Learning goals and lesson guide
**Estimated reading time:** 8 min read.
**Level:** Beginner. **Study time:** Allow 25–30 minutes with a calculator. **Prerequisites:** Basic arithmetic and the distinction between a result and a prediction. Every dataset in this lesson is fictional and created for teaching.
Player A scores 100 points across five games. Player B scores 120 across ten. B has the larger total, while A has the larger average per game. Neither statement alone establishes who is the better player or who will score more tomorrow. Statistics answer particular questions, and the denominator determines which question you are answering.
By the end of this lesson, you should be able to calculate a mean, median, percentage and combined rate; identify missing denominators; and explain why a small sample should not be treated as a stable forecast. You will also learn to preserve units, periods and source definitions in a simple statistical note.
## 1. Write the unit beside the number
The number 20 could mean points, minutes, matches, percent or a rate per 100 opportunities. Without a unit, it is not a complete statistic. Begin every note with what is counted and over which sample.
“Twenty points per game across five games” is more useful than “averages 20.” Add the competition, date range and any filter when they matter. A playoff-only figure is different from a full-season figure, and a home-only sample is different from all games.
Data sources can define similar labels differently. Before combining tables, check whether they use the same counting method. A statistic labelled per game should not be compared directly with one labelled per minute unless you explain the conversion and its limitations.
## 2. Calculate the mean and median
For scores of 8, 12, 20, 25 and 35, the total is 100 and the mean is 100 ÷ 5 = 20. The median is the middle value after sorting: also 20 here. The agreement is accidental; the two summaries are calculated differently.
Now use 8, 12, 15, 20 and 45. The mean remains 20, but the median is 15. One large performance raises the mean while the middle observation remains lower. Neither summary is inherently dishonest; they describe different features of the sample.
Keep the individual results when possible. A mean can hide a wide range of outcomes. A player who scores 20 every time and one who alternates between 5 and 35 can share the same average while presenting very different variation.
## 3. A percentage requires a numerator and denominator
If a fictional shooter makes four of ten attempts, the percentage is 4 ÷ 10 × 100 = 40%. If another makes one of two, the percentage is 50%. The second observed percentage is higher, but its smaller sample supplies less information about a stable underlying ability.
Report “one from two” with the percentage instead of presenting 50% as if it came from hundreds of attempts. A perfect one-from-one record does not establish a 100% future chance. The observed fraction is a description, not a guarantee.
The denominator must match the question. Wins divided by all completed matches differs from wins divided by only home matches. If draws or void records exist, state how they are treated. Silent exclusions can make a record look stronger without improving its meaning.
## 4. Combine rates with their underlying counts
Suppose a player makes one of two shots in one game and nine of 30 in another. The game percentages are 50% and 30%. Their simple average is 40%, but the combined shooting percentage is ten makes from 32 attempts, or 31.25%.
The difference occurs because the games contribute unequal numbers of attempts. To calculate the overall rate, add numerators and denominators, then divide. Averaging percentages equally answers a different question: the average of the per-game percentages.
| Game | Makes | Attempts | Percentage | | --- | --- | --- | --- | | A | 1 | 2 | 50% | | B | 9 | 30 | 30% | | Combined | 10 | 32 | 31.25% |
This lesson applies beyond shooting. Serve points, conversion rates and other opportunity-based measures should retain their denominators. Do not merge a small sample with a large one by giving both equal weight unless that is deliberately the question you intend to answer.
## 5. Distinguish totals from opportunity-adjusted measures
A team playing more matches can accumulate more wins, goals or points without having a higher rate per match. A player receiving more minutes can accumulate more statistics without performing better per minute. Opportunity matters when comparing totals.
For a fictional example, A produces 30 points in 60 minutes and B produces 24 in 40. A has more total points, while B has the higher observed points-per-minute rate: 0.6 versus 0.5. This does not prove B would maintain that rate over a longer workload. Opponents, fatigue and role may differ.
Use adjusted rates to ask better questions, not to erase context. A per-minute rate from a small reserve role may not transfer to a starting assignment. Later lessons explore possessions and efficiency; for now, simply keep the exposure measure beside the result.
## 6. Separate percentage points from relative percentage change
If a rate increases from 40% to 50%, the absolute difference is ten percentage points. Relative to the original 40%, the increase is 10 ÷ 40 = 25%. Saying it rose “ten percent” is ambiguous because readers may interpret it as a relative change to 44%.
Use explicit wording in a statistical note: “The observed rate rose by ten percentage points, from 40% to 50%.” If a relative change is useful, state it separately. This matters when comparing shooting rates, win rates or model forecasts.
Also consider rounding. A displayed 50% might represent a value rounded from slightly below or above 50%. Retain more precision in working calculations and round for presentation at the end. Do not manufacture a meaningful difference from two rounded figures that may conceal the same underlying value.
## 7. Beware selective samples
“Won four of the last five” may be true while omitting a longer poor record. A date window chosen only after seeing the outcomes can create an appealing story. Ask why that window was selected and whether it was defined before the analysis.
Context changes can justify a focused sample, such as a documented role change, but they do not remove small-sample uncertainty. Record both the reason for the filter and the number of observations remaining. Avoid trying many filters and reporting only the most impressive one.
Opponent quality, venue, competition level and missing data also matter. A table is not automatically comparable merely because both rows use the same column names. If the sample definitions differ, explain the difference rather than forcing a ranking.
## 8. Build a short statistical note
Write five lines: the question, sample definition, calculation, contextual limitation and conclusion. For the fictional 100-points-in-five-games example, the conclusion is “The player averaged 20 points in this five-game sample.” It is not “The player will score at least 20 next game.”
Add a second calculation showing how often a threshold was exceeded. With 8, 12, 20, 25 and 35, only two results exceed 20.5. That observed two-from-five fraction describes the sample but does not automatically become a reliable probability for a future event.
This combination of average, threshold frequency and limitation is more informative than one headline number. It shows the reader what the data say and where interpretation begins.
## 9. Review questions and explained answers
1. What is the mean of 10, 15 and 35? 2. What is their median? 3. Combine two makes from four attempts with eight makes from 20. 4. Is a rise from 30% to 36% six percentage points or a six-percent relative increase? 5. Does five wins in five matches prove the next match is certain to be won? 6. What should accompany a filtered “last five games” statistic?
### Answer key
1. Twenty: the total 60 divided by three. 2. Fifteen, the middle sorted value. 3. Ten makes from 24 attempts, approximately 41.67%. Do not average 50% and 40% equally to obtain the combined rate. 4. Six percentage points, or a 20% relative increase from the original 30%. 5. No. It is a small observed sample, not a guarantee. 6. The date range, competition, reason for the filter, sample size and relevant limitations, including any role or opponent differences.
## 10. Completion check
Before using a statistic, ask what was counted, what it was divided by, which observations were included and what conclusion it can support. If those answers are available, the number becomes useful evidence. If they are missing, the responsible conclusion is narrower than the headline suggests.
Review [probability and margins](https://betting.crazywingo.ph/article/implied-probability-bookmaker-margins-beginners), [odds](https://betting.crazywingo.ph/article/read-betting-odds-calculate-payouts), [market identification](https://betting.crazywingo.ph/article/sports-betting-basics-for-beginners), [market types](https://betting.crazywingo.ph/article/moneyline-spread-total-parlay-beginners) and [budget boundaries](https://betting.crazywingo.ph/article/betting-budget-limits-avoid-chasing-losses) when needed. Next, the course examines bonus wording and turnover calculations.