I use to follow the theory that a clean bore is an accurate bore. Lately every thing I put together produces good results. I will clean my rifle before I go to the range and just starting shooting groups. Fouler shots aren't necessary in my opinion after experiencing same accuracy with or without a fouler. Each barrel is different, but consistency in regiment helps to produce consistent results. The bigger factor is allowing your barrel to stay at a consistent as close to a consistent temperature from shot to shot.
I do not clean between groups because there should be no need to. It usually rakes at least one fowler after cleaning to settle down a bullet and sometimes more. In my factory barrels it usually takes abot 3-4 fouler to settle down a barrela nd then they are good for 50- 70 rounds before they need another cleaning.