A mathematician reads customer behavior through a few numbers: what each customer costs to win, what each one returns, and whether a change to a page moved sales or only looked like it did. Spend $200 on ads to win 5 customers and each one cost $40, and if those customers bring in $300, the campaign returned 50% on the $200.
Psychology explains why people buy. The arithmetic below tells you which of those reasons pays, and it is the same arithmetic a sportsbook runs on its own customers.
Cost of acquiring a customer
The cost of acquiring a customer (CAC) is what you spent divided by the number of customers it produced. $200 in ads that bring in 5 customers is $200 / 5 = $40 each.
Divide it the other way round and you get customers per dollar, 0.025, which is a different number. Keep CAC per channel, not only for the business as a whole. A channel at $40 and another at $120 average out to a figure that describes neither.
Return on investment
Return on investment (ROI) is what a campaign brought in minus what it cost, divided by the cost. With $300 back on a $200 campaign, ROI is ($300 – $200) / $200 = 50%.
The number that decides whether to keep spending is lifetime value (LTV) against CAC. A customer who costs $40 and brings in $30 a year pays back in about 16 months. One who stays three years returns $90 on the $40, so the channel earns.
Testing one change at a time
Every change you make to a page (a button color, a comparison table, a shorter form) is a variable. The only way to know what it did is to change that one thing and measure it against a version without it, which is an A/B test.
Say 1,000 visitors see version A and 50 buy, a 5.0% rate, and 1,000 see version B and 65 buy, 6.5%. B looks better. A two-proportion test gives a z-score of 1.44, below the 1.96 needed for 95% confidence, so the gap could be chance. With 4,000 visitors on each side and the same rates, z is 2.88 and the result holds.
Regression does the same job with several variables at once. It estimates how much each one moves sales while holding the others still, and a variable whose effect is not statistically different from zero can be dropped.
Traffic is not customers
Visits are the easiest number to count and the easiest to misread. Automated traffic from bots can inflate visits without a single buyer behind it. A sharp rise in visits with a fall in time on site and in pages per visit is the pattern to check before celebrating.
Measure the steps after the visit: how many read past the first screen, how many start a signup, how many finish it. Robert Cialdini’s work on persuasion names reciprocity (giving something first) and social proof (showing that others already buy) as reasons people act. Both cost money, and both can be put through the same CAC and ROI sums.
How a sportsbook applies the same math
A sportsbook’s margin is built into its prices. When both sides of a game are -110, each side implies 52.4%, and the two add up to 104.8%. The extra 4.8 points is the book’s cut, and on a balanced book it keeps about 4.5% of every dollar bet.
That margin is what pays for the book’s welcome offers, so a bonus is an acquisition cost like any other. Our sportsbook reviews compare what each book offers, and our betting guides cover the rest of the math, from implied probability to bankroll size.