Regarding Dynocharts of stock bikes. I did a quick search. The first one that came up was a -16 with full Acra.
Here is the Dyno chart:
And the numbers:
So how much extra power does the Acra system add? A search at Acras own webpage gave the following values:
The links to where I found these pictures:
http://www.akrapovic.com/en/moto/product/13234/BMW/R-1200-GS-ADVENTURE/2016/Optional-Header-SS?segmentId=1&brandId=44&modelId=369&yearId=4008
https://www.youtube.com/watch?v=r_fCoVy1F00
As for the claimed variations that may improve the engine more or less, keep this in mind:
While there are variations, carburetor engines may have been jetted wrong, and ignition may be out. But on modern engines with digital engine management system, all parameters are based on engine Top Dead Center position. This sets the ignition and gives feedback for the fueling. The fueling is also kept within parameters based on feedback from the O2 sensor. This assures that the fueling and ignition is optimized, and there is not very much more you can do without messing with mechanical changes. Thus, claiming that the tweaked fueling gave an extra gain on a particular engine because it was out of parameters does not hold water. If the engine performs below standard, just tweaking the fueling will not be enough.
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Looking at the dynochart provided by gazuk shows a interesting point. Look at the AFR graphs. The graph shows a fairly well controlled fueling, which can only be achieved by using feedback from the lambda. Most likely HT tweaks the AFR and gets the same effect as the AF-XIED. Tweaking the ignition timing may make less sense, sins the engine management system already sets the ignition based on all available parameters.
As mentioned earlier, the stock fueling at WOT is fairly good, so extra fuel tweaking will not do very much on the Dyno. However, at powersettings at less than WOT, extra fuel will be noticed. Also, the extra midrange fuel will make the Adaptive map a bit richer, which will be noticed when you open up the throttle.