Holy Shizzle and I thought this suggestion was going to be a simple one! (for TL;DR go to the summary at the bottom)

Pricing time, 1 exists.

Sale 1:

http://www.tf2outpost.com/trade/19502530 Offered for and sold for a Cloud 9 Cold killer (3-5 buds) plus small sweets (pink painted villians veil + pink painted birdman of alcatraz totalling ~2-3 keys worth, taken as 0.1 buds here)

Proof of offer: http://www.tf2outpost.com/trade/19353448

As the Baker boy was offered for the Cold killer rather than the other way around no overpay will be calculated

4.1 buds

Proof:

Buyers backpack before: http://backpack.tf/profiles/76561198045030062?time=1399359600 - Cold killer, veil and birdman all visible

Buyers backpack after: http://backpack.tf/profiles/76561198045030062?time=1399446000 Baker's visible, Cold killer, viel and birdman no longer in bp

Sale 2:

http://www.tf2outpost.com/trade/18943683 - Offered for and sold for a Spellbound Prince Tavish's Crown (4-4.7 buds) 4.35 and with a Smoking bonk boy (2.2 - 2.6 buds ) + ~ 8 keys ish (sweets)

Proof of offer: http://www.tf2outpost.com/trade/18958691

Again with this trade as it was the bakers that was offered rather than the other way around overpay will not be calculated.

4.35 + 2.4 + ~0.4 = 7.1 buds

Proof:

Buyers backpack before: http://backpack.tf/profiles/76561198047809145?time=1396594800

Buyers backpack after: http://backpack.tf/profiles/76561198047809145?time=1396767600

*Please Note*

In the offer the guy wanted the crown, bonk boy and smoking bakers, but in the history only the crown and bonk boy disappears. However in the before snapshot there was a bud, but after the bud is missing and 11 new keys are seen in the backpack. I checked the history for the bud and it was sold to a key trading bud bot. But it doesnt explain where the extra ~8 keys have gone, as it does not appear that 8 keys worth of items have been purchased with those keys. The other traders backpack isnt helpful either as he is a very active trader and evidence of any keys are not seen. My deduction therefore is that the trade wanted more than just the crown and the bonk boy, so he got the other guy to trade in his bud for keys (which at a month ago would roughly be 18-19 keys from a bot) of which he then kept 11 and used the other 7-8 keys in this trade. Therefore as it was not obvious exactly how many keys were used in this trade i am rounding down the final price of this trade from 7.15 to 7.1 as it is not clear how many keys the guy got from the bot, nor how many he used in the trade.

Sale 3:

http://www.tf2outpost.com/trade/18878039 Sold for a Scorching Bombing run (2.5 - 2.7 buds) + 1 bud pure

With overpay calculated: (2.6 * 0.9 ) + 1 = 3.3 buds

Proof:

Sellers backpack before: http://backpack.tf/profiles/76561198074431107?time=1396249200

Sellers backpack after: http://backpack.tf/profiles/76561198074431107?time=1396508400 - Bombing run +bud visible

Buyers backpack before: http://backpack.tf/profiles/76561198001880399?time=1396335600 - bombing run + bud visible

Buyers backpack after: http://backpack.tf/profiles/76561198001880399?time=1396453934 - bakers visible, bombing run +bud no longer in bp.

Sale 4:

http://www.tf2outpost.com/trade/16218067 - Straight swap with a terror watt Cold Killer (4 - 4.1)

As it cannot be determined who offered on who's trade (neither the bakers nor the cold killer had either trader post on it) i will not be applying overpay. 4.05 buds

Proof:

Buyer before: http://backpack.tf/profiles/76561198074431107?time=1395212400

Buyer after: http://backpack.tf/profiles/76561198074431107?time=1396249200

Seller before: http://backpack.tf/profiles/76561198071912427?time=1396076400

Seller after: http://backpack.tf/profiles/76561198071912427?time=1397286000

This seller was the unboxer, so no further trades can be found as this hat is 1 of 1 in existence.

Summary

One trade of 4.1 buds

One at 7.1 buds

One at 3.3 buds

Another one at around 4.05 buds (which i am going to round up for bp.tf site sake)

Conclusion:

Well, what to do about this hat? We have seen sales that are almost 4 buds apart with one at 3.3 and another at 7.1

Then we have 2 at 4.1 buds.

Seeing as the most recent trade was 4.1 buds (all the other three are over a month old) i am weighting this price the heaviest.

Therefore as there are 2 trades at 4.1 buds, i will rule the 3.3 bud and the 7.1 bud trade as outliers.

Hence: Set price to 4.1 buds

Comments, feedback and suggestions are always welcome.

:)