Hey, my apologies if I've come a little late to the party, but today I got the (crazy) idea to try and find out some maximum values for the four TF2 familiars and the Aperture Science HPD. These are the bonus items that can be found in the Tavern and are one-of-a-kind (unless you can trade with someone else for another one or buy one from them). Unfortunately, despite being interested in a lot of geeky computer stuff, having dabbled in 3 different languages, being a fairly proficient macro/script writer and having a beginning of an understanding about a computer's memory, I couldn't grasp a single thing about what people said regarding the modding tools - actually, I couldn't even find the EXE file to run them. So, I just did it the old fashioned way: deleted my save files, started a new file, broke the crates, checked the items, then started again. I did this for something over 3 hours and got around 150 tests in, and I found out some pretty interesting stuff regarding how the game generates (at least these) items.
First of all, I'll post the data for each of the familiars. It's not pretty or anything so please bear with me. Heavy
Hero ATK: 15, 16, 18-23
Max Levels: 20-29
Best actual drop I got: 23 / 18 / 29 Pyro
Tower ATK: 15, 18-23
Max Levels: 20-28
Best actual drop I got: 20 / 18 / 28 Medic
Hero HP: 13, 18-23
Max Levels: 20-28
Best actual drop I got: 6 / 18 / 28 Engineer
Tower HP: 13-23
Max Levels: 20-28
Best actual drop I got: 22 / 19 / 28
The familiars are where the really interesting info is in this research. First of all, it was apparent to me for most of the process that the ATK was dependent upon the familiar, the bonus stat was always 13-23, and the levels were 20-28. What I also learned is that, barring a few exceptions (that I think I'm still missing values for), there is always a median that is exactly between the lowest value and the highest value (which means there's always an odd number of values). 13-23 does this with 18 and 20-28 does this with 24. The ATK values also do this, except for the Medic and the Engineer, and I think I just didn't find all their values.
The median is significant when dealing with Bonus Stat randomization because (in the case of these items, at least) it makes a cut-off point so that everything below the median is very hard to get (so you're far less likely to get crappy items). If you look at those values for each familiar, I always had 18-23 (18 being the median), but only on the Engineer did I get everything below 18, and on the others I only got a few values under. I got 18-23 very consistently. While 23 is rare, 13 is extremely rare and I only ever saw it twice. This use of the median also worked with the HPD's Ammo stat (or at least I think it was Ammo, I didn't actually pay attention to what it was!), which you'll see later. All this didn't apply to the ATK value though, and those were very frequently at their lowest, and not too occasionally at their highest.
For a while, I had it dialed in to where the familiar's max ATK value, median Stat Bonus value, and (of course) Max Level value were the best combination I could find; I found a couple of these combinations more than once for specific items. My best Engineer find kind of threw it off (especially since I don't have an exact median for its Stat Bonus value), and then, on what I ended up making my last run, the Heavy popped up with a 29 Max Level, the first I'd seen, with lowest ATK and median Stat Bonus. I made sure to take a screenshot of it; you can see it here. I swear that none of these are hacked. I spent some time on this and I'm interested in actually knowing true stuff about this game, because I love it!
Anyway, I'll post results for the gun now. Aperture Science HPD
Ammo: 115, 116, 121, 122, 129, 138, 140-152, 154-161
Hero HP: 3-6
Hero SPD: 4-6
Hero ATK: 2-6
Hero CR: 4-6
Tower HP: 4-6
Tower FR: 4-6
Tower ATK: 2-6
Tower RNG: 2, 4-6
Max Levels: 12-26
Best actual drop I got: 112 / 159 / 6 / 4 / 6 / 4 / 4 / 4 / 6 / 4 / 26
That was a really sick drop. Didn't quite max the Ammo, but I had three 6s in Stat Bonuses and (of course) the highest Max Levels. Again, the Ammo stat rarely made it under the median, which I believe to be 138, and I'm missing quite a few values below that point. With so many stats though, this gun is VERY variable. Also, it's not a guarantee that everything will "add up". The stats do seem to be bounded to each other in an interesting way - I don't think I'll ever see an item drop with max everything even when it has as few possibilities as the Medic - but at the same time, you don't always get as good a deal as other times. One time, I got a 112 / 155 / 4 / 4 / 4 / 4 / 4 / 5 / 4 / 5 / 26 HPD, which is basically less of everything; less ammo, less 5s than 6s and no 6s. I also got some pretty weak Heavy drops before the 29er. So, it's strange and, ultimately, pretty random how it works, but I think I learned some interesting stuff and I thought I would share it, even if it might be rendered inaccurate in a later patch (I used 7.12b by the way). Maybe there's something to learn from this data... or maybe it's just a fun read and not really worth too much in the end.
If anyone wants to continue this with better tools at their disposal, I'd be interested to see what results they get. I never did get the Medic and the Engineer to give me an exact median for the Bonus Stats...