Card Harshness
Card Harshness compares how often a team is shown cards for the fouls it commits with the card rate of the opponents it faced.
The metric
Cards per foul is the number of cards shown to a team divided by its fouls committed. The card presents the reciprocal—fouls per card—in casual language because “one card about every five fouls” is easier to read.
A lower fouls-per-card value means cards were shown more frequently. The headline is a transparent rate that can be recomputed from the published inputs; it is not a regression score.
Baseline and expected cards
The baseline pools how often this team’s opponents were carded for their own fouls in their other matches, excluding matches against the team being examined.
Expected cards equals the team’s fouls multiplied by that pooled opponents’ cards-per-foul rate. It describes what the team’s card total would be at the rate of the schedule it faced.
The mirror reading
The mirror asks how often those same opponents were carded when they played this team, compared with their own baseline in other matches.
It is a companion reading, not a gate. A one-sided finding is still shown when the mirror does not corroborate it.
The central limitation: severity blindness
The event data does not measure how severe or how clearly bookable each foul was, nor the severity of each card. A harsher card rate can therefore reflect genuinely more-bookable fouls rather than different treatment of comparable incidents.
Card Harshness identifies a rate difference. By itself, it does not establish whether comparable fouls were treated differently, intent, or why the difference occurred.
Confidence bands
The confidence interval treats each foul as a binomial trial that did or did not result in a card and uses a 95% Wilson interval on cards per foul.
Strong means the interval separates the team rate from its baseline. Moderate means the interval overlaps the baseline but is reasonably narrow. Limited means the interval is wide relative to the observed rate, the baseline is unavailable, or the sample cannot support a stable reading. The band changes wording strength, never whether a finding is shown.
Strength of schedule
The schedule lens compares the opponents-faced card rate with the tournament-wide card rate. When that difference is material, the card shows it as a separate plain-language note.
Strength of schedule is never silently baked into the headline. The original rate, expected-card arithmetic, and per-match inputs remain visible.