usually you'll see market movement in the days leading up to the market report as to what the report is "expected" to say.
In other words, if traders are expecting a bullish report, you'll see prices moving up prior to the report date. But, if the report turns on to be bearish or not as bullish - not what was expected, then this is when we can see big price moves.
Just be careful trading on report days is the best advice I can give. Use stops and/or futures options to minimize risk.