Two related subjects
Probability and statistics are close cousins that point in opposite directions. Probability starts from known rules and asks what is likely to happen: given a 20 percent critical hit chance, how often will two hits in a row crit? Statistics starts from observed results and asks what they suggest about the rules or the player behind them: given these 30 match results, what can we say about my true win rate? Game analysis uses both, often within the same question.
This tour covers the main ideas at an entry level. Each is simple on its own; the skill lies in remembering which one applies.
Probability basics
A probability is a number between 0 and 1 (or 0 and 100 percent) describing how likely an event is. A 25 percent chance is the same as 0.25, or one in four. Something that cannot happen has probability 0, and something certain has probability 1.
Independent events
Two events are independent when one does not affect the other. If each attack has a 20 percent chance to crit and attacks are independent, the chance that two attacks both crit is found by multiplying: 0.2 times 0.2 equals 0.04, or 4 percent. The chance that a first attack crits does nothing to the second. Many errors in judging luck come from treating independent events as linked, as in “I have missed five times, so a hit is due”.
“At least once”
Often the question is whether something happens at least once in several tries. The trick is to work out the chance it never happens and subtract from 1. With a 10 percent chance per try and 5 tries, the chance of no success is 0.9 to the fifth power, about 0.59, so the chance of at least one is around 0.41, or 41 percent.
Expected value
The expected value is the average result over many repetitions. For a six-sided die the possible results are 1 to 6, each with probability 1 in 6, and the average is 3.5, a value you will never actually roll. In games, expected value is used to compare choices with different chances and rewards; it describes the long run, not the next attempt.
Describing a set of results
Statistics begins with summarising data.
Mean and median
The mean is the sum divided by the count. The median is the middle value when results are sorted. They can differ when a few extreme values exist. Take kill counts of 8, 12, 10, 6 and 34 over five matches. The total is 70, so the mean is 14. Sorted, the results are 6, 8, 10, 12, 34, and the median is 10. The one big game pulls the mean up, and the median better reflects a typical match. Reporting both is a good habit.
Spread
Averages hide how much results vary. Two players can both average 10 kills with one very consistent and the other swinging between 2 and 20. Simple measures of spread include the range (highest minus lowest) and standard deviation, a number describing the typical distance from the average. You do not need to compute it by hand to appreciate the idea: a wider spread means any single result is a weaker guide to what comes next. Spread is also why damage ranges and critical hits matter; they add variance around the same average.
Distributions
A distribution describes how often each result occurs. Many outcomes cluster around a central value with fewer extremes on either side. Others are lopsided, such as the time to get a rare item, where many players finish early and a smaller group takes far longer. The shape matters because it tells you whether the average is a sensible summary.
From data to conclusions
Samples and uncertainty
You usually see only a sample of all the games you could play. A sample result is an estimate of the underlying truth, and smaller samples give rougher estimates. If you win 6 of 10, your true win rate could well be anywhere from around 30 to around 90 percent; the data cannot narrow it much. Larger samples shrink that uncertainty. This is the reason sample size appears in nearly every serious discussion of reading results.
Correlation and causation
Two things are correlated if they tend to move together. Players who use a certain character may have high win rates, but that does not show the character causes wins; stronger players might simply prefer it. Correlation is a reason to investigate, not a conclusion. Randomised comparisons, or at least careful matching, are needed to show cause, and most casual analysis cannot offer that.
Base rates
A base rate is how common something is in general. If a character is played by few people, a high win rate from a small group of specialists says little about how it would do in everyone’s hands. Remembering the base rate stops you from reading too much into striking but unrepresentative numbers.
Where you will see these ideas
- Item and loot tables apply probability directly, as in drop tables that assign weights to each outcome.
- Rating systems such as Elo ratings use observed results to estimate relative strength and update after each match.
- Balance teams study win rates to judge whether options are fair, and win rate balance is one measure of how close they are to even.
- Your own tracked results rely on means, spread and samples.
A word on humility
These tools describe patterns; they do not predict individual events. A 60 percent favourite loses four times in ten. Models rest on assumptions that may not hold, and data can mislead when it is incomplete or gathered carelessly. Used with that in mind, probability and statistics give you a clearer way to think about games, without making any promise about how a given match will go.