Why your ninety-five per cent shot missed

The shot that decides a mission is nearly always a high-percentage one, which is why the misses that matter are the ones that should not have happened. The complaint is as old as the genre and it has never been settled, partly because the people arguing are talking about three different things.

Ninety-five per cent means you miss one shot in twenty. A single campaign involves hundreds of shots; four hundred is a conservative estimate for a long one. At ninety-five per cent, twenty of those four hundred miss. Not one, not three. Twenty.

The arithmetic gets worse when the shots come in pairs. Two ninety-five per cent shots both landing is about ninety per cent likely, so a turn that needs both of them to work fails one time in ten. Four of them in a turn and you are down to eighty-one per cent. A plan made of high-probability steps is a lower-probability plan, and the number nobody computes is the one that actually decides the mission.

Two well-documented habits of thinking do most of the damage here.

The first is expecting randomness to look tidy. Three misses in a row feels like proof that something is wrong with the game, when in a genuinely random sequence clusters like that are not only possible but required; a sequence with no clusters in it would be the suspicious one. There is also no force correcting a run of bad luck. A die that has come up badly four times is not owed anything.

The second is that the record you keep is one-sided. Nobody remembers the twenty-five per cent shot that landed and saved a soldier, because it felt like competence rather than luck. The misses get filed as the game cheating and the unlikely hits get filed as good play, so after forty hours your honest impression of the odds is wrong.

Fire Emblem has shown players one number and used another for most of its history. The system is called true hit, or 2RN, because instead of rolling once against the displayed chance it rolls twice and averages the two results.

Averaging pulls results towards the middle, which means anything above fifty per cent lands more often than the screen says and anything below fifty lands less often. A displayed ninety per cent is really about ninety-eight. A displayed thirty per cent is really about eighteen. It was introduced in The Binding Blade and used through to Awakening, dropped for Fates and Shadows of Valentia, which used a different hybrid, and brought back in Three Houses.

The intent is not hard to read. The designers decided the displayed number should mean what players already assume it means, so they bent the maths to fit the assumption rather than bending the assumption to fit the maths.

Firaxis never advertised this, but players reading XCOM 2's own configuration files found hit-chance multipliers attached to the difficulty settings. On Rookie the player's chance is multiplied by 1.2 and on Veteran by 1.1, while Commander leaves it at 1.0. The assist applies to shots already above fifty per cent, is capped so nothing exceeds ninety-five, and is switched off on Legendary. There is also a hidden bonus that applies after you miss, and goes away the next time you miss.

So on the two easier difficulties the game is quietly on your side and the number on screen understates your odds, while on the hardest setting the number is exactly what it says. The players who complain loudest about the dice are, on average, the ones getting the most help.

Two reasons, and neither is laziness.

The first is that feeling cheated is worse than being beaten. A player who loses a soldier to a decision they can see was theirs will try again. A player who loses one to a number that felt impossible blames the game, and blaming the game is where people stop playing. Bending the odds towards what players expect buys back that trust, and most of them never find out.

The second is that nobody reads these numbers as probabilities. Ninety-five per cent is read as yes. Thirty per cent is read as no. If a designer wants a displayed number to carry a decision, the number has to mean roughly what the player thinks it means, or it is not information, it is decoration.

A number you cannot trust cannot be reasoned with. The player who works out that two shots at sixty per cent are better than one at ninety is doing exactly what the genre asks of them, and a hidden adjustment makes their arithmetic wrong in a direction they cannot see. Skill at the game stops being skill at the game as described.

It also spends trust that does not come back. Once a player knows one number was adjusted, every other number in the game is in question, including the honest ones. X-COM: UFO Defense (Mythos Games and MicroProse, 1994) rolled once, told you nothing, and killed people for it, and nobody has ever accused its numbers of being polite.

Four things that hold whichever game you are in.

We are not announcing how RAD Tactics resolves a shot. The principle is worth stating anyway, because it is the part that is actually a design decision rather than a setting: a number shown to the player is a promise. Rolling honestly and bending the odds are both defensible. Showing a number that is wrong in a direction the player can never learn is the one option that is not.