News : Parents, talk to your kids about Expected Value

Parents, talk to your kids about Expected Value


By Neil T Stacey


With the end of the old PTQ system and no way to qualify for the Pro Tour on the entire continent, South African players with Pro Tour aspirations are forced to look at overseas travel as a serious option. The elephant in the room is cost. From the perspective of a South African player, the cost of international play is exceedingly high, and the returns just aren’t that great. Two options exist, as far as international travel are concerned; RPTQs and GPs. So the question is how these options stack up in terms of Expected Value.

EV for a particular course of action is determined by multiplying the benefits of the possible outcomes resulting from that action by the probabilities of those outcomes. Adding those together and deducting the cost of that action lets you come up with a long-term average benefit for any particular course of action. In this case, there are a lot of intangibles that can’t be quantified directly, so I will add up the expected tangible benefits and costs, and allow the reader to decide what the intangibles are worth to them.

I used to do some rough calculations to get an idea of the cost of a trip to Europe for a big tournament, and found that travelling to GP Copenhagen, with a cheap hotel room for Friday night and Saturday night, would cost somewhere in the vicinity of $900. Entry fee for the tournament, which is Modern format, is 400 Danish Krone, or around R700(!). Visas are 30 Euro, so our hypothetical GP traveller is already forking out around R12 000 so far, without the cost of transport around town and food. Let’s assume our hero walks a lot and doesn’t eat much, and partially offset these costs by assuming that he/she would have been spending some of that money anyway if they were at home. This gives a neat round-number estimate of R12 500 for a bare-bones trip without few frills and not much free time.

For the truly adventurous, it is possible to cut costs by spending only one night in a hotel, but that would entail sleeping on the plane during a Friday night flight and arriving on Saturday morning ready to play. Doable, but rough.

So what exactly is our hero getting for that R12 500, in terms of expected value? For GPs with attendance between 1200 and 2399 players, total prize payout is $44 000 which corresponds to an average payout between $18 and $37, depending on the exact attendance.  At Copenhagen you also get a sweet Kiki-Jiki playmat and a promo Griselbrand, so there’s that.

But that’s not what we’re about. If we’re flying to GPs, we are aiming to go deep, get on camera, and qualify for the Pro Tour. So what are the odds of managing that? Wizards has generously helped us with this calculation by simplifying the qualifying criteria. Rather than giving PT qualification based on placing, it’s awarded to everyone with a record of 13-2 or better.

Let’s assume that our hero is better-prepared for this tournament than the average player in the room. With how much it has cost to get there, he or she had better be. Generously, we can assume a 55% win rate. This is pretty good at GP level, particularly for someone who rarely gets to play tournaments of this sort.

If our hero has two byes, then he/she has a 2.69% chance of a 13-2 record and a seat at the Pro Tour. I used a binomial coefficient to work this out, for those interested. Under the same assumptions, expected payout increases as well.

Predicting the expected payout is tough because there are a number of unknowns affecting the relationship between record and placing. Fortunately, Frank Karsten wrote an article a while ago where he compiled historical data from previous GPs to get a good estimate of the correlation between record and payout. That article can be found here: I implemented Frank’s methodology to predict our hero’s expected payout and it’s up to $121, which at least covers entry fee plus a little profit.

Without byes, this scenario is much uglier with a 1.07% chance at making the Pro Tour and an expected payout of $70.

From a cash standpoint, playing Magic at all doesn’t make a lot of sense, so let’s look at what’s really important; how much is playing at the Pro Tour really worth to you? If we deduct value of playmat and promo as well as average prize payout from our expenses then, with byes, from a purely economic standpoint our hero is paying around R10 400 for a 2.69% chance of getting there. This only becomes worthwhile if a place at the Pro Tour is worth nearly four hundred thousand rand to you. Note that the average payout at the Pro Tour is around $700. So from that standpoint, it’s an absurd proposition.

Unless you genuinely believe that your win percentage at GP level will be way in excess of 55%, then paying to fly to GPs in hopes of qualifying for the Pro Tour is hilariously bad value. For interest’s sake, Kai Budde’s lifetime win percentage at Grands Prix is 64.4%, which would correspond to a 10.5% chance of qualifying for the PT at a GP with 2 byes in hand. If you think you’re as good as Kai Budde then firstly, you’re wrong, and secondly, you’re still looking at a lousy equation.

So if your goal is reaching the Pro Tour, RPTQs are vastly superior to GPs. They are easier on the pocket, being single-day events with free entry. They also offer a far higher chance of making it to the Pro Tour. The recent RPTQs mostly had fewer than 50 competitors. There are no byes at these events and the standard of competition will be a bit higher than at a GP, so let’s assume our hero is average in that field. If we assume 40 players, then with 4 slots available we can call that a 10% chance of making it to the Pro Tour, nearly 4 times higher than playing a GP with two byes in hand and close to 10 times higher than playing a GP without byes.

So if your main objective is to qualify for the Pro Tour, then RPTQs are vastly superior to GPs. If your goal is to get South African players on camera and in the spotlight, then the question is a bit more complex. The first thing to remember is that Pro Tour success garners far more attention than results at GPs. Therefore, a significantly higher chance of getting to the Pro Tour means a commensurately higher chance of recognition on the biggest stage of all.

