by caliban // May 6, 2021
Hey all, it's your occasional Goldfish analytics article from caliban. This time, we're going in depth on whether it's worth it for youto play in the current Arena Open (and any future ones, unless theychange the prizes or entry fees.) Note that we're working with probabilities, so of course nothing is guaranteed for you personally, we can only calculate the odds and the average results.
Arena Opens are probably the most exciting events on Magic:The Gathering Arena (MTGA) that anyone can join. To make day 2 in a Sealed Open, you need7 wins before 3 losses in Bo1Sealed -or- 4 wins before any losses in Bo3 (Traditional) Sealed. On day 2, it's a new Bo3 Sealed pool, and if you finish with6 wins and2 losses, you win $1000, and if you manage 7 wins before 2 losses, you win $2000! There's also a decent amount of gems for lower places on day 2.You can find more specific information about the prizes from Wizardshere.
Frank Karsten analyzed Arena Opens last year here, and found that your expected value (EV) was positive if you had ~52% win rate in the format. That's strikingly low! To have a positive EVin other MTGA limited events, you need much higher win rates - Traditional draft ~62%, Premier draft~66%, and Quick draft ~75%. These other events also providereward packs to grow your collection, which we don't have for the Open, but most players do lose gems in them over time.
Just so everyone's on the same page, here's how you can think ofthe EV for this event. If a large number of players with 52% win rates in the format all entered, and you subtracted all their entry fees and added all their winnings, it would average out to$0-$1 per player. That's the EV for a 52% player. Of course, a lot of 52% players would have lost a small amount, and a smaller number of them would have won a large amount. That may sound discouraging, but that doesn't mean you shouldn't enter! IfEV is positive, in most cases it's worth itto enter an event. You won't get that many chances to enter into events with this high EV, so you should take advantage, even if the most likely result isn't winning $2000.
My analysis agrees with Frank'sand goes a little further. (Though Frank did some more analysis I can't see it because it'sbehind a paywall) I created a Google sheet that calculates the EV, based on three variables.
- Entry Fee: Gold, Gems, Gold (Std), Gems (Std). Right now, we're talking about Sealed Opens, which are 500 more gems than Standard Opens, but this same analysis applies to all of them. This is one of the only limited events you can enter with Gold at a 5-1 ratio, so take advantage of that.
- Tax Rate: 0-50%.Since we're working with both dollars and gems, we needto convert between them, and the value of gems depends on your local tax rate. I live in a state with 10% tax, so it's 181.8 gems per dollar.
- Day 2 Match Win % Decline: 0-10%. Competition on day 2 will be more challenging. There's no easy way to measure it, but we can look at data from MTG Elo project to at least get an idea. Top 100 pros average out to a -3.5% match win rate decline between GP performance and Pro Tour performance. That comparison's not the same as this event, and I'm not claiming it is, but it's at least a ballpark value for going from "anyone can join" tournaments to "elite" tournaments. I'm sure I personally decline more than top pros, so Iset mine at -5%. (Note: Except for this "decline", all other win rates in this article are game win rates. When needed, we useyour game win rate to calculate your equivalent match win rate. Because day 2 is only Bo3, it made more sense to adjust your match win rate for that day directly.)
The first two variables (Entry Fee, Tax Rate) barely effect EV for high win rates, but they do impact EV more strongly for low win rates. The third variable, which we can only guess at, does have a large impact across the board. If your win rate is 70% and your decline is 0%, your EV is ~$1000. But with a 10% decline, your EV drops sharply to ~$275.
Let's take a look at a single run (which is what Frank Karsten looked at in that initial tweet).
I only looked at win rate from 50-70%. Below 50%, you probably should not enter this event. Above 70% in this event, you're probably already in the MPL.
So for example, I calculated my win rate in Strixhaven limited as 62%. That means that I can expect my single Bo1 run to have a 27% chance to qualify for day 2, or 21% for a Bo3run. I would expect on average to play 7 games in Bo1 or 6 in Bo3. I would expect to get back almost 1200 more gems on average in a Bo3 run, but that comes with a lower chance to qualify, so if I wanted to keep going, I'dhave to do more runs, on average. Iwould have anEV of $53-$64, for Bo3 and Bo1, respectively.
More interesting is examining "doing runs until you qualify,"which is how I assume many of us will approach it.
