The goal

One of the questions I find myself asking often in splinterlands is whether an investment is worth it. And a card is an investment just like any other. If you buy it to rent it out, determining its ROI is simple: how much did you pay, and how much on average is it renting for.

For ranked matches, this is much harder to determine, since each card is only used occasionally, you might lose to RNG, and its resulting effect is hard to disentangle with the ELO ranking we use is splinterlands.

What follows is my attempt to develop a system to quantify the ROI from a single card, given the current state of one's collection. I will then show the results in practice for a card I've had my eye on for a while: Conqueror Jacek. Ideally, this is something I'll continue to iterate on moving forward and continually evaluate cards.

The method

The general idea for the strategy is to isolate the effects of a single additional card on my overall ranking and rewards. To do this, I will rent a single card for 2 days, and make no other changes to my deck during that time. I will then observe how many wins I get with the card, converting that into a quantifiable value, and compare that to the cost of card. This will give an approximate ROI.

First, there are some components that I think are necessary for this to work:

1. A botted account. This only works if choosing cards is objective, and a bot is exactly that. Otherwise, I might want a card to perform well and will use it often. I use ArchMage (and highly recommend it!), but any botting service will do.
2. 0 changes to the deck during each 2-day period. If any changes are made (e.g., selling a card), it will make the effects of the card in question harder to isolate.
3. A relatively-stable economy. The ROI calculation will depend on the average daily earnings and overall account value. If those change too much in a short period of time, these calculations will not be terribly meaningful.

Assumption 1 - Every win is due to the card in question

If the card is used in a battle, and the battle is won, I will assume it would have otherwise been a 50/50 toss-up without the card in question. This is a strong assumption that puts the card in the most favorable position possible. On the flipside, if a card cannot prove its worth under these circumstances, it is definitely not a good buy.

Assumption 2 - The value of a win

Calculating how much a single win is worth is a bit tricky. It has two components - the immediate component of SPS, RP, and chest progress and the long-term component of higher ranking.

The value of the first component (SPS+RP) I will value at 2 SPS ($0.054 at time of writing) for the win and given I win ~10 daily chests with ~25 wins in a day, I will add 10/25 the median value of a diamond chest ($0.103 at time of writing). This is $0.157. However, since the baseline chance of winning the battle was 50%, the card only "earned" half of this, or $0.0785.

The second component is a little harder. I am going to assume each win will, during the season, lead to getting to Champion league one battle sooner, so I'll add on 50% of the rewards of a Champion victory: 0.5(SPS: 50.027=$0.135, 40% of a Champ chest: 0.4*0.585 = $0.234)= $0.1845.

In total then, I will assume every victory with the card in it equals $0.263 in rewards. Since we'll have the card for 2 days, we'll take the number of wins with the card, and multiply $0.26 by the number of wins with the card and then further by 180 for the year to get its total return for a year. We then divide this by the cost of the card to get its ROI.

Assumption 3 - Is the card worth it?

Now that we know the card's ROI, we need to decide if it is worth buying. In other words, what value of ROI does it need to cross to be worth considering? This baseline ROI is the ROI currently earned by an account.

Historically, my account has been worth ~$4k, and earns ~$91 per season, for a yearly ROI of 59% (see my post on this here).

However, cards have been going up in value and I recently added some CL and RW cards to my collection, and it is now worth ~$8000. If my rewards stay the same value, my current ROI is ~33%. As I showed in the previous article, I could also rent cards for ~40% APY. So any card I am considering buying needs to have an ROI >33-40% under this metric to be worth it. (I'll likely opt in favor of not buying the card if something is right on the cusp, given how favorably my assumptions are for buying the card.)

This effectively means that for every $117 of card price, it needs to result in 1 additional victory to be worth it. Anecdotally, I recently purchased Immortalis for ~$150, and it wins multiple battles every day, more than earning its ROI (Earth is really good in reverse speed and Immortalis is good in anything favoring magic, so he comes up somewhat regularly).

Limitations

This approach is of course not perfect. As I said, this is a much more complicated process than determining the ROI from renting, as it is dependent on so many other things. Although I am generally happy with this approach, there are two major limitations I want to explicitly mention.

1. Specific per account. The results from the test will be wholly dependent on what deck you already have. As an extreme example, if you rent Chaos Dragon but have no Dragon summoners, you will of course get 0 return from that Chaos Dragon. But if you have a whole dragon deck, that Chaos Dragon might help you win some additional high mana fights. The takeaway from this is that any findings I post should be taken with a grain of salt when it comes to your deck. Hopefully the approach is easy enough for you to do yourself, and so these posts will illustrate the method, if not a universal rating of cards.

2. Sample size. Because of the HUGE number of possible rulesets, the many cards available, the variability of your opponents, etc., the sample size needed to accurately identify the individual contribution of a single card is enormous. Probably in the 1000's of battles. And here we're going to be doing ~100 per card. So it's possible some cards' results will be swayed by random chance (e.g., the ruleset a card excels in never came up, so it looks like it had 0 value). So these results, even for my deck, are not definitive and I will likely reiterate down the line. But I think 100 battles will be enough to get an idea, especially since I'm not starting from 0 knowledge - this will be more akin to a Bayesian updating of priors than a true Frequentist baseline. One thing I will do if I do buy any cards based on the evaluations here is monitor them over time as well to see if they continue to perform similarly, or if the first 100 battles were a fluke.

The first test - Byzantine Kitty

I want to start this method off with the big one. My gut is that yes, Kitty will win games, but is too expensive to make up for it. Using the numbers above, if Kitty costs $2600 for a max copy, it will need to win 22 matches in a 48 hour period to give at least a 40% ROI. Given that you win ~50% of matches, and that Dragon is available in ~50% of matches, and that ~50% of matches are a high enough mana value for Kitty to be worth it, even if kitty is used every time this happens, it will likely lead to ~12 wins, only about half of what it needs to to earn its keep. So my baseline expectation is that Kitty will not be worth the high cost even if it helps me win a large number of battles.

How did it do?

I rented Kitty for 2700 DEC/day on 25 Jan for 48 hours. In that time, I played 100 games, and used Kitty in 17 of them. Of those, I won 13. So over a year, Kitty would be expected to return 13180$0.263=$615.42, for an ROI of 615.42/3300=19%. This is less than the 44% I could get putting $3,300 into an SPS LP. It's also less than the 30-40% I could get buying and renting $3,300 worth of cards. It's even less than just buying and staking $3,300 of SPS.

So Kitty, while probably the single best card in the game, is costed appropriately. Even using it ~20% of the time and winning 13 matches, it is too expensive for it to pay for itself. Cheaper cards, while individually less impactful, will likely yield much better results.

Feedback and future cards

So that's my strategy. I'm going to use this now that my deck is pretty complete with the cheaper cards and I don't want to spend $150+ without a good reason. I'll probably run through the CL legendary summoners next, but also want to hear from you! Which cards should I evaluate? Anything I should change in my approach?

Referral

Want to participate in Splinterlands? Want to try adding cards to your collection (although I recommend not starting with Kitty)? Use my referral link and I'll hook you up with some cards and DEC to get started: https://splinterlands.com?ref=badrag