I think I can safely say that nobody understands quantum mechanics. Bullet mechanics? Well now that's a different thing entirely.

Sale #1:

http://www.tf2outpost.com/trade/23938611 - 1:1 with a Miami Nights Professor's Panama(1.8 x 0.9 = 1.6 buds)

History of Panama: http://www.tf2outpost.com/item/440,3265349735,109,5

History of Professor's: http://www.tf2outpost.com/item/440,3220336598,384,5

Sale #2:

http://www.tf2outpost.com/trade/24033865 - 1:1 with a Purple Energy Football Helm, Pecularity added 25 refined, 1 TOD ticket and 1 Antarctic Parka. Sale was on December 7th, 2014. (13.25 keys = 1 bud)(12.66 refined = 1 key)(1 TOD ticket = 5.66 refined)

Actual trade: http://i.gyazo.com/88782920336f0fb07f67d55435033da7.png

Effect of Football Helm: http://i.gyazo.com/15123b81b6284001b3729e99926b3d60.png

Effect of Pecularity: http://i.gyazo.com/03bc49181d4bd5be02e5dc49d315eddb.png

Math: x = Football Helm(1.3 * 0.9 = 1.2) - sweets(0.3) = 0.9 ~1 bud

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Mini for the Football helm:

http://www.tf2outpost.com/trade/23739437 - Sold along side a Peace Sign Billy Cock + 4 keys + Black Rail Spikes(1.2 keys) + 10.66 refined + 1x Ye Ole Rustic Color for a Strange Ace's High Bonk Boy. Sale was on November 22nd, 2014. (15.25 keys = 1 bud)(10.88 refined = 1 key)

Actual Trade: http://i.gyazo.com/f18a16a32a76a39c3f4c7eead1787684.png

Effect of Bonk Boy: http://i.gyazo.com/0904cc2507cd80726dd8748e964be6e0.png

Effect of Billy Cock: http://i.gyazo.com/697bc7bef0bbdeb91ef0cb5f9fd86a17.png

Effect of Football Helm: http://i.gyazo.com/04829730b2fcb0420350008f9cd23cd3.png

Math: Bonk boy(2.9 buds) = Football Helm( x ) + Billy Cock(1.2 buds) + Sweets(0.4 buds)

2.9 = 1.6 + x

x = 1.3 buds

Thank you, have a nice day!