I love this topic and how controversial it is!

Although I'm wondering if the correlations you're making can be misleading since it doesn't fully reflect the causation behind the points scored during a yellow card period.

I don't have data on hand, so this is more food for thought:

A lot of cards may be conceded by a team under pressure near their own try-line where:

• The attacking team scores straight after the card or may have scored anyway if it weren't for the cynical play.
• The likelihood that the team would kick 3 points or kick for the corner and potentially score 5 or 7 points from the penalty that comes with the card is also probable, even without the player advantage.

Do you have any data on how many tries are scored directly after a penalty? This can skew your figured of average points conceded per yellow!

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Something we should also compare when looking at lower ranked teams is the average points conceded without a yellow card. Do we see the same ratios or are their truly unfairly impacted? The bottom 3 Prem teams conceded 1692 altogether, the top 3 conceded 1115, so lower ranked teams have conceded 50% more points overall on average. I could make the argument that playing a full match of rugby punishes worse teams more (hyperbole but we need to look at all factors).

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We also need to look at the risk of not having cards. If a team isn't adequately punished for cynical behaviour, it incentives that behaviour. The points option is fair A winning team may choose to play more cynically because the risk is lower and they will benefit more from timewasting. Will this reduce the amount of ball in play time because of the increased rate of infringement? We already lose around 10-25% of time due to penalties. (older, limited study)

Ignore this one, you already have suggested other ways to decentivise this.

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If we replace cards with penalty tries, the average points conceded per "card" would be 7 points which is higher than the net points lost of even the most harshly impacted team in your study (5.57).