Hi Benjamin,

Not sure what you are asking here. Your idea is very interesting. I see some really cool potential, though I would likely approach it differently. If you can capture a specific character and record their wins/losses also, you could build a Bayesian model for success. After all, you're in a situation where you have moves preceding moves. What complicates matters is the opponent. Is that why you're looking at the Kendall Tau?

Either way, cool stuff. You should proceed with it!

PG

I am looking for funding. I would do the research myself. However I don't have the means to actually experiment with a game like street fighter as I don't know the programmers who made this game. Secondly I haven't really explained the Kendall Tau formula really for you. Maybe that's why you asked.

Here is the explanation:

Viewed in a simple manner, every fight move is responded by the opponent by another move. E.g. Fighter 1 makes move A.. Fighter 2 responds with move B.

Let's say Fighter 1 can make moves A1, A2, A3. Fighter 2 can make moves B1, B2, B3.

What happens is this:

Fighter 1 makes move A1. Fighter 2 makes move B2. Then Fighter 1 makes move A3, e.g.  You get the pairings:

(A1,B2). (A3,B1), (A2,B3)

In the Kendall Tau formula you have two observables X and Y which you order by rank, e.g. in this table:

X    rank(X)    Y   rank(Y)

13     3            2       1

10     2            4       2

5       1            5       3

You have the pairings (13,2), (10,4), and (5,5).

What matters however are the ranks, not the values in this formalism.

So you reorder the table first:

X   rank(X)    Y   rank(Y)

5     1             5      3

10   2             4      2

13   3             2      1

Then you compare the pairings:

(x[1],y[1]) with (x[2],y[2])  :    x[1]y[2]    , i.e. discordant

(x[1],y[1]) with (x[3],y[3]) :     x[1]y[3]    , i.e. discordant

(x[2],y[2]) with (x[3],y[3]) :     x[2]y[3] ,   i.e. discordant

Then you can use the Kendall Tau formula.

I can do the same formalism with the pairings of the fighter game (A1,B2). (A3,B1), (A2,B3), if I know the strength of the moves, i.e.

Fighter 1:  Move A1 is stronger than Move A2 but weaker than Move A3

Fighter 2:  Move B2 is stronger than Move B3 but weaker than Move B1

Then I rank the moves of each player and can calculate the Kendall Tau formula for each fight.

Let's assume this works.You get this sorted table for the above pairings:

A    rank(A)     B       rank(B)

A2    1             B3       3

A1    2             B2       2

A3    3             B1       1

Then you can compare the pairings as I have done above and evaluate how many concordant and discordant pairs there are. Then you can calculate Kendall Tau for each game.

Sometimes Fighter 1 loses, sometime Fighter 2 wins, but what are the values of Kendall Tau? The outcomes depend on the sequence of the moves each player makes.