Visualising Streaks (for the sake of our eyes)
What now ? This may as well be the question that I pose myself as I try to fathom the complex situation that I got myself into. We may have established that streak matchmaking yields more healthy-looking win rates above 50% (approximately 52~53%) for most players. Under the hood, it does lead to a higher average number of games played compared to matchmaking with no streaks given the same level of targeted win rate. Yet disappointingly, this is still somewhat of a speculation as we cannot see what really goes on in terms of how and which metrics that players produce are processed and utilised.
Fortunately, there is something else we can do if we are curious enough. No, we cannot ‘look inside’ and start from the origin of the question of whether streaks actually exist or not. But we can start from the very results and work our way backwards to the origin. Yes, it is not a direct approach when compared to the former, however it is the next best thing.
By tweaking the codes used until now, a certain number of game results for a certain number of players were created for each type of matchmaking; Perfect Matchmaking(PerfectMM), Near-perfect Matchmaking(NearPerfectMM) and Streak Matchmaking(StreakMM). This time, the emphasis while generating the records were not on when they would reach the required net amount of games won but the total number of games played. Each record per player would be represented as a series of 0s and 1s where ‘0’ signifies a loss and ‘1’ a win, resembling something like a Python list (eg. [1,0,0,1,1,1,1,0, … ]).
One thousand games per player across one thousand players were generated five times each with different random seeds for each of the three matchmaking types. This amounts to a total of 5 million game results generated per type. However, because data structures such as a list, an array or a matrix are difficult for our human eyes to comprehend, another form had to be devised strictly and simply for the sake of better understanding via our human eyes.
Step 0.
Pixels (height x width)
A given series of N results of a player is to be visualised in the form of a rectangular (or a square) image as below.
The white pixels in an image represent 0s or defeats whereas black pixels mean 1s or wins. The image on the left above is from a series of 100 games with alternating results starting off with 0 (0,1,0,1,0,1, …). The one on the right resembling a chess board is similar but with every 10 games, the results swap places (0,1,0,1,0,1,0,1,0,1 => 1,0,1,0,1,0,1,0,1,0).
Each of the three images above are what a series of 300 games(of 1,000 games) may look like in a 20px by 15px setting. As labelled atop each plot, we may or may not be able to ‘feel’ or verify the difference in patterns with our naked eyes. For example, the image on the left and the one in the middle may look ‘different’ only to some extent. However, the rightmost picture resulting from streak matchmaking certainly does show an apparent discrepancy when compared to the other two. It clearly illustrates longer contiguous lines of pixels, either coloured white or black more frequently.
Next: Chapter 6
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