win_loss_analysis.m

function win_loss_analysis(rank_at_game, label, win_rate_average_half_length)

if nargin < 3
    win_rate_average_half_length = 20;
end

n_games = length(rank_at_game);
result_at_game = zeros(1,n_games);
streaks = zeros(1,n_games);
streak_count = 1;
last_result = true;

%Get rank vs game, streak counts
for n=2:length(rank_at_game)
    %ignore draws
    if rank_at_game(n) == rank_at_game(n-1)
        result_at_game(n-1) = 0;
        continue;
    end
    if rank_at_game(n) > rank_at_game(n-1)
        win = true;
        result_at_game(n-1) = 1;
    else
        win = false;
        result_at_game(n-1) = -1;
    end

    if (win == last_result)
        streak_count = streak_count+1;
    else
        streaks(streak_count) = streaks(streak_count)+1;
        streak_count = 1;
    end
    last_result = win;
end

figure
plot(rank_at_game);
xlabel('Game Number');
ylabel('Skill Rating');
title(strcat("Skill Rating vs Game, ",label));
figure
errorbar(streaks/n_games, sqrt(streaks)/n_games);
xlabel('Streak Length');
ylabel('Number of Streaks / Number of Games');
title(strcat("Streak Frequency, ", label));
axis([0 25 0 0.5])

%get win probability by rank, sort by SR, then do a smoothed average, then
%fit
[sorted_rank_at_game, indices] = sort(rank_at_game);
q= result_at_game';
sorted_result_at_game = q(indices);

win_rates = zeros(1, n_games - 2*win_rate_average_half_length);
win_ranks = zeros(1, n_games - 2*win_rate_average_half_length);
win_rate_index = 1;
for i = win_rate_average_half_length+1:n_games-win_rate_average_half_length

    win_tot = 0;
    for j = i-win_rate_average_half_length : i+win_rate_average_half_length
        win_tot = win_tot + (sorted_result_at_game(j)+1)/2.0;
    end
    win_rates(win_rate_index) = win_tot/(2*win_rate_average_half_length + 1); % 0 to 100 percent
    win_ranks(win_rate_index) = sorted_rank_at_game(i);
    win_rate_index = win_rate_index + 1;
end

ft = fittype( '1-.5*(1+erf((x-a)/(b*sqrt(2))))', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.Lower = [0 1];
opts.StartPoint = [2500 400];
opts.Upper = [5000 5000];

[fitresult, gof] = fit( win_ranks', win_rates', ft, opts );
coeffs = coeffvalues(fitresult);
mu = coeffs(1);
sigma = coeffs(2);
pd = makedist('Normal', mu, sigma);

for i=1:5000
        dist(i) = 1 - cdf(pd, i);
end

% Plot fit with data.
figure
hold all
plot( win_ranks', win_rates', 'DisplayName', 'Data' );
plot(dist, 'DisplayName', 'Fit');
legend( '-DynamicLegend' );
xlabel('Skill Rating');
ylabel('Win Probability');
axis([0 5000 0 1]);
title(strcat("Win Probability vs Skill Rating, ", label));
newline = sprintf('\n');
txt = ['mu = ', num2str(mu,4), newline, 'sigma = ', num2str(sigma,3)];
text(500, .1, txt);

%auto correlation function calculation
ac_length = 10;
ac_count = zeros(1, ac_length*2+1);
ac_error = zeros(1, ac_length*2+1);
ac_func = zeros(1, ac_length*2+1);
ac_func_sq = zeros(1, ac_length*2+1);
for n = 1:n_games
    for m = n-ac_length:n+ac_length
        if m > 0 && m <= n_games
            if(result_at_game(n) == 0)
                continue;
            end
            ac_count(m - n +ac_length+1) = ac_count(m - n +ac_length+1) + 1;
            if(result_at_game(n) == 1)
                ac_func(m - n + ac_length + 1) = ac_func(m-n+ac_length+1) + result_at_game(m);
            else
                ac_func(m - n + ac_length + 1) = ac_func(m-n+ac_length+1) - result_at_game(m);
            end
            ac_func_sq(m-n+ac_length+1) =  ac_func_sq(m-n+ac_length+1) + result_at_game(m)*result_at_game(m);

        end
    end
end

for n = 1:ac_length*2+1
   ac_error(n) = sqrt(ac_func_sq(n) / (ac_count(n) - 1) - ac_func(n)*ac_func(n)/(ac_count(n) * (ac_count(n)-1))) / sqrt(ac_count(n));
   ac_func(n) = ac_func(n) / ac_count(n);
end

figure
ac_func_x = -ac_length:ac_length;
errorbar(ac_func_x, ac_func, ac_error);
xlabel('Game Differential');
ylabel('Auto Correlation');
title(strcat("Win/Loss Auto-correlation function, ", label));

end