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Dreamhack [E-Sports Prospectus]

Blogs > Primadog
Post a Reply
Primadog
Profile Blog Joined April 2010
United States4411 Posts
Last Edited: 2011-06-19 17:46:57
June 17 2011 21:51 GMT
#1
Working on a new version of the E-sports Prospectus. In any case, here's a run of the Dreamhack group stage:

Changes made to the Prospectus algorithm
+ Show Spoiler [Prospectus v1 Formulas] +

+ Show Spoiler [Projecting a game result] +

A player's expected score is his probability of winning. Thus an expected score of 0.75 could represent a 75% chance of winning and 25% chance of losing.

If a game has been played, a win is equal to an expected score of 1.0 and a lose is equal to an expected score of 0.0. If a game has not been played, an expected score E is determined for each match-up. It is calculated using an the TLPD.I rating of the two players in the match using the following formula,

[image loading],
where [image loading] and [image loading]



Example: NASL day 4-5 game 3 is a matchup between (T)IdrA (2297) and (T)PainUser (2000). Expected score of (T)IdrA in this matchup is 0.85. In the other words, (T)IdrA is expected to win 85% of games he played against (T)PainUser, based solely on their TLPD.I rating.

An aside on the ELO formula: Rating spread of 100 means the better player is twice as likely to win the matchup. Rating spread of 200 means about three times as likely. Rating spread of 400 means about ten times as likely.


+ Show Spoiler [Projecting record and points] +

All match-ups in NASL divisional play is best-of-3 (bo3). A player's record in NASL is the number of division matchup won by the player. A player's points in NASL are the number of individual game wins minus the individual game loses of the player in divisional play. Record has a value range between 0 and 9 and points have a value range between -18 and 18. If a matchup has been played, the record and points of that matchup are the actual results, otherwise the following formulas are used:

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


The projected points P is the number of games won minus the games lost in all permutations:
Projected Points = Expected value of WW, LL, WLW, WLL, LWW, LWL
P = 2 * EE - 2 * (1-E)(1-E) + E(1-E)E - E(1-E)(1-E) + (1-E)EE - (1-E)E(1-E)
P = 2 * [ E(1-E)(1-E) + EE(1-E) + EE + (1-E)(1-E) ]


Example: Continuing the previous example of Day 4-5 game 3, the projected record of IdrA for this matchup is .94 with 1.57 point; and the projected record of Painuser for this matchup is .06 with -1.57 point. Notice that .94 + .06 = 1 and 1.57 + (-1.57) = 0 as expected.


Since NASL week 9, I have been testing out several different iterations of the Prospectus algorithm with race Elos as additional variables. The solution is non-trivial, since the standard expected value of the Elo formulas only accepts two inputs, Player A's Elo Ra and Player B's Elo Rb:

[image loading],
where [image loading] and [image loading]


Where does Player's match-up Elo fit in this formula? Preliminary tests show that simply swapping player Elo with his match-up based Elo dramatically reduce predicative accuracy. It also do not make sense within the StarCraft Metagame: A player's ability in one matchup is not completely independent against another. MC may be better at PvP than PvT, but he certainly is not Bronze-League.

Obviously, player's Elo should remain a factor. How so? I see two ways to approach this, one is to say that racial-Elo is twice as important as regular Elo, another is regular Elo is half as important. [... Will continue this tangent on a subsequent piece]

Formula adjustment for Prospectus v2
[image loading]
where R_B' = R_B + Elo.against.A.race and R_A' = R_A + Elo.against.B.race



Projection
  • Group A: (T)Strelok, (P)NaNiwa
  • Group B: (Z)MorroW, (Z)DIMAGA (wins tie-break over (T)BRAT_OK)
  • Group C: (T)Kas, (T)IdrA
  • Group D: (P)MC, (Z)Sen
  • Group E: (Z)Moon, (P)HuK
  • Group F: (T)ThorZaIN, (Z)July (wins tie-break over (P)HasuObs)
  • Group G: (P)elfi, (T)GoOdy
  • Group H: (T)Bomber, (P)MaNa



Details
Group A			
Player Record Map
Strelok 4-1 (9-3)
Naniwa 4-1 (8-4)
Ret 3-2 (7-5)
Moman 2-3 (5-7)
Jimpo 1-4 (3-8)
Tyler 1-4 (3-9)


Group B			
Player Record Map
Morrow 4-1 (8-4)
DiMAGA 3-2 (7-5)
Brat_ok 3-2 (7-5)
Nightend 2-3 (5-7)
Socke 2-3 (5-7)
DieSTar 1-4 (3-9)


Group C			
Player Record Map
Kas 4-1 (9-3)
IdrA 4-1 (8-4)
SaSe 3-2 (6-6)
Naama 2-3 (5-7)
merz 1-4 (3-9)
Grubby 1-4 (4-8)


