A somewhat philosophical and mathematical observation about auctions. Let’s start with a few premises:

We are considering the selling at auction of one (1) item

By definition, Alpha is a bidder willing to pay more than anyone else, anywhere, for this one item. Beta is the runner-up bidder, willing to pay more than anyone else, anywhere, except for Alpha

Anytime an auctioneer is selling 1 item, or any item, the last two bidders are the only two bidders needed — as they are, by definition, the final bidder and the bidder just before. If they are Alpha and Beta, no other bidders, anywhere, would be needed

If there are other bidders present, such as Theta, Gamma, Delta, Omicron, etc., they really are unnecessary, as Alpha and Beta want this item more than any of them do

No matter if we had just Alpha and Beta, or Alpha and Beta and 10,000 other bidders, the price would end up the same

As I write this article, there are approximately 6.8 billion people on earth. If an auctioneer is selling this one item at auction, and has all 6.8 billion people online, in the crowd, on the phone, or with absentee bid in hand — Alpha will buy the item, and Beta will be the bidder on just before Alpha outbids him a final time.

That is our premise.

I have stated publicly for decades that the more people in attendance at an auction, the more money that will be produced. While I maintain this is true, another way to say it, for one item, is “the more people in attendance, the more likely Alpha and Beta will be there.”

Let’s use an example:

We’re selling a rare 13th Century Ceramic Mask. Dr. Alfred Lindsey is the foremost collector on earth of such items, and Prof. Bentley Garrett is probably the second-most avid collector. Many consider them, together, the foremost collectors of such items on earth.

It appears that Dr. Lindsey has a bit more resources available, and a bit more interest than Prof. Garrett, and so we believe that Dr. Lindsey is indeed Alpha and Prof. Garrett is Beta.

We hold our auction and Dr. Lindsey and Prof. Garrett are both present, either online, in the crowd, on the phone, or otherwise. I think it would be fair to say that upon, “Sold!” that the true maximum value of this mask would be obtained. We base that conclusion on the premise that something is worth only what someone else is willing to pay for it — and that if we have Alpha and Beta competing to purchase this item — we have maximized market price.

What are all auctioneers looking for? Alpha and Beta.

Let’s use another example:

We’re selling a box of various older kitchen utensils including a 1940’s spatula and a green handled potato masher. Karen collects these types of kitchen items, and has the bid at $10; Ralph also collects these types of items, and bids $11. Karen, nor anyone else bids again, and Ralph buys this box for $11.

Yes, there are probably other collectors of these types of kitchen items around the globe. Yet, it’s likely nobody would have bid over $11 for these, considering their quantity, age and condition. Could we conclude Ralph was Alpha and Karen was Beta that day, at that time? Quite possibly.

What are all auctioneers looking for? Alpha and Beta.

As auctioneers look out over their crowds at a live auction, or review the number of bidders signed up to bid online, or the number of absentee bids placed, or the number of phones at the ready for phone bidding — the question remains — are Alpha and Beta participating?

Our mathematical analysis suggests that we can assign a probability to the chances that Alpha and Beta are present, dependent upon the number of bidders.

Certainly it could be argued that in this day and age, every auction everywhere that is findable online has the potential to find Alpha and Beta. Or, certainly, any auction that is advertised online has the potential to be found by Alpha and Beta.

Why do we care about the probability of having Alpha’s and Beta’s attention? Because it requires resources to publicize any auction. For this one item, does it make sense to hold only live bidding with absentee and phone bidding available, or does it make more sense to allow Internet bidding?

Should we mail out to all collectors in the United States?

Should we mail to all collectors on earth?

Should we run full-page ads in all newspapers in the northern hemisphere?

Should we run television advertisements during the Super Bowl, and other highly-watched shows?

Should we hire a company to put our auction advertisement on a blimp and have that airship circle the earth?

In other words, where is the *point of diminishing returns* where one more bidder doesn’t materially increase the odds of getting Alpha and Beta to participate?

Here’s my suggestion of the formula for one item:B = number of bidders X = chances of having Alpha and Beta present

X = [[[(2*B)/(B+1)]-1]*min{B,1}]^2

Some sample results:B = 0, X = 0 (No bidders, chances of Alpha and Beta are 0) B = 1, X = 0 (Only 1 bidder, chances of Alpha and Beta are 0) B = 2, X = 11% (2 bidders, 11% chance they are Alpha and Beta) B = 3, X = 25% (3 bidders, 25% chance two are Alpha and Beta) B = 4, X = 36% (4 bidders, 36% chance two are Alpha and Beta) B = 5, X = 44% (5 bidders, 44% chance two are Alpha and Beta) B = 6, X = 51% (6 bidders, 51% chance two are Alpha and Beta) B = 7, X = 56% (7 bidders, 56% chance two are Alpha and Beta) B = 8, X = 60% (8 bidders, 60% chance two are Alpha and Beta) B = 9, X = 64% (9 bidders, 64% chance two are Alpha and Beta) B = 15, X = 77% (15 bidders, 77% chance two are Alpha and Beta) B = 25, X = 85% (25 bidders, 85% chance two are Alpha and Beta) B = 50, X = 92% (50 bidders, 92% chance two are Alpha and Beta) B = 100, X = 96% (100 bidders, 96% chance two are Alpha and Beta)

and so forth.

What does all this mean?

The more bidders, the better. However, there reaches a point where for any one item, the chances of having Alpha and Beta bidding on that item, at that point in time, is not materially increased by having an additional 1 bidder, 10 bidders, 100 bidders, 200 bidders, or even 1,000 bidders.

Auction marketing costs money — including our own time. The point of this article is that at some point, additional publicity and/or marketing becomes not prudent — because the cost of that additional bidder is more than the increased return from their participation.

Because, all we want is Alpha and Beta. In fact, all we need is Alpha and Beta.

*Mike Brandly, Auctioneer, CAI, AARE has been an auctioneer and certified appraiser for over 30 years. His company’s auctions are located at: **Mike Brandly, Auctioneer**, **Keller Williams Auctions** and **Goodwill Columbus Car Auction**. His Facebook page is: **www.face book.com/mbauctioneer**. He is Executive Director of **The Ohio Auction School**.*

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