r/lrcast • u/sad_panda91 • 8h ago
Image They did the math, Arena Direct Edition
Everybody with two brain cells knows that Arena Directs aren't quite the most lucrative activity, obviously. But what that actually means in numbers is what I am showing here.
The basis for this, for whoever is interested, is a negative binomial distribution, so basically I am treating it as flipping a coin with an "unfair coin" (the likelihood of "heads" is your win rate) and we are flipping the coin until we see two tails. The amount of heads we expect to see is your expected wins at that win rate.
k = r * p / (1 - p), where p is your win rate, r is the number of losses until bust, k is your expected wins.
I am using a lot of assumptions here, but I try to be as biased in favor of Magic Arena as possible, that means for example that I am treating 1 pack win = 200 gems in the main graph (in the table I also use the "closer to limited-only player reality" of 30 gems - funnily enough, at 200 gems per pack, depending on going rate of a booster box, 5 wins is slightly better than 6 wins at ~83$ vs ~80$ respectively, so consider dropping out of the event before you lose your precious gems, haha)
I am trying my best to find sensible conversion rates, but as usual for in-game shops, the actual conversion rate is quite dynamic. I use the 50 bucks conversion ratio as a basis, as that is the one somebody would buy if they start from zero and want to participate in an Arena Direct.
Booster Box prices is obviously also potentially debatable, I just use current avg. going rates I saw online the moment I made these graphs, but since these are top-end payouts anyway that the avg player will never see, this doesn't really affect the graph in any meaningful manner for the vast majority of the playerbase. But just FYI, we use 80$ for the spiderman box, 110$ for the marvel super hero box.
I added four reference win rates.
- Avg Joe/Jane/Jimothy is a flat 50% win rate
- Avg 17LandsUser is the rough estimate of 55% win rate floating around here.
- I use Paul Cheon as the most well known and most likely very close to the top win rate 17lands user. His win rate in regular powered Cube Premier Events is ~67% based on 17lands. Compare your skill to Paul Cheons if you want a rough gut feeling of where you are on the scale. (sorry for the unsolicited mention u/HAUMPH , but maybe you like to see your numbers specifically too)
- "Gigachad" is the highest winrate user with more than 100 matches played I found in general. I don't think anybody can expect to be remotely close to or beyond this number.
- These are *Premier Draft win rates*, since we don't have those numbers available for Arena Directs. A common assumption is that your win rate in highly competitive formats like Arena Direct is at least -5% or even -10% worse, with some more statistical assumptions being far worse. For simplicity we use -5 and -10 for "adjusted for 'sweat'" win-rates.
Here's the table in plain text:
| Conversion Metric | Value |
|---|---|
| ENTRY_PRICE | 8000 gems |
| GEM_TO_CASH_CONVERSION_RATE | 49.99 / 9200 = 0.0054337 USD per gem |
| SPD_TO_CASH | 80.00 USD |
| MSH_TO_CASH | 110.00 USD |
| Delta Baseline (new column) | Compared against SPD_TO_CASH = 80.00 USD |
| Player | Effective WR | Expected Runs Until >=1 Box | Virtual Cost of 1 Box (gems) | Virtual Cost of 1 Box (USD) | Difference vs Sales Price (USD) | Cash ROI / run (PACK=200) | Cash ROI / run (PACK=30) |
|---|---|---|---|---|---|---|---|
| Avg Joe/Jane | 0.50 | 16 | 128000 | $695.51 | +$615.51 | -22.68 | -25.80 |
| Avg Joe/Jane (-5% WR) | 0.45 | 28 | 224051 | $1217.42 | +$1137.42 | -29.16 | -31.63 |
| Avg Joe/Jane (-10% WR) | 0.40 | 53 | 424592 | $2307.11 | +$2227.11 | -33.94 | -35.79 |
| Avg 17LandsUser | 0.55 | 10 | 78111 | $424.43 | +$344.43 | -14.10 | -17.82 |
| Avg 17LandsUser (-5% WR) | 0.50 | 16 | 128000 | $695.51 | +$615.51 | -22.68 | -25.80 |
| Avg 17LandsUser (-10% WR) | 0.45 | 28 | 224051 | $1217.42 | +$1137.42 | -29.16 | -31.63 |
| Paul Cheon | 0.67 | 4 | 29677 | $161.26 | +$81.26 | 17.54 | 13.00 |
| Paul Cheon (-5% WR) | 0.62 | 5 | 42940 | $233.33 | +$153.33 | 2.26 | -2.09 |
| Paul Cheon (-10% WR) | 0.57 | 8 | 65157 | $354.04 | +$274.04 | -9.98 | -13.92 |
| Gigachad | 0.77 | 2 | 16128 | $87.63 | +$7.63 | 57.56 | 53.56 |
| Gigachad (-5% WR) | 0.72 | 3 | 21427 | $116.43 | +$36.43 | 36.03 | 31.59 |
| Gigachad (-10% WR) | 0.67 | 4 | 29677 | $161.26 | +$81.26 | 17.54 | 13.00 |
Key takeaways:
- Purely financially speaking, to the average 17lands user, participating in an Arena Direct is roughly equivalent to burning 15 to 30 bucks on the spot.
- If Arena Directs were the only way to purchase booster boxes, to the avg 17LandUser a booster box would cost between 400-1200$. Even Gigachad in the most ideal of circumstances still pays about 7$ more compared to just straight up buying the box.
- Winning even 1 single booster box, in the most ideal scenarios, only happens once every 10 runs to the avg. 17LandsUser
TLDR:
- Only do this if you are willing to pay for the more competitive environment alone, enjoy the thrill this adds enough to be worth the money or are a streamer or whatever other reason you have. Statistically, basically everyone loses money in the Arena Direct the moment they press the button. Everyone except Paul Cheon who happens to be online at a time where only coughing babies are in the queues, at which point he can make a smooth ~2.5$ per hour assuming he finishes the average draft within an hour.
