I don't know the exact numbers they use for their statistics (I think it used to be 1 minute).
If a train is delayed by 10 minutes you can ask for a ticket to take to work to show your boss that being late was not your fault.
Don't get me wrong, the punctuality is much better than most European countries I have lived in and quite a lot of the time the are perfectly on time, but the west has raised the Japanese public transport system to near mythical status.
In August 2012, 99.1% of all stops happened within fifteen minutes of the scheduled time, 94.2% happened within five minutes. Looking only at long-distance trains, 75.8% of all stops where reached within five minutes of the scheduled time and 90.5% of all stops were reached within fifteen minutes of the scheduled time.
You might be using a train connection that – for whatever reason (construction work, etc.) – is consistently late. Sucks for you, doesn’t mean train in Germany are in general late. Most are on time.
Every 10th train was late for more than >15min.
Yes, Regios may be better. That doesn't help when, for example, you need to catch a plane in a different city.
Local trains are more prone to delays, for example the Yamanote line in Tokyo being the most notorious due to ahem, being the preferred line used by Tokyoites to say bye-bye to this world.
For local city train lines a delay of more than 5 minutes will result in the driver profusely apologizing on and on, and the line to start issuing "certificates" that people can get to show their employers blaming the lateness on the train line.
Leaving 6 minutes (let alone 11) later than the schedule is definitely considered late. If you're changing lines, which in practice most people have to do when commuting in Tokyo, a 5 minute delay can result in an even bigger total delay (e.g. if the next train you take is an express one, and it comes every 15min).
Delays longer than that are usually due to bodily accidents which is an euphemism for "someone just jumped in the tracks", and typhoons and other natural accidents. The former is more common.
What I found more amazing when I fist came is that buses also come on time! Although of course short delays are more common than with trains, they're pretty much on schedule. The flip side is that they run very slowly and stop every other block. When I used to commute by bike I often kept up with buses for long stretches.
For trains like JR that run longer distances and less frequently, delays of 15-20 minutes due to accidents or weather can happen. This seems to happen once every few months or so.