Tournament selection imperative

I've been running some numbers, and realize I've been much too fast and loose in my tournament selection. Here's a rough approximation of my typical tournament selection thought process: "I'll start with a 50K or 80K buy in. If I feel like I'm 'on', I'll move up to a 150K or 200K buy in. If not, I'll stay at the lower level buy ins." There are several things wrong with this philosophy, but the most basic one is purely mathematical. In order to maximize your profit potential, it's imperative that you choose just one buy in and stick with it. The reason is simple; if you're able to win just slightly better than one in six tournaments, and come in second in just slightly better than one in six, you'd better make sure your winnings cover your buy ins for the tournaments where you don't make the money. If you lose a huge buy in tournament, winning a lower buy in tournament won't cover that loss.

If I'd realized this in the beginning, I'd now be in tournament black, all other things being equal. Of course, all other things aren't always equal; it's certainly possible that some buy in levels will be tougher to win than others, because of tougher competition typically buying in at those levels.

Counting last night's 8 tournaments, I've now played in 85 sit and gos, winning 14 of them and coming in second 16 times. Here are the profits I would have made at each buy in level, if I'd played all the tournaments at that level:

 $50,000 buy in:  $92,000

 $80,000 buy in: $171,000

$150,000 buy in: $373,750

$200,000 buy in: $512,500

As it turns out, my current tournament delta is $-78,910; the reason I'm in the red is that my losses in bigger buy in tournaments weren't covered by my wins in lower buy in tournaments.

Here's how I've done at each buy in level:

  buy_in    count      delta

$150,000       11   $766,250
 $50,000       13   $134,600
    $300        1       $850
  $2,000        1    $-2,110
 $80,000       52  $-348,000
$200,000        7  $-630,500

At first glance, my choice seems clear: I should choose the $150,000 buy in level and stick with it. However, there are a couple of flaws associated with this choice. First, my sample size isn't big enough. Second, fairly often I switched to the $150,000 level since I was on a losing streak, felt my luck would turn around, and wanted to hit a home run to recoup my losses. Given my skill level and the fact that I'd usually lost several tournaments in a row when I chose a $150,000 tournament, statistically I was more likely to win those tournaments than the lower buy in ones. This advantage goes away when you're playing exclusively at one level.

I'm going to go with my gut and pick the lowest buy in, $50,000, as my solitary buy in level. I pledge to play at least 100 straight tournaments at this level; at that point, I'll do another tournament report card and reassess.

buy_in entry_fee num_players num_hands place winnings

 80000      1000           6        40     4        0
 80000      1000           6        25     5        0
150000      1250           6        31     2   315000
 80000      1000           6       106     2   168000
 80000      1000           6        25     5        0
200000      1500           6         4     6        0
 80000      1000           6        23     4        0
150000      1250           6        65     2   315000

delta: $-111,000
balance: $5,051,821