How many more ? Are We THERE Yet ?
Paul, currently sitting at Gold 3 0lp, wants to make it to Emerald 1 in Split 2 of Season 2023. This requires an additional 1000 lp gain. Supposing every win yields 25 lp and every defeat deprives him of 25 lp, the same amount, he approximately needs a surplus of 40 (= 1000 / 25) games won. So, with the win rate from Chapter 2, how many games would Paul need to play ?
For a simple start, let us look at another fictional player, Chris. He somehow has a magical win rate of 100%. This means that in order to achieve that 40 net matches, he only needs to play 40 times. Obviously, this is not hard to grasp but how should we form this into a formula ? The answer is the amount of net games won(N) divided by a denominator that is equal to double the win rate minus one (2wr -1) or N / (2wr — 1). If an incompetent player such as the person writing this with a win rate of 0% were to attempt it, the journey would never end as the resulting value would reach negative games (40/-1 = -40) suggesting that he should quit. If Thanos, with a perfectly balanced win rate of 50%, were to play, his saga also would not end as the denominator equals zero ( = 2 x 0.5 -1) and the number of games required would reach ‘infinity’ (plus, one should not try dividing anything by zero).
So what of Paul ? At least Paul boasts a win rate of 50.74%. It being somewhat above the threshold of 50% or 0.5 is crucial as it means that he can stack wins over a certain number of total games played. In this case, it equates to 40 / ((2 x 0.5074)-1) which yields 2701.2793 games. To make up for marginal errors, we may safely assume that he needs to play around 2710 games.
Just for the sake of fun, let us interpret these results. If we assume that each game is 30 minutes long on average and multiply 2710 games by 0.5 hours per game, it would give us 1355 hours of playtime. Also, given the current two splits per year system, with the second one being around 168 days, we need to play 16.1309 games per day without skipping.
If the ranked system wanted to mitigate the efforts required for this climb, certain measures may be implemented to make it easier for a regular player to reach up to 10 ~ 15 net games won. This would result in values ranging approximately(simply adding 10 for padding) from 1700 to 2035 games that need to be played after such checkpoint or ‘plateau’.
Also, for the purpose of moving forward, it is worth noting that, supposing that a game usually lasts 30 mins, one cannot play more than 17,520 (2 x 24 x 365) games in a year. It is physically impossible to do so as this number was calculated assuming one plays non-stop around the clock for 365 consecutive days. It may also be safe to say that, while generously rounding this number to 18,000 and dividing it by 2, one cannot play more than 9,000 games per split in a two-split per year system (or no more than 6,000 games in three-split per year setting).
Next: Chapter 4
Previous: Chapter 2