The Elephant: a Probability Exercise

We evaluate how fast can the GSL absorb a mass BW transition,

as proposed by "The Elephant in the Room."

I. Introduction

One of the most controversial editorial published on TeamLiquid.net, "The Elephant" hit a sore spot within the StarCraft fanbase. "The competition in SC2 thus far has been a farce" instantly become a galvanizing meme and divisive force between SC2 and BW fans, generating hundreds of pages of debate within weeks. Even now, the topic resurfaces each time new ammunition appears for either side - the spectacular GSL debut of (T)

fOrGG, FXOBoss' vague blogs, or forGG's poor Code S run. It will probably never run its course until the foretold flood finally hit.

We will make no attempt to settle the score in this post.

Instead, this is an attempt to see how well the newer, more flexible GSL format can cope with the predicted sudden talent influx. Has the GSL made sufficient incremental steps to accommodate a rapidly shifting talent pool? Will 2012 be the year were Code S properly includes the Top-32 players of the world? How fast will ex-BW pros elbow out the pretenders?

II. 2011 GSL Format

To judge finesse, we must first have something to compare with.

Until late 2011, the GSL tournament was under a completely different format. Inflexible, the format's most glaring flaw was limiting player shifts between Code S and Code A (with one Foreigner seed) to only 8 each season. This resulted in players often lingering in Code S beyond their welcome and difficulty for rising stars to compete for the big prize. This fault would later force a complete revamp in tournament format by GSL November. We will use the last format before the revamp - GSL October (details http://wiki.teamliquid.net/starcraft2/2011_Global_StarCraft_II_League_October#Information ) - as the control comparison sample.

If "The Elephant" is true, then all ex-BW pros belong in Code S. Suppose 20 ex-BW pros transitioned suddenly ( with 20 the typical size of a BW team). How many season will it take to fit them all in there?

For simplicity's sake, let's assume all ex-BW pros are far more skilled than the existing talent pool of SC2, that they win 100% of their sets against anyone but each other. Let's also assume that the brackets distributed them in such a way that ex-BW pros only meet at the latest round possible. Finally, let's assume that they won all the Code A spots available from the Preliminaries.

In that case, for the following GSL season:

12 will qualify for Code , occupying all available spots; 8 will have to requalify.
All 12 advanced to ro16;
8 advances to ro8, 4 eliminated by each other;
1 wins Code and earns Code status.
The other 7 advance to Up-N-Down;
6 wins their respective group and earns Code .

Thus, every season a maximum of 7 ex-BW pros can advance into Code S. 20 players, then, will take 3 GSL season, under the 2011 format.

III. 2012 Format; 100% set winrate; 20 players

How does the same conditions compare under the 2012 GSL format (details http://wiki.teamliquid.net/starcraft2/2012_Global_StarCraft_II_League_Season_1 )?

The answer is surprisingly simple! Under the new format, 20 players can qualify for Code [image loading]

each season, and up to 24 Code [image loading]

spots are up for grasp. Therefore, it's theoretically possible all 20 ex-BW players to advance into Code [image loading]

, in a single season!

How much more efficient is the format? A 2012 season lasts 8 weeks compares to 2011's 5-week season. Since the 2011 format will take 3 seasons to complete "The Elephant" transition, the new format accelerates the transition by an entire 7 weeks!

2011 format: Week-0 12 | Week-6 7 13 | Week-11 14 6 | Week-16 20
2012 format: Week-0 20 | Week-9 20

IV. 2012 Format; 60% Set Winrate; 20 Players

Of course, even for ex-BW pros, sweeping all sets would be rather difficult and unrealistic. Luckly, we have (T)

fOrGG to thank for a single available datapoint in how well a top ex-BW pro can do. According to TLPD, he has a match winrate just shy of 60% and won 7 of his 12 GSL matches. A 58% match winrate is equivalent to 62% set winrate (all relevant matches are bo3's), based on the following formula:

+ Show Spoiler [set winrate] +

Each match-up is a bo3 with game 3 not played if the results are already determined (WW or LL). The possible winning permutations then are WLW, WW, LWW, with the possible losing permutations of a bo3 are WLL, LL, LWL. Projected record R is determined using expected value E for a win and 1-E:

Projected Record = expected value of WLW or WW or LWW 
R = E * (1-E) * E + E * E + (1-E) * E  * E 
R = 2 * E * E * (1-E) + E * E

For simplicity's sake, let's simply assume that all the ex-BW pros have a 60% set winrate. Furthermore, they also have a 60% success rate for advancing through group stages. We will also give them the benefit of the doubt by rounding up with remainders. For simplicity's sake, let's also assume they all advance through the preliminaries.

Given this, how many will secure Code [image loading]

status in the first season? In the first season:

20 players qualify for Code through preliminaries into the ro48;
12 players {20 * 60%} advances to the ro32, 8 drop out;
8 players {12 * 60%} advances to ro24, 4 moves into Up-N-Down;
5 players { 8 * 60%} won ro24 and earned Code , 3 moves into Up-N-Down.
5 players won their Up-N-Down group and earned Code .

Thus, next season will start with 10 players are in Code [image loading]

and 10 in Code [image loading]

. Due to the convoluted format, the flowchart becomes a bit more complicated, thus I'll simply leave my notes in the spoiler. Season 2 will end with 14 players in Code [image loading]

; season 3 with 15 [image loading]

, and so forth.

+ Show Spoiler [Case 3 notes] +

2011 format: Week-0 12 | Week-6 7 13 | Week-11 14 6 | Week-16 20
2012 format: Week-0 20 | Week-9 20
2012 format & 60%: Week-0 20 | Week-9 10 10 | Week-17 14 6 | Week-25 15 5

Two observations from this result:

Ex-BW pros no longer sweeps in a single season. It will take longer than 2012 for all the ex-BW pros to join Code .
As the talent pool improve each season, even ex-BW pros will find it harder to make Code .

V. 2012 Format; 60% Set Winrate; 6 Players

What if the assumption that a mass transition is wrong? What if only a small number of BW pros change game? Let's assume only 6 BW pros made the jump:

6 players qualify for Code through preliminaries into the ro48;
4 players {6* 60%} advances to the ro32, 2 drop out;
3 players {4 * 60%} advances to ro24, 1 moves into Up-N-Down;
2 players {3 * 60%} won ro24 and earned Code , 1 moves into Up-N-Down.
2 players won their Up-N-Down group and earned Code .

A funny thing happens next season, with 4 players in Code [image loading]

and 2 in Code [image loading]

, all 6 advances to Code [image loading]

+ Show Spoiler [Case 4 notes] +

2011 format: Week-0 12 | Week-6 7 13 | Week-11 14 6 | Week-16 20
2012 format: Week-0 20 | Week-9 20
2012 format & 60%: Week-0 20 | Week-9 10 10 | Week-17 14 6 | Week-25 15 5
2012 format & 60% & 6 players: Week-0 6 | Week-9 4 2 | Week-17 6

VI. Conclusion

This exercise was never an attempt to answer "The Elephant", but we did never-the-less found some interesting results. Under the 2012 format, GSL has become much more adaptive to a talent pool in flux. As long as the talents coming in are not all superman (yet high caliber like (T)

fOrGG), we can expect an orderly and efficient induction into Code S. However, this orderly induction only happens up to a transition of a certain size. Above which, a progressively stronger talent pool will naturally make it harder for even ex-BW pros to admit into Code S.

Instead, some of our current talents would remain in place of the ex-BW pros. Math says so.

The Elephant: a Probability Exercise

Completed

Ongoing

Upcoming