Saturday, July 18, 2015

Solo Queue Ladder Analysis: How Long Does It Take for a Season 4 Gold Player to Return to Gold in Season 5?

One way to examine the effectiveness of the ladder is to look at how well a player can retain his rank after a reset. For example, if a player who is Gold is actually worthy of being Gold, we should expect to see this player to keep being Gold (or perhaps higher) after a ladder reset. Today, I am going to present some statistics on how the players' ranking have moved from late January 2015 (Season 4) to early July 2015 (mid-way of Season 5) - roughly a six months period.

First let's see how the players have moved. The table below presents the ladder transition from Season 4 to Season 5 for ~1 million players on the NA server who have ranked solo queue ladder records in both seasons.

For example, we see that after six months, 80.83% of Season 4 Bronze players remain in Bronze in Season 5; on the other hand, 53.94% of Season 4 Platinum players remain in Platinum whereas 10.6% of them are now Diamond or above.

Below is a more visual representation of the transition of these players.

Therefore, we see that more than half of the players who have records in Season 4 and played in Season 5 have retained their original rank (or better) after about six months. While this is interesting by itself, it does not take into account of the fact that many players are below their Season 4 ranking because they haven't played much. So for the next study, we will also take into the number of wins (number of games would be better, but they are not as readily available as number of wins via Riot API) into account. We are interested in, for example, how many wins it takes for a Season 4 Gold player to return to Gold (or higher) in Season 5?

As it turns out, the amount of wins required to return to Gold heavily depends on if the player was, say, Gold 5 or Gold 1. As you will observe below, a Gold 1 player from Season 4 will retain Gold in Season 5 far quicker than a Gold 5 player.

This is time-to-event plot similar to the one I used for the AFK analysis where our event of interest is to retain the same rank (e.g. Gold) from Season 4. The plot shows that the chance of a Season 4 Gold player staying below Gold in Season 5 (vertical axis) decreases as the player wins more games (horizontal axis). In particular, it suggests that a Gold 5 player in Season 4 has about 40% chance of staying below Gold after 100 wins (purple line); for Gold 1 players, this percentage is only about 2% (red line). Overall, as the player goes up within the Gold tier, he is able to more  quickly retain the Gold tier after a ladder reset. I believe this is good evidence that the League system is actually working fairly well.

For some of the technical notes on this entry, click here.

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