# Mastering the Metrics-2: 7 Arbitrage Problems To Solve [With Answers]

Without a good understanding of arbitrage metrics and how they correlate, it’s kind of hard to imagine how a regular arbitrageur guy (or girl) even analyzes their advertising campaigns. Or find out what exactly needs to be improved to achieve higher ROI.

We would say, it’s not just hard but borderline possible.

If you want to avoid going down the path of chaos and want to bring in some system to your ad spends and their results, train your understanding of metrics. In the previous material, we tackled problems relevant to crypto advertisers. In this section, we’ll focus on gambling.

We’ll explore 7 problems with arbitrage metrics of varying complexity in the world of gambling and show you the step-by-step solutions.

Task #1

- CTR = 1.5%;
- Click2Inst 2k1;
- CPM = $10;
- Inst2Dep = 30k1.

Question: What CPA bid should you go for so that the campaign breaks even?

Answer: $40.

Solution: First, let’s find out the cost per install (CPI). After 1,000 views, you will get 1,000 * 1.5% = 1,000 * 0.015 = 15 clicks.

Since the Click2Inst ratio is 2k1, the number of installs will be 15 / 2 = 7.5. You pay $10 for 1,000 views, which means 1 install costs $10 / 7.5 = $1.33.

To get 1 deposit, you need 30 installs, so the cost for getting a deposit will be 30 * $1.33 = $40.

With a $40 CPA bid, the campaign will break even.

Task #2.

- CPC = $1.
- Inst2Dep = 30k1.
- CPA = $40.

**Question**: How well should the app convert to break even on the campaign?

**Answer**: Click2inst = 1.33k1.

Solution: The app’s conversion rate is expressed as the ratio of clicks to installs (Click2Inst) or the conversion from click to install.

Let’s start by calculating the install cost at which the campaign breaks even. Since you need 30 installs to get deposits, the Earn per Install is $40/30 = $1.33.

The cost per click (CPC) is $1, so CR(Click2Inst) = ($1 * 100%) / $1.33 = 75.2%. Click2inst = 1.33k1.

Easy peasy.

Task #3

- Inst2Reg for Landing page 1 = 12k1
- Reg2Dep for Landing 1 = 6k1
- Inst2Reg for Landing page 2 = 10k1
- Reg2Dep for Landing 2 = 8k1.

**Question**: Which landing page should you choose if you’re being paid on a CPA basis?

**Answer**: Landing page 1.

Solution: It’s simple, compare the Inst2Dep for both landing pages.

Inst2Dep for Landing 1 = (12 * 6)k1 = 72k1.

Inst2Dep for Landing 2 = (10 * 8)k1 = 80k1.

Since 72 is less than 80, Landing 1 is more cost-effective.

Task #4

- CPA = $120
- CTR = 0.8%
- CPM = $10
- CR(Click2Inst) = 100%

**Question**: What conversion rate from install to deposit do we need to achieve a 50% ROI?

**Answer**: 64k1.

Solution: ROI = (profit – expense) * 100% / expense.

From this formula and given that ROI = 50%, we can calculate the profit-to-cost ratio (profit/expense) which is 1.5.

Let’s get back to our CPA bid, which is $120. Then the cost to get a deposit should be $120 / 1.5 = $80.

Now, let’s calculate the cost per install. With a CTR of 0.8%, it means that out of 1,000 views, 8 users make a click.

With CR(Click2Inst) = 100%, all 8 clicks result in installs. For 1,000 views (CPM) at $10, the cost of 8 installs is $10. So the cost per install should be $10 / 8 = $1.25.

To achieve a 50% ROI, the cost should be $80. So, the required number of installs for a deposit should be 80 / 1.25 = 64, making the conversion rate from install to deposit 64k1.

Tasks #5&6

With an offer come two payment models: CPL = $15 and CPA = $130;

The rest is given:

CPM = $6;

Click2Inst = 2.5k1;

Inst2Reg = 10k1.

**Question 1**: What should the CTR of the creative we use be to break even on CPL?

**Answer 1**: 1%.

**Question 2**: What should the registration-to-deposit conversion rate (CR) be for the CPA model to become 50% more profitable?

**Answer 2**: 5.78k1.

Let’s see how we got those numbers.

**Solution 1**: Let’s calculate the target cost per install (CPI) using Inst2Reg and the CPL bid to break even.

CPI = $15 / 10 = $1.5.

Taking into account Click2Inst, you need to get 2.5 clicks for the cost of CPI. So the cost per click is $1.5 / 2.5 = $0.6.

With a CPM of $6, you get 10 clicks for $6/$0.6 = 1,000 views.

CTR = (10 * 100%) / 1,000 = 1%.

**Solution 2**: CPA/CPL = $130/$15 = 8.67. This means that with a registration-to-deposit conversion rate of 8.67k1, the CPL model is as profitable as the CPA model.

To figure out what conversion rate we need to see for CPA to be 50% more profitable, divide the previous result by 1.5.

The target Reg2Dep = 8.67/1.5 = 5.78k1.

Task 7 (With Two Questions)

- ROI = 33%;
- Spend = $1,020;
- CPC = $1;
- Click2Inst = 1.77k1;
- Inst2Reg = 4k1;
- Reg2Dep = 12k1.

**Question 1**: What is the CPA bid for the buyer?

**Question 2**: How many deposits did the buyer get?

**Answers**: CPA = $113; 12 deposits.

Solution:

First, let’s find out the cost per install (CPI) = CPC * Click2Inst = $1 * 1.77 = $1.77.

Then comes the cost per registration (CPR) = CPI * Inst2Reg = $1.77 * 4 = $7.08.

The buyer will pay CPR * Reg2Dep = $7.08 * 12 = $84.96 for deposits.

To find the CPA bid, use the ROI formula with the expense part being $84.96, and as per the given condition, ROI = 33%.

So, CPA / $84.96 = 1.33, which means CPA = $84.96 * 1.33 = $113.

The number of deposits can be found by dividing the spend by the buyer’s cost per deposit = $1,020 / $84.96 = 12 deposits.

***

Such brain teasers can be useful because that’s exactly what affiliates have to deal with in their everyday work.

Was any hard? If it was a piece of cake, congrats, you have a good grasp of metrics and their interplay.

If it was challenging, even a bit, stay tuned; we’ll gather more tasks to crack for honing your math skills without putting your advertising budget at risk.