To finish in highest league or in a league where you’re competitive?

There have been some people who think that it might be better for a player to finish in a league where they are highly competitive rather than to push for the higher league where their win rate might drop.
As an example, a player has a choice to finish the Season at either (i) Gold 1, or (ii) at Diamond 3.
The rationale is that if they finish at Diamond, then after the Season reset, they will spend a lot of time at Gold, and their wins at Gold will net them very few Diamond reward chests. Worst case scenario – they spend the entire season at the lower level.
So, in short, the hypothesis is that if you’re competitive at Gold level, then you are better off winning more Gold chests than winning relatively few Diamond chests.

Let’s start by examining the relationship between the number of reward shares and end of season (EOS) chests obtained.
The splinterland team only gave 4 data points describing the number of Rshares required to get {1, 10, 50, 100} chests. But, as the figure below shows, a cubic model appears to fit the data well. Given a cubic relationship, it becomes increasingly difficult to qualify for each following reward chest.

Indeed, it clearly will be EXTREMELY difficult to win 150 Season reward chests.

The model used in in the Figure suggests you’d need roughly 24 million RShares to get 150 Gold chests and 35 million Rshares to get 150 Diamond chests!
This equates to 1850 wins to get 150 Gold chests & 1020 wins to get 150 Diamond chests respectively (i.e. the higher league requires fewer wins per chest). The #win calculations assumed no bonuses for Guild/Alpha/GF cards. The #wins required scales back proportionate to the bonus level.

How does time at the lower level affect results?

We can examine different scenarios where a player spends most (or all) of their time at Gold compared to a player that quickly regains their Diamond league level in the new season.
Let’s make a few assumptions:

1. The player has Gold level summoners (level 6) and so, in my experience, the win-rate between playing at high level Gold and low-level Diamond is not that different. I will assume the same win rate for each league.
2. The player wins 20 games/day.
3. No bonus rate is applied.

The following table looks at how many reward shares would be won if they player took between 1 and 15 days to regain their Diamond level.

• Row 1 is the scenario where all 15 season days were spend at Gold. Conversely, the final row (row 15), is when the player regains Diamond league status after just 1 day.
• Column 5 shows the total reward shares the player would get, broken down by their time in Gold (column 3), and Diamond (column 4).
• Columns 6 & 7 shows, respectively, how many Gold & Diamond reward chests they’d get for each level of Total Rshares.
o E.g. if theplayer spent 11 days in Gold and 4 days in Diamond (and assuming) they won 20 games per day, they’d get either 83 Gold chests (if previous season high was at Gold) or 63 Diamond chests.
o Clearly, for any set level of total season RShares, the player would obtain more Gold chests (i.e. they finished the previous season at Gold) than Diamond chests.

Key results of the table are plotted in the following figure.
Here, the horizontal blue lines show the number of Rshares obtained at different proportions of time at Gold:Diamond. For example, the top horizontal blue line shows the estimated number of Rshares won if the player spent only 2 days in Gold and 13 days in Diamond. The intersection of this horizontal line shows that such a player would win either 104 Gold chests or 83 Diamond chests (depending on how they finished the previous season).

So which strategy is better for earning?
I will use the chest values estimated by Tales of the Cryptmancer (ToC) in his excellent video:

Based on the stats that Splinterlands released, ToC estimated that (after the reward rework), each gold chest will be worth approximately $0.78, and each Diamond chest will be worth approximately $1.51.

Using these amounts, EoS Rewards (as $) are shown in the final 2 columns of the following Table. These columns represent the amount won dependent on whether the previous season was Gold (column 6) vs Diamond (Column 7).

In every instance, it is better for the previous season to be at Diamond .. even if you never make it bacl to Diamond in the current season (i.e. all 15 days are sepnt in Gold).

I know I made some assumptions - the key one being the same win rate .. but I believe the differences in the amount ($) won is large enough that it seems unlikely that win rates would alter the fact that seems better to go for as high as you can.
Even if you NEVER regain your former league (e.g. you stay in Gold) the fewer Diamond chests are worth more than the Gold chests.