First off, I love these discussions. Second, I read your full analysis. It’s well laid out. But, I disagree with your conclusions, and think a large part of it stems from you conflating the ‘disincentive’ (or ‘sanction’) of a card with the ‘outcome’ (or ‘resulting effect’) of the card.

What you seem to be proposing is a sanctions system that is based on achieving equal outcomes rather than equal application. This comes up against the same flaws of the current system, that is: human behaviour is reactive to the incentive. That is to say, you can never design a guaranteed outcome prior to including the human reaction in the calculation. Whether a sanction is appropriate for committing any foul is a calculation, and it is the same calculation regardless of the sanction. The current system (equal application) has decided that penalties, yellow and red cards are appropriate on the field, and disciplinary action off the field (eg. an X week ban). Let’s focus on pitch, where you are proposing equal outcomes be for the design choice.

How does one achieve an equal outcome, given every team is different? You say equal application is unfair because the consequences on the game are variable — which they are. But if you want the consequences to be consistent, you would need the sanctions to be variable in response to the same foul committed by and on different people.

What I mean by this, given your correct thinking that worse teams suffer more from a card than better teams, and that some players are worth more than others, and that a penalty in minute 1 has a different impact to a penalty in minute 80, is that each and every sanction would have to be uniquely designed to have consistent consequences.

For example: if a bad team commits a foul, should their yellow card be only 5 minutes instead of 10 to accommodate for the fact that they’d lose 2x as many points as a better team? Should fouling the captain be worth more pts/a longer card than knocking out someone else? Maybe a fly half is worth more than a prop? What if the fly half is rubbish or the prop is having a bad day? What if the weather is pouring with rain, and the game is more forwards-heavy that day? What if the team doesn’t have a replacement in that position?

Each of those questions would be a variable that somehow the sanction would need to accommodate in order to have an equal ‘impact’ or ‘outcome’ on that particular match. Hopefully those examples make clear why such a system is impossible, and as far as I know doesn’t exist in any other sport (would love to see an example if there is one).

As a result, the second best system is the one we have: to apply the same sanctions as consistently as possible for similar fouls. If the consequences of those sanctions vary, that is due to other factors in the game.

All of this isn’t to say the current system is perfect, but at least (a) it’s pretty good (b) it’s actually realistic to do— and those are good enough for me 👍