Bid strategy and risk pricing

Two contractors can price the same project with the same cost estimate and still submit very different bids, because the final markup is a strategic decision. Bid too high and the firm loses; bid too low and it wins work that earns nothing or loses money. This lesson looks at the decision from several angles: the winner's curse, simple probabilistic bidding models that use the firm's bid history, the explicit pricing of identified risks, the number of competitors, and unit price strategies such as unbalancing, including where they cross from clever into improper. The models are aids to judgment, not substitutes for it.

The winner's curse

Every estimate contains errors. Some items are overestimated and some underestimated, and on a given project a firm's total estimate may be a few percent high or low compared with what the work will actually cost. When several contractors bid, the one whose estimate is most underestimated is the most likely to be low. Winning therefore tends to select the bids with the largest underestimates, a phenomenon called the winner's curse. The more bidders there are, and the larger the estimating uncertainty, the stronger the effect.

The practical lesson is that a firm's expected profit on the jobs it wins is lower than the markup it adds, on average, unless its estimates are unusually accurate. Firms counter the winner's curse by improving estimate accuracy (better takeoff, leveling and review), bidding fewer projects with more care, investigating large gaps between their bid and the next one (Lesson 10), and adding somewhat more markup when the field is large and uncertainty is high.

import random, statistics
random.seed(7)
# True cost 10.0 ($M); each bidder's estimate has a random error (SD 4 %); all add 5 % markup
true_cost, sd, markup = 10.0, 0.04, 0.05
for n in (2, 4, 8, 12):
    profits = []
    for _ in range(20_000):
        bids = [true_cost * random.gauss(1, sd) * (1 + markup) for _ in range(n)]
        profits.append((min(bids) - true_cost) / true_cost)
    print(f"{n:2d} bidders: average realized margin on cost of the winner "
          f"{statistics.mean(profits):+.1%}")

 2 bidders: average realized margin on cost of the winner +2.6%
 4 bidders: average realized margin on cost of the winner +0.7%
 8 bidders: average realized margin on cost of the winner -1.0%
12 bidders: average realized margin on cost of the winner -1.8%

In this simulation every bidder intends a 5 % markup, but the winner's realized profit shrinks as the number of bidders grows, and with many bidders the average winner loses money. Real bidders differ in efficiency and markup as well as in estimating error, but the pattern is robust and matches the experience of many contractors in crowded markets.

Probabilistic bidding models

If a contractor keeps a history of its own cost estimates and its competitors' bids, it can estimate the probability that a bid at a given markup would have been lower than each competitor's. A classic approach, associated with Lawrence Friedman's work in the 1950s, records for each past bid the ratio of a competitor's bid to the firm's own estimated cost. The distribution of these ratios shows how often the competitor bid above any given markup. The probability of beating that competitor at markup m is the share of past ratios greater than 1 + m. Assuming competitors bid independently, the probability of beating all of them is the product of the individual probabilities.

Expected profit is the markup times the cost times the probability of winning. At a low markup the firm wins often but earns little; at a high markup it earns a lot when it wins but rarely wins. The markup that maximizes expected profit lies in between. Other models, such as one proposed by Marvin Gates, combine the competitors' probabilities differently, and modern approaches use regression or machine learning on larger datasets, but the logic is the same.

import random
random.seed(11)
# Bid history: ratios of three known competitors' bids to Northline's estimated cost
history = {
    "Competitor A": [random.gauss(1.075, 0.045) for _ in range(30)],
    "Competitor B": [random.gauss(1.090, 0.055) for _ in range(25)],
    "Competitor C": [random.gauss(1.060, 0.040) for _ in range(18)],
}
cost = 12_000_000
best = None
for pct in range(0, 16, 1):
    m = pct / 100
    p = 1.0
    for ratios in history.values():
        p *= sum(r > 1 + m for r in ratios) / len(ratios)
    ev = m * cost * p
    if best is None or ev > best[2]:
        best = (m, p, ev)
    if pct % 2 == 0:
        print(f"markup {pct:2d} %: P(win) {p:5.2f}  expected profit ${ev:>9,.0f}")
print(f"Best markup about {best[0]:.0%} (P(win) {best[1]:.2f}, expected profit ${best[2]:,.0f})")

markup  0 %: P(win)  0.97  expected profit $        0
markup  2 %: P(win)  0.72  expected profit $  172,871
markup  4 %: P(win)  0.54  expected profit $  257,600
markup  6 %: P(win)  0.34  expected profit $  241,920
markup  8 %: P(win)  0.12  expected profit $  119,467
markup 10 %: P(win)  0.01  expected profit $   16,000
markup 12 %: P(win)  0.00  expected profit $    3,413
markup 14 %: P(win)  0.00  expected profit $        0
Best markup about 4% (P(win) 0.54, expected profit $257,600)