Here, at my 62% win rate, I need to do 3.7 Bo1 run to qualify, or 4.8 Bo3 runs to qualify, on average. The EV is much higher (since we assume you willeventually make day 2), and this time Bo3's EV is the slightly higher one, $238-$253. I can expect to play 4 more games on average to qualify via Bo3. Of course, this assumes an unlimited amount of time (and gold) to qualify, and that's not really the case. Although you do have 21 hours to enter, and that's enough time for a lot of runs. Some with 62% win rate will qualify on the first run - some will on the 8th run or later, there's no guarantee. But on average, it'll take about 3.7 runs.
Bo1 vs.Bo3
Wizards did a pretty good job of balancing the overall EV for Bo1 and Bo3. But no matter how you slice it, Bo1 is superior for several reasons.
- You have a higher chance of qualifying each run. For me, this is themost important factor.
- Though you lose more gems each run, you need to do less runs overall, and play less games overall.
- The extra amount you lose in entry fees pales compared to the value of making day 2.
- The variance of losing your first match can make Bo3 very frustrating, though of course Bo1 has its own variance to consider.
If you are on an extremely limited budget (you can't easily spend $40-$120 of MTGA currency),you couldconsider Bo3, as on average it gives you more gems back to qualify. But really, if yourbudget is that limited, you probablyshouldn't enterthis event at all. You need to be able to roll with some variance to qualify for day 2, which is where the big rewards are.
Gold vs. Gems
As I mentioned, this is one of only 2 limited events MTGA has where you can spend gold at a 5-to-1 ratio. (The other being Challenge draft, which so far was only for Kaladesh Remastered.) If you have gold, spend all of it before spending gems. Essentially, the 22500 gold entry fee is the equivalent of spending 3375 gems, instead of the normal 4500 gem entry fee. You save more than 1100 gems each run just by entering with gold! That really makes it a lot easier to qualify without losing too much value, even if your win rate is ~52-58%. There's really no reason to not spend gold on this event, we've never seen a ratiobetter than 5-for-1.
Explore the numbers yourself!
If you're read my analytical articles before, you know I won't leave you with just a couple ofimages of spreadsheets. No way, I love giving you access to these kind of things, so you can enter your own tax rate, and guess at your day 2 decline, and generally play around with it and see how the EV changes.
This should open a folder on my g-drive. Click on the Google sheet named "Arena Open Calculations v1.0" in this folder and right click. Select "Make a Copy". Now you should have a copy on your g-drive that you can mess around with to your heart's content. (It does require you to have a Google account of some kind, sorry.)
The Bottom Line
- While previously the break even point (where you have positive EV) was 52% win rate, if you include a reasonable-guess 5%decline on day 2, it becomes 54%. That's still extremely low! Even if you go allthe way up to a 10% decline (which seems high), it's still a positive EV at 57%win rate.
- In general, you should already betracking your win rate, either via your own spreadsheet, or an arena tracker like 17lands. You want to be confidentthat your win rate is at least 54% in Strixhaven limited before committing to play until you qualify.
- Even if your win rate is 50-53%, and therefore your EV is slightly negative, if you have some extragold you might want to try 1-2 runs to see if you can get lucky and qualify. I wouldn't say that I'm endorsing this, but ifyou're otherwise going to spend that gold on different MTGA limited events with worse EV, it's worth considering.
- Always enter with gold. Use every single bit of gold you have before spending any gems.
- Always play Bo1, unless your priorities are different than the typical Arena Open player (who wants to qualify as fast as possible, and is willing to spend $40-$120 in MTGA currencyto qualify.)
- There's no easy way to account for the level of competition on Day 1, and it's unclear thatcompetition will bethat much different than the"normal" events you used to calculate your win rate. Probably a bit tougher, but it's hard to say. Just use your previously calculatedwin rate.
- Though it may be counter-intuitive, note that you're actually much more likely to win $2000 than $1000 on day 2. There's more ways for it to happen, and obviously, it's more likely you'll sweep as your win rate goes up. At 50% win rate, you have a 2.75% chance of going 6-2 on day 2, and 3.5% chance of going 7-0 or 7-1. At 70% win rate, you have a 7.5% chance of going 6-2, and a whoppinga 45% chance of going 7-0 or 7-1. (This all assumes no day 2 decline.)
I hope this helps you decide whether the Arena Open is right for you.If you're aStrixhaven limited player with a 50%+ win rate and some extra gold and a free Saturday, it likely is. Good luck to everyone in the Arena Open!
