# Ratios

Understanding ratios and how to compute them can be greatly simplified with real-world examples. We’ll use common sports statistics to illustrate this concept.

### Understanding Ratios

A ratio is a way to compare two quantities by dividing them. It tells us how much of one thing there is compared to another. Ratios can be written in three ways: using the word ‘to’, using a colon (:), or as a fraction. For example, a ratio of 5 to 3 can be written as 5 to 3, 5:3, or 5/3. Ratios come up all the time in sports betting, whether it be for a specific statistic, or a way of representing odds. It’s very important that you understand ratios, and furthermore the relationship between decimals, percents and ratios.

### Computing Ratios

**Identify the Quantities**: First, you need to identify the two quantities you are comparing.**Divide the Quantities**: Then, divide one quantity by the other.**Simplify the Ratio (if needed)**: Sometimes, you can simplify the ratio by dividing both numbers by their greatest common divisor.

### Basketball Example: Assist-to-Turnover Ratio

In basketball, the assist-to-turnovers ratio is a common statistic used to measure a point guard’s efficiency. It intuitively compares the number of assists a player records to the number of turnovers they commit.

**Step 1**: Identify the Quantities

- Assists (A)
- Turnovers (T)

**Step 2**: Compute the Ratio

- Ratio = Assists ÷ Turnovers = A/T

**Step 3**: Simplify (if possible)

- If A is 10 and T is 5, then Ratio = 10 ÷ 5 = 2. This means the player makes 2 assists for every turnover.

### Baseball Example: Strikeout-to-Walk Ratio

In baseball, we often evaluate pitchers by examining their strikeout-to-walk ratio. This obviously compares the number of strikeouts to walks recorded by a pitcher.

**Step 1**: Identify the Quantities

- Strikeouts (K)
- Walks (BB)

**Step 2**: Compute the Ratio

- Ratio = Strikeouts ÷ Walks = K/BB

**Step 3**: Simplify (if possible)

- If K is 90 and BB is 30, then Ratio = 90 ÷ 30 = 3. This means the pitcher strikes out 3 batters for every walk allowed.

To convert decimals to ratios and vice versa, especially in the context of sports statistics, you need to understand the relationship between these two forms of representing numbers.

### Converting Decimals to Ratios:

**Understand the Decimal**: To recap from earlier lessons, a decimal represents a part of a whole, and can be converted to a percentage by multiplying by 100. For example, in baseball, a batting average of 0.300 means the player gets a hit 30% of the time they bat.**Multiply by a Common Factor**: To convert this into a ratio, you multiply the decimal by a common factor to get whole numbers. For 0.300, multiplying by 1000 is a good choice, giving you 300.**Form the Ratio**: Now, form a ratio of this number to the common factor. In our example, 300 hits out of 1000 at-bats. So, the ratio is 300:1000.**Simplify the Ratio**: Simplify this ratio by finding the greatest common divisor. For 300:1000, it simplifies to 3:10.

### Example in Basketball:

**Decimal to Ratio**: A basketball player’s free-throw shooting percentage expressed as a decimal is .85. To convert this to a ratio, multiply by 1000, which gives 85. The ratio is then 85:100, which simplifies to 17:20. So, the player makes 17 free throws out of every 20 attempts.

### Converting Ratios to Decimals:

**Understand the Ratio**: An NFL team with a win-loss record of 10:6 means 10 wins for every 6 losses.**Divide the First Number by the Second**: To convert this into a decimal, divide the first number of the ratio by the second. In our example, divide 10 by 6, which equals approximately 1.667.**Convert to Decimal Format**: This result is the decimal equivalent of the ratio. In sports terms, this could represent a win rate or efficiency.