The model suggests a markup around the point where expected profit peaks. It ignores many things: whether the competitors will actually bid this project, their current workload, the firm's own need for work, the risk profile of this particular project and the strategic value of winning. It also relies on reasonably large, comparable histories, which few firms have for every competitor. Its value is in disciplining the conversation: a firm that habitually bids at a markup with a very low probability of winning, or one that wins almost everything at thin margins, can see it in the numbers.

Pricing identified risks

Markup is not the only place where risk belongs. Many risks can be identified during the bid and priced explicitly: an aggressive schedule with liquidated damages, a soils report that hints at rock or groundwater, a design that is visibly incomplete in one area, an owner with a history of slow payment, a key subcontractor with limited capacity. A risk register lists each risk with an estimated probability and cost impact. The expected value of each risk (probability times impact) gives a starting point for a risk allowance, and the register shows management where the bid is exposed. CON-350 covers risk management, insurance and bonding in depth; here the focus is on how risk enters the price.

Expected values are a starting point, not a final answer. A firm with limited financial capacity may price large, low-probability risks more heavily because one occurrence could be ruinous. A risk that can be transferred (to a subcontractor through its quote, to an insurer through a policy) or reduced (by a different method or schedule) may need little or no allowance. Risks that remain are either priced explicitly, covered by contingency (Lesson 9) or reflected in the markup. The key is to avoid both double counting (pricing the same risk in contingency and markup) and silent omission.

Competition and the number of bidders

Bid results from public tenders consistently show that the low bid falls, relative to the owner's estimate, as the number of bidders rises. With two or three bidders the low bid is often close to or above the estimate; with eight or ten it is often well below. Contractors use this when deciding both whether to bid (Lesson 1) and how much markup to carry. Information about who obtained documents, who attended the site meeting and which competitors are currently busy or hungry all feeds into the final markup decision. Collusion is illegal (Lesson 1), but intelligence gathered lawfully about the market is part of good bidding.

Unit prices and unbalanced bids

On unit price contracts, the total bid is the sum of each unit price times the owner's estimated quantity, but payment depends on actual quantities. A bidder that believes some quantities are underestimated can raise their unit prices and lower others, keeping the total competitive while increasing revenue if its belief is correct. Raising the prices of items performed early (such as mobilization or excavation) and lowering later items front-loads cash flow. Both are forms of unbalanced bidding.

Owners guard against unbalanced bids. The FAR distinguishes a bid that is mathematically unbalanced (some prices significantly overstated or understated relative to cost) from one that is materially unbalanced (where there is reasonable doubt that award will result in the lowest overall cost to the government, or the bid is so front-loaded it amounts to an advance payment); a materially unbalanced bid may be rejected. State transportation agencies apply similar rules. Front-loading a lump sum contract's schedule of values for cash flow is a related practice; owners and architects reviewing pay applications usually require a schedule of values that reflects the real value of the work.

Estimators should understand unbalancing because they will encounter it from both sides: as bidders deciding how to set unit prices, and as general contractors leveling unit-price quotes from subcontractors. A modest, defensible adjustment based on a genuine view of quantities is common; extreme unbalancing that could not be justified by cost invites rejection, disputes and reputational damage.

Putting the decision together

On bid day, the final markup decision combines several inputs: the firm's target margin for the type of work, the bidding model or bid history, the risk register and contingency, intelligence about competitors, the firm's current backlog and capacity, and the strategic value of the project. Many firms use a short bid review meeting with a standard agenda so that these inputs are discussed every time. Recording the reasoning makes it possible to learn from results: if the firm loses repeatedly by small margins with a particular competitor, or wins and then loses money on a particular type of project, the record shows where the strategy needs to change.