Is there any reason to advance past rank 20?

Solution 1:

You now get rewards based on how high a rank you achieve:

Highest Rank Bonus

We love receiving feedback from the Hearthstone community. One thing that we’ve been hearing a fair bit of is that, when playing on the Ranked Play ladder, people often feel hesitant to continue playing after reaching a particularly good rank. It simply feels like too much of a step backwards if they lose a rank or two. Based on that feedback, we’re making a change that we think will help put players’ minds at ease so that they can continue enjoying Ranked Play and pursuing even greater heights.

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Beginning this month, each player’s Quest Log will display the highest rank they have reached during the month and recognize their accomplishment. Additionally, we’ll be awarding players who progress past rank 20 with some minor rewards as a way of congratulating them for their achievements. Eligible players will receive a treasure chest at the end of each season containing the season’s Ranked Play card back, one or more golden cards, and some Arcane Dust. What’s in the chest is determined by your highest rank over the course of the season. For example, a player whose highest rank was 17 will receive a golden common card, 20 dust, and the season card back.

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Below is an example of what a player who reaches rank 5 might receive.

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Solution 2:

At the end of the season when the ranks reset, you receive bonus stars based on your rank. Each rank below rank 25 you are, you start the next season with one bonus star, i.e. as if you'd won an extra game. This can even start you below rank 20 for the next season if your rank is good enough.

As well as the card back for reaching rank 20, there are rewards for reaching Legendary rank (the rank after rank 1).

Reaching legend rank during any season will permanently unlock the Legend card back, which is based on the legendary rarity symbol. enter image description here

Rankings are also used for tournament qualification. Certain Blizzard-run tournaments will invite players from each region who reach the highest rank at the end of a season.