Statistical Analyses of Bids for Federal Offshore Leases
Authors: Dougherty E.L. , Lohrenz J. 
Published: December 2007

Statistical analysis of bids for federal offshore leases shows that the relative magnitude of the high bid and the amount of "money left on the table" each varies with number of bids in a way that is predictable. Joint bidders tend to bid on more sought-after leases and tend to bid higher than their solo-bidding competitors.

Introduction
Offshore bidding is big business. Since the first sale was held on Oct. 13, 1954, the total of bonuses paid to the federal government through 1974 exceeds $14 billion. This huge amount of money was spent as the result of bids prepared and submitted by the managements of prepared and submitted by the managements of companies desiring to produce oil and gas from the tracts offered for lease. The submitter of the competitively highest bid received the lease and the opportunity to find and produce oil and gas therefrom.
Both the management and those who prepare bids for companies and the federal government as "owner" of the leases have a cogent interest in bidding behavior, each from their point of view. Further, the public also has a real interest because a substantial part of the oil and gas used by the public is derived from the leases - and the $14 billion spent for the leases.
The fact that bids for an individual offshore lease are distributed lognormally has been observed many times. In light of the great uncertainty in estimating physical parameters from exploratory measurements and physical parameters from exploratory measurements and of the multiplicative process used to decide upon bids, the observed distribution of bids is to be expected based on the central-limit theorem. Furthermore, previous analyses have indicated that the observed bid distribution is consistent with the hypothesis that, in any given sale, all bids are drawn from a lognormal distribution with the same standard deviation.
We accepted these results as a starting point for our analyses; the consistency of our results confirms the adequacy of these statistical postulates. In our analyses we considered all leases issued to competitive bonus bids through 1974. Our analyses consisted of four major parts:We first determined the standard deviation of the logarithms of bids for all sales. We found that by deleting abnormally low bids we obtained a consistent pattern of results and that no significant time trend in the standard deviation of bids by sale was indicated.We analyzed the manner in which the high bid relative to the mean bid on a tract varied with number of bidders, nl. We concluded that observed behavior is consistent with the hypothesis that the high bid is the largest value of a random sample of size nl drawn from a population whose mean is that for the lease and whose population whose mean is that for the lease and whose variance is that for the sale.We analyzed the way in which "money left on the table" varies with number of bidders, nl. We concluded that observed behavior is consistent with the hypothesis that the highest and second highest bids are the largest and second largest values of a random sample of size nl drawn from the bid population.We compared solo bids with joint bids and concluded that joint bidders tend to bid on more sought-after (and, apparently, more valuable) leases and that they tend to bid higher, on the average, than their solo-bidding competitors.

Standard Deviation of Bids by Sale
Our examination of historical bids revealed that inordinately low bids have been submitted occasionally, possibly with less than normal technical evaluation. possibly with less than normal technical evaluation. JPT