100th post thesis: adjusting AF based on WTSD

rzk · #1 07-03-2007, 04:35 AM

for my 100th post, i'd like to share the results of a little calculation which you might find useful. you might have been wondering: if two players have the same AF but their other stats are different, which one is more aggressive and by how much? my calculation will help answer this question.

examining data from PAHUD reveals the following rough relationship between WTSD and fold to bet percentages (averaged over flop, turn, and river):

Code:<hr /><pre>WTSD fold to bet call or raise
----------------------------------------------------------
30 42 58
35 35 65
40 28 72
45 20 80
</pre><hr />

now, AF is defined as [#bets or raises]/[#calls]. but what if we are interested in a different (and, in my view, more important) measure of aggression: [#bets or raises]/[#total decisions in response to a bet]. this measure doesn't depend on how "foldy" the player is and so is the most direct measure of how often he/she bets or raises. let's call this new measure AGG. the last column of the above table suggests that AGG can be estimated from AF and WTSD as follows:

Code:<hr /><pre>WTSD AGG
--------------------------------------
30 AF*58/100
35 AF*65/100
40 AF*72/100
45 AF*80/100
</pre><hr />

now, obviously nobody is going to start using this AGG measure - even if it's a more useful measure of aggression, who wants to do this kind of math while playing poker? so i'll define a slightly different measure, one that's much easier to calculate and that can be used exactly like we have always used AF. i'll call this measure the "adjusted AF" or simply AF" and define it to be:

Code:<hr /><pre>AF" = AGG*100/65
</pre><hr />

this way, for a standard 2+2 tag with WTSD=35, AF" is exactly equal to AF, but for other player types it's a little different, reflecting their true aggression. more precisely, we have from the table above:

Code:<hr /><pre>WTSD AF"
--------------------------------------
30 AF*58/65
35 AF
40 AF*72/65
45 AF*80/65
</pre><hr />

this definition makes it extremely easy to adjust AF to produce AF", because the above table can be restated as follows:

Code:<hr /><pre>WTSD AF"
--------------------------------------
30 AF - 10%
35 AF
40 AF + 10%
45 AF + 20%
</pre><hr />

as an example, suppose we have 4 players with AF = 2.0 and WTSD = 30,35,40, and 45. their adjusted AF would be as follows:

Code:<hr /><pre>WTSD AF"
--------------------------------------
30 AF - 10% = 1.8
35 AF = 2.0
40 AF + 10% = 2.2
45 AF + 20% = 2.4
</pre><hr />

the interpretation of this data is very simple. for example, the last row of the above table shows that a player with WTSD=45 and AF=2.0 bets and raises as often as a standard 2+2 tag with AF=2.4.

bottom line: for players with non-standard WTSD, it makes sense to adjust AF slightly (usually by around 10%).

(edited to improve the appearance of tables and correct a couple of typos)