How does average stack size (in BBs) change throughout a tournament?

Question

I played a NLHE tournament with a Starting Stack Size of 25000 and Level 1 Blinds of 50/100.

So that means we started with 250 big blinds each.

There were ~1000 entrants, so 25 million chips in play.

By Level 20 there were 100 players left, and the blinds were 5000/10000 with 1000 Ante per player (10 players per table, so 10000 in Antes).

So the average stack size at Level 20 was 250k, which was 25 big blinds, and the total pot size at the start of each hand was 25k (1/10 of the average stack).

Is it normal for the blinds and antes to dwarf the stacks so much?

What trend am I looking at? I can't imagine a tournament where the final table consists of players who have 1 big blind each, but why do stack sizes (when counted in BBs) seem to be getting smaller? Is it just the result of people gradually tightening up until the bubble, so does it rebound afterward? And is this typical for every tournament?

Is the relationship linear? a curve? Can someone show me a visualization of it?

Answer 1

There are two factors that effect the average stack size in BB given how many chips are in play:

• The number of players left in the tournament
• The size of the blinds

As the number of players left goes down, the average stack size in BB will increase if all else is kept the same.

As the size of the blinds increases, the average stack size in BB will decrease if all else is kept the same.

These two effects tend to balance each other out, but it largely depends on the type of tournament and how the players are playing. The overall trend will be a decrease in average stack size (BB) because the effect of blinds going up is much stronger than players getting knocked out on average stack size.

I don't think there is a mathematical graph or formula for this besides the basic formula for calculating the average stack size. The smaller the average stack size (in BB), players should be getting knocked out more frequently than if the average stack size is larger.

here is a rough visualization of how the graph would look, the graph goes upwards when players get knocked out and it takes a sharp decline when blinds increase. This would change a lot depending on how fast players are getting knocked out and how many are left in the tournament. the tournament would also end long before average stack size reaches 0BB.