My first suggestion :S

Most of these things on Outpost have parts and/or Killstreaks on them, so a regular Strange Big Earner is not easy to come by.

Selling/Sold for 1.33 ref:

http://www.tf2outpost.com/trade/13654194 (Lots of adds for the Big Earner)

http://www.tf2outpost.com/trade/7043844 (Offers of 1.33 ref, and even 2 ref for it)

http://www.tf2outpost.com/trade/17637925 (Selling as a set, but was offered 1.33)

http://www.tf2outpost.com/trade/17638561 (Selling at current bp.tf price, 1.33 ref, but was offered 1.66 ref)

http://www.tf2outpost.com/trade/17636688 (Selling at current bp.tf price, 1.33)

http://www.tf2outpost.com/trade/17333626 (Offers of 1.33)

1.55 ref

http://www.tf2outpost.com/trade/15982306 (Sold 19 at 1.55, 3 for 1.66, and 1 for 2 ref)

1.66

http://www.tf2outpost.com/trade/17504468 (2 bookmarks, was offered 1.44 ref but retracted)

http://www.tf2outpost.com/trade/1813882 (Inactive trade, but received an offer of 1.66)

http://www.tf2outpost.com/trade/17690969 (My own trade; I already received an add for it and a trade offer of a Genuine Distinguished Rogue painted Australium Gold [all in less than 12 hours], worth around 2.77 ref or so counting the paint as half value ---> http://imgur.com/LAHdRnq )

1.77

http://www.tf2outpost.com/trade/16647059 (Rejected an offer of 1.44, and the Big Earner listed on his trade has been sold)

1.88

http://www.tf2outpost.com/trade/16468176 (Big Earner listed in the trade has been sold)

Classifieds

http://backpack.tf/classifieds/search/id/52c8aa924dd7b8de5c8b456d (Only 2 sellers for unmodified Strange Big Earners, the cheapest being 1.33 ref and the other one being 2.66 ref)

On account of my own Strange Big Earner, I found someone willing to 1:1 any of his cosmetics listed in his trade ( http://www.tf2outpost.com/trade/17675754 ) for a S. Big Earner, so I then traded it for an Anger, worth 3.33 ref on bp.tf ---> http://imgur.com/Vt6Eobc

Conclusion

Not many sellers out there with unmodified Strange Big Earners. There are still sellers and buyers at 1.33 ref out there, but buyers seem to be willing to cough up 1.66 ref if necessary. Sales at above 1.66 ref are also possible but do not get offered as much by buyers as 1.66 does, and thus, should be excluded from the range for now.

Again, this is my first suggestion, so please leave any constructive criticism to help me improve.

To address the issue of inadequate 1.66 proof, here are some more 1.66 sales (taken from previous suggestions)

http://www.tf2outpost.com/trade/16430931

http://i.imgur.com/xXCGlZb.png

http://i.imgur.com/H8mTjPi.png (Worth 1.66 on bp.tf)

http://i.imgur.com/gPG8QHK.png (Worth 1.66 on bp.tf without paint)