Streak Diff ? — Size(s) of Streaks
Visualising the streaks in the previous chapter was meant to provide us with a general idea and a conceptual image of what records of games look like using pixels. We now have undeniable proof that different matchmaking schemes such as PerfectMM, NearPerfectMM and StreakMM yield different patterns. But for those who are willing to investigate deeper, the next logical step would be to observe them with numbers.
The most striking irregularity when comparing patterns from PerfectMM or NearPerfectMM to StreakMM is the length of continued 0s or 1s. The lines in an image are what we would call streaks. Evidently, the sizes(lengths) of these streaks are different in many ways in terms of average(arithmetic mean), mode and maximum. But why ?
How does a streak form ? Paul’s win streak can only start if the immediate game before is also a win. If Paul unfortunately loses, his win streak ends. However for the purpose of pattern analysis, despite its length of 1, even a single win(or a single loss) has to be considered technically as a streak. Every streak is at least of length 1.
*The definition of a streak has been altered in this chapter compared to what it was in previous chapters, for the sake of simpler analysis. Now a streak is strictly a series of consecutive identical events.
For initiation, let us break down five example records of ten games as shown in tables below.
The first of the five tables represent a record of ten games (W, W, L, L, L, W, L, L, W, W). In order, this series includes a win streak of 2, a losing streak of 3, a win streak of 1, a win streak of 2 and finally a win streak of 2. In short, it entails three win streaks of sizes 2, 1, 2 and two losing streaks of sizes 3, 2, all in their respective orders.
The following tables may be fairly easy to understand except the last one. It represents a record of ten games where the results alternate. This creates five win streaks and five losing streaks all with the equal length of 1.
The two last columns of each table attempt to show us the averages and standard deviations of each streak type. However, for tables 2 through 4, it is crucial to note that the latter kind is not calculable in some of our tables as some records only have one streak of each. It is also worth mentioning that the standard deviation of streak size is 0 as all streaks, whether it be win or losing, have an equal length of 1.
Initial Analysis of Streaks from Generated Games
Now that we know how to calculate certain metrics about streaks, one million games were generated for each matchmaking scheme. The following tables show their respective averages, standard deviations, maximum and minimum values.
The key takeaway here is that the sizes of streaks can be different in terms of their arithmetic means and the standard deviations that derive from such means, given that the algorithms used are meaningfully different. This is somewhat obvious as they are designed to produce different outcomes.
Additional Processing of Data
From the histograms above, we see that the distributions for all win streaks and losing streaks are heavily right skewed for all matchmaking variants, resembling a Poisson distribution. This is natural when considering that anything that is not a win streak is a losing streak and vice versa. However it forces us to have only ‘half the picture’ and makes further analysis more challenging. Although there may be methods to address this issue, a simpler fix was devised. Since each pair of histograms are derived from the same run of a million games, the two images can be combined into one histogram, to more of a normal-looking distribution.
A win is a ‘+1’, a loss is a ‘-1’ and therefore a win streak with a length of 5 is a ‘+5’ and a losing streak of 10 games is a ‘-10’. This idea can be implemented by multiplying ‘-1’ to the lengths of losing streaks. Then the same calculations were carried out.
We see that all the averages of streak sizes are approximately 0. Also, the standard deviations have changed from 1.41 to 2.45 for PerfectMM and NearPerfectMM. The same can be said for StreakMM as it has increased from around 3.4 to 4.8. The purpose of the combining was to achieve some degree of normality of data. Despite the absence of values at the zero mark, the distributions of streak lengths now look ‘friendlier’ and more open for further analysis.
For example, F-tests were performed to determine if the given variances are the same or not, as shown in the table below. According to these values, keeping in mind that they may vary depending on the random seeds used to generate the game results, we would have to reject the null hypothesis that the variance in streak sizes from StreakMM is equal to that from PerfectMM (or NearPerfectMM).
Next: Chapter 7
Previous: Chapter 5