algo

The algorithm should be purely additive. You simply add points for attending a tournament, with exponentially smaller rewards the lower the placement.

There is no reason to deliberately implement "punishment" in the algorithm. You can allow players to 'mess around' without it hurting their rankings. This is also the best solution to player anxiety.

If you think this overly rewards attendance, this is easily adjusted for. The reward decreases exponentially the lower your placement, meaning that if you get a placement that is generally lower than what you usually get, it won't really make a meaningful difference to your rank overall.

Here is a fairly simple implementation of the algorithm.

1) Assign points to players for every tournament they attend using formula P = Entrants/Placement. PP is the sum of all the points a player has collected during the year.

2) Assign points to players for every tournament they attend (again, from scratch) using formula
P = [ Number of players who placed above or equal to player including player himself + { Sum of, for every player placed below player, [(TheirPlacement-1)*(1-TheirPP)/(Entrants-1)+TheirPP] } ] / Placement

This implementation uses number of attendees as the starting point for valuing the importance of a tournament. It then calculates every player's overall point tally, and then uses that to calculate the value of a tournament more precisely. When doing so, the strength of players who placed equal or above to the given player is set to 1 (so you aren't rewarded for who you lose to), and the strength of players placed below the given player is weighted (linearly) according to their placement, so that it only matters if they were performing close to their standards.

One thing worth noting is how to handle tied placements. Should two players who placed below the top 4 be both 5th place, or both 6th place? Most places use the former, but if it were the latter, then the first value in the second formula ("Number of players who placed above or equal to player including player himself") could be replaced with just Placement. And I feel like that would be more just. But not a massive deal.

PS: I'm not sure if people believe that looking at player-specific wins/losses is something that should be included in an algorithm. I don't believe that it is necessary or even good. What if the given player was 'having a bad day'? How much credit should the other player really get?

That is all.