Auction Theory and Bidding Strategy: How I Optimise Paid Media Spend with Maths

Introduction: Paid Media Is a Market, Not a Menu

Most advertisers treat paid media as a price list. They assume that if they increase their budget, or raise their bids, they will get more traffic. But ad platforms like Google Ads and Microsoft Advertising are not stores, they are auction based marketplaces. Every impression is bid for. Every click is won or lost based on algorithmic competition.

To win more effectively, you need more than budget. You need to understand the auction. In this article, I explain how I apply auction theory, from second price mechanics to reserve pricing and bidder strategy, to improve paid media performance across ecommerce and SaaS accounts. This is not theory for theory's sake. It is how I get more reach, lower cost per acquisition, and better return on ad spend without simply spending more.

Understanding Second Price Auctions

Most major ad platforms, including Google and Microsoft, operate on a second price auction model. This means:

You do not pay what you bid, you pay just above the next highest eligible bid.

If you bid £4.00 and your nearest competitor bids £3.10, you might pay £3.11 (subject to quality score and ad rank modifiers).

This encourages truthful bidding, since overbidding does not increase cost unless others bid higher. But it also means that strategic positioning, where you appear and how your ad ranks, depends on factors other than raw bid.

The Second Price Formula

Let $b_1$ be your bid, and $b_2$ the second highest bid. In a basic second price model:

$$p = b_2 + \varepsilon$$

Where $\varepsilon$ is the platform defined increment.

On Google, this price is also influenced by ad quality, which leads us to:

$$\text{Ad Rank} = \text{Max Bid} \times \text{Quality Score}$$

and

$$\text{Actual CPC} = \frac{\text{Ad Rank of next competitor}}{\text{Your Quality Score}} + \varepsilon$$

This means improving your quality score directly reduces your cost per click.

Reserve Pricing and Thresholds

A reserve price is the minimum bid necessary to enter the auction. Ad platforms do not always disclose this, but you can infer it when impressions stop even though your bids look high enough.

In practice:

• Low CTR ads hit hidden thresholds
• Irrelevant landing pages reduce ad rank
• Poor historical conversion data depress eligibility

I detect reserve effects by monitoring impression share drops at stable bid levels. When I see impressions suddenly collapse, I know the effective reserve price has moved.

To address this, I improve asset relevance, adjust match types or increase quality signals through structured landing pages.

Practical Example: eCommerce Quality Score Fix

For a homeware brand, impressions dropped 40% despite steady bids. Investigation showed that landing page load time had increased after a site update. We:

1. Optimised page speed from 4.2s to 1.8s
2. Improved headline relevance to match ad copy
3. Added structured data for products

Within two weeks, impression share recovered and CPC dropped 18%.

Bidder Collusion and Smart Bidding Herding

Platforms are not immune to herding behaviour. When many advertisers use similar smart bidding settings, like Maximise Conversions, they begin to mimic each other. This creates collusion like effects:

• All bids chase the same segments
• Prices rise without equivalent performance gain
• Conversion volatility increases

I counter this by using:

• Target CPA or ROAS with very narrow thresholds
• Manual bidding for long tail keywords
• Bid adjustments by device, time or audience layering

This creates spacing. My campaigns compete on different terms or signals, avoiding artificial competition with algorithmic neighbours.

How I Model Bidding Strategy With Maths

I build probabilistic models for keyword level auction dynamics. For each keyword, I consider:

• $v_i$: value per conversion (profit per sale or lead)
• $c_i$: cost per click
• $p_i$: estimated conversion probability (from historic data)

Expected profit per keyword:

$$\pi_i = p_i \cdot v_i - c_i$$

I prioritise spend on keywords with highest $\pi_i$. When automated bidding pushes spend toward low $\pi_i$ queries, I apply negative keywords or bid caps.

Keyword Profitability Table

Keyword Type	Avg CPC	Conv Rate	Value	Expected Profit
Brand	£0.45	12%	£85	£9.75
Category	£1.80	3.2%	£85	£0.92
Long tail	£0.90	5.1%	£85	£3.44
Competitor	£2.40	1.8%	£85	-£0.87

This shows why blindly scaling competitor terms often loses money.

Example: Smart Bidding with Guardrails

For a DTC food brand, Google's smart bidding overspent on branded traffic and low value general queries. I rebuilt bidding as follows:

• Applied custom labels based on margin tiers
• Set ROAS targets by product group
• Excluded terms with high CPC and low $p_i$ even if CTR was high

Performance:

• CPA dropped by 19%
• ROAS increased from 2.8 to 4.2
• Spend rebalanced toward profitable terms with lower competition

Auction Behaviour and Seasonality

Auction prices fluctuate. During peak times, Black Friday, quarter end, or tax season, competition surges. I model auction dynamics as a function of seasonality:

$$b_t = b_0 + \alpha S_t + \varepsilon_t$$

Where:

• $b_t$ is bid at time $t$
• $S_t$ is seasonal intensity (e.g. Google Trends index)
• $\alpha$ is sensitivity to seasonality

I use this to pre plan budget reallocation and avoid overbidding into noisy periods unless justified by $v_i$ uplift.

Final Thought: Market Mechanics Are Your Edge

Paid media is not just about ads. It is a dynamic market. You do not have to outspend competitors, you have to outthink them.

When I use auction theory to inform bid logic, spend allocation and landing page structure, I get better outcomes from the same budget. It is not magic. It is maths, and it works in the real world.

If your paid media costs keep rising while returns stagnate, it might be time to stop guessing and start modelling. I can help you build a smarter bidding strategy that is mathematically defensible, commercially realistic, and built for profit, not just traffic.