---
title: "Bid-Shading Calculator"
category: Bidding
canonical: https://plato.ai/tools/bid-shading/
---

# Bid-Shading Calculator

What should you bid in a first-price lead auction to maximize expected profit, given what the lead is worth and how competitors bid?

Free interactive calculator at https://plato.ai/tools/bid-shading/ (runs in the browser).

## How it works

In a first-price auction you pay what you bid, so bidding your full valuation wins often but earns nothing when you win. This calculator finds the bid that maximizes expected profit per auction, given what a lead is worth to you and how high the strongest competing bid usually is. Use it to see how much to shade a bid, and how the answer moves when competition gets stronger or less predictable.

For every bid from $0 up to your valuation, the calculator multiplies the margin you keep when you win (value minus bid) by the chance that your bid beats the highest competing bid, and picks the bid where that product peaks. The highest competing bid is modelled as a normal distribution with the typical value and spread you set.

`Expected profit = (Value − Bid) × P(win at Bid), where P(win at Bid) = Φ((Bid − typical competing bid) ÷ spread) and Φ is the standard normal CDF`

## Frequently Asked Questions

### What is bid shading?
Bid shading is bidding less than your true valuation in a first-price auction, by an amount chosen to maximize expected profit given how likely each bid is to win.

### Should I shade bids in a second-price auction?
No. In a second-price auction you pay the second-highest bid, so bidding your true value is the best strategy. Shading only pays when you pay what you bid.

### Where do the competing-bid inputs come from?
From your own bid and win history at the exchange, plus any clearing prices it shares. The defaults ($60 valuation, competing bids around $40 give or take $10) are an example. Real systems estimate the win curve per segment and treat lost auctions as censored data, since you usually only learn that someone bid more.

### Why not always bid a fixed percentage of value?
Because the best discount depends on competition. Tightly clustered competing bids let you bid just above the pack, while stronger competition means you should shade less. Try moving the competing-bid sliders to see the optimal bid change.

## Read the article

[The Winner's Curse: Avoiding Overpayment in Lead Auctions](https://plato.ai/md/winners-curse-lead-auctions.md)