In my opinion, you can only really do this in macro-global type positions ( such as currencies ). Soros has had great success doing this over the years . . . But then again, his bets are truly fundamental in nature and not all that frequent.
You guys have it all WRONG There is NO difference between averaging up or down. The ONLY difference that exists is between averaging up and down WITH the trend or COUNTERtrend. The last one is the hardest to do.
Nice post! I don't think that a strong trend can be anticipated. I always enter half size and hope that this trade will turn out to be a strong winner that I can add to several times along the way. There was a FTSE trade in 2008 that stood out for me, I managed to capture 300+ points over a 5 day move while adding 5 times along the way. It makes sense, have a small size on the average trade, but have much more size on the big winners. One way to be bigger on your big winners in day trading is to go big at the beginning and scale out as it goes against you. If you drop half of yor size and it turns around and goes back in your direction you can always put that half back on.
IMHO averaging up is a great way to approach trading. It's not the holy grail though. Your bottom line will depend far more on your discipline and position sizing than anything else.