However, GPs offer more of a spectacle in and of themselves than RPTQs do. Very few of the last batch of RPTQs had any sort of coverage taking place, whereas most European GPs have video coverage and commentary. The downside is, you have to be doing pretty well to get feature matches at a GP so it’s a low likelihood proposition. On average, South African Magic won’t receive much exposure from having our players simply attend GPs. It’ll be more than we’ll get at an RPTQ, but it won’t amount to much.

RPTQs also don’t offer Pro Points, whereas GPs do. Top 8 competitors on average receive 5 Pro Points, while a 13-2 record guarantees 4 Pro Points. If we assume that 16 players end up with 13-2 records or better at a typical GP, then a 13-2 record corresponds to an average of 4.5 Pro Points. With a 2.69% chance of going 13-2 or better, a 6.6% chance of going 12-3 or better and a 13.5% chance of going 11-4 or better, a player with a 55% win rate and two byes in hand will receive an average of 0.45 Pro Points at a GP. It’s difficult to attach a strict monetary value to Pro Points, but R12 500 seems steep for less than half a point.

To sum up, travelling to play in a European GP will optimistically cost R12 500 and get you on average $121 or so, a 2.69% chance at getting to the Pro Tour. Travelling to an RPTQ will cost about R2000 less and will get you about a 10% chance of making it to the Pro Tour, along with a high value promo card and prize support that varies between locations.

If we assume that Pro Tour qualification is a big motivator, then RPTQs offer better EV. However, neither RPTQs nor GPs offer enough value for it to make economic sense to travel to one. As an individual, travelling to play overseas has to be about the experiences, and GPs offer a unique spectacle. They’re also open entry so you can plan a holiday around one without the risk of finding yourself not qualified for the tournament. PPTQs are hard to find in these parts, sadly for good reason. There is a high cost to running PPTQs since they require a Level 2 judge and locally there is very little incentive to play them. Consequently, it just doesn’t make sense for stores to run them.

For an individual travelling on your own dime, GPs look like a better bet unless you happen to win a PPTQ and happily discover that you can conveniently plan a holiday around playing the RPTQ.

If the money is coming from some other source instead then the prospects are a little different. Several proposals have been made with regard to how to do it and they all have one common denominator: a qualifying tournament to determine who gets access to the funds.

This qualifying tournament could as easily be a PPTQ as a GPT so in that respect both options are equally appealing. The question, then, is which of the two offers more value to whoever is supplying the money.

If the money comes from entry fees to the qualifying tournament, then the interested parties are the players themselves. That means a diverse range of interests. Some players would be excited for the opportunity to play in a GP and that is sufficient motivation by itself. Others would be motivated more by the prospect of a good shot at making the Pro Tour and would therefore prefer that it be a PPTQ. There is some added value in that the qualifying tournament will be an enjoyable competitive experience in and of itself, and that’s what makes this proposition better than zero-sum. The other source of added value here is that players will derive value from someone else going overseas. I would estimate that this value is not too significant. Keraan Chetty, who is both a really nice guy and arguably SA’s best player, recently played a pair of GPs in Paris and Florence and not many of us got too excited about it.

If the money is instead being supplied by a (highly generous) store that is looking to increase sales by stimulating competitive Magic in the country, then their interest lies in the extent to which a player going overseas will stimulate sales. I don’t believe there was much of a visible spike in sales with either Adam Katz’s top 8 at GP Manchester or Keraan’s top 8 at GP Moscow. A big showing at a Pro Tour could be a different prospect altogether, so if a store is gambling on a chance at stimulating sales they would have a better chance of a big payoff if they opt for the PPTQ route. Then again, any feature match time at a GP could be rewarding, so that is a consideration.

If the money is supplied by an NPO set up for the express purpose of boosting competitive play in South Africa, then the EV of the PPTQ route is higher. Top competitive players will gravitate toward the much higher personal EV of playing an RPTQ as opposed to a GP, and in terms of competitive experience, the standard of play will be higher at an RPTQ than at a GP.

If the money is supplied by an NPO set up for the purpose of generally growing Magic in the country, then sending someone overseas offers a lousy return in terms of those goals. Rather use the resources locally, putting them toward building tournament attendance and/or teaching new players.


Quick summary:


I don’t blame those of you who have scrolled straight to the bottom. My conclusion is that the answer to the GP/RPTQ question depends on who the interested party is. Here are the best EV options for the different interest groups.


Individual planning a holiday around playing internationally: Go for a GP.

Store or distributor looking to boost sales: Opt for an RPTQ, but it’s marginal.

Players putting entry fees toward a plane ticket for the winner: The best option depends on player preference.

NPO focused on competitive play: RPTQ, hands-down.

NPO focused on general growth: Plane tickets shouldn’t be that high on the priority list. If it gets to the point of having enough surplus to put a little bit of it toward travel, which option is better should depend on the preference of donors to the fund.

MTGO Grinder: Get back in the basement. Sunlight is overrated. Jokes aside, online PTQs don’t come with plane tickets and the cost of flights to the EU or the US are higher than the average payout at the Pro Tour. MTGO is a truly awful prospect right now. Here’s hoping that WOTC rectify this sometime soon, since it’s also just about the only arena where we have the same opportunities as everyone else.