Group D			
Player Record Map
MC 4-1 (9-2)
Sen 4-1 (8-4)
TT1 3-2 (6-6)
Adelscott 2-3 (5-6)
ClouD 2-3 (5-7)
Naugrim 0-5 (2-10)


Group E			
Player Record Map
Moon 3-2 (8-4)
Huk 3-2 (8-5)
Tarson 3-2 (7-5)
LaLush 2-3 (6-6)
Bischu 2-3 (5-7)
Fury 1-4 (3-9)


Group F			
Player Record Map
Thorzain 4-1 (8-4)
July 3-2 (8-5)
Hasuobs 3-2 (7-5)
SjoW 2-3 (6-6)
Machine 1-4 (5-7)
Sushi 1-4 (3-9)


Group G			
Player Record Map
elfi 4-1 (9-3)
Goody 4-1 (8-4)
White-Ra 3-2 (7-5)
BYOC 2-3 (5-7)
Jinro 1-4 (3-8)
PredY 1-4 (3-9)


Group H			
Player Record Map
Bomber* 4-1 (8-4)
Mana 4-1 (9-3)
Happy 3-2 (7-4)
BYOC 2-3 (5-7)
Haypro 2-3 (4-8)
Xlord 1-4 (2-9)
*No TLPD.I Elo, replaced with TLPD.K Elo



Accuracy Analysis:
Accuracy for the Dreamhack Prospectus are measured under four indices:
  1. Top2: How many of the 16 advancing players did the Prospectus called correctly?
  2. Order: How does the projected player group-play ordering compare with reality?
    If the Prospectus called ABCDEF but the actual ranking are BCAEDF, it is said to incurred 2 ordering error.
  3. Records: How accurate are the projected records compared to the actual group results?
  4. Maps: How close are players' total map wins and loses compared to the projection?

[image loading]

*
Thank God and gunrun.
Phayt
Profile Joined October 2010
Canada346 Posts
June 17 2011 22:16 GMT
#2
Neat. For the most part this all looks pretty believeable, with the exception of group G I think. Personally I expect White-Ra and Jinro out of that group, and I think seeing NEITHER of them make it would be quite odd. Not that elfi aren't also very good I suppose.

Anyways, these predictions are always fun to see, keep it up dude
tree.hugger
Profile Blog Joined May 2009
Philadelphia, PA10406 Posts
June 17 2011 23:04 GMT
#3
Primadog, want to bet a dinner on prediction accuracy?

^^
ModeratorEffOrt, Snow, GuMiho, and Team Liquid
Primadog
Profile Blog Joined April 2010
United States4411 Posts
June 17 2011 23:08 GMT
#4
On June 18 2011 08:04 tree.hugger wrote:
Primadog, want to bet a dinner on prediction accuracy?

^^


I believe I still have a pizza from OCSurfer to be redeemed, sure, why not.

What accuracy index are we gauging projection performances?
Thank God and gunrun.
Primadog
Profile Blog Joined April 2010
United States4411 Posts
Last Edited: 2011-06-19 17:57:39
June 19 2011 17:41 GMT
#5
[image loading]
  • Called 13 players' Dreamhack records in group stage perfectly
    + Show Spoiler [Perfect calls] +

    (Z)Ret 3-2
    (P)Tyler 1-4
    (Z)DIMAGA 3-2
    (P)NightEnD 2-3
    (Z)Sen 4-1
    (P)Adelscott 2-3
    (Z)Naugrim 0-5
    (T)FuRy 1-4
    (T)SjoW 2-3
    (Z)Machine 1-4
    BYOC 2-3
    (T)Jinro 1-4
    (Z)HayprO 2-3

  • Called 24 more players' records within 1 match-up of actual result
    + Show Spoiler [Near Misses] +
    (T)Strelok 3-2
    (P)NaNiwa 5-0
    (Z)MoMaN 1-4
    (T)Jimpo 2-3
    (T)BRAT_OK 4-1
    (T)DieStar 0-5
    (Z)IdrA 3-2
    (T)Naama 1-4
    (T)meRz 2-3
    (P)MC 5-0
    (T)ClouD 3-2
    (Z)Moon 4-1
    (T)Tarson 2-3
    (Z)LaLuSh 3-2
    (P)Bischu 1-4
    (T)ThorZaIN 3-2
    (P)HasuObs 4-1
    (Z)Sushi 0-5
    (T)GoOdy 3-2
    (T)Bomber 5-0
    (P)MaNa 3-2
    (T)Happy 2-3
    BYOC 1-4
    (Z)XlorD 2-3

  • Missed 11 players by 2 or more match-ups
    + Show Spoiler [Misses] +
    (Z)MorroW 2-3
    (P)Socke 4-1
    (T)Kas 1-4
    (P)SaSe 5-0
    (P)Grubby 3-2
    (P)TT1 1-4
    (P)HuK 5-0
    (Z)July 5-0
    (P)elfi 1-4
    (P)White-Ra 5-0
    (T)PredY 3-2
Thank God and gunrun.
]343[
Profile Blog Joined May 2008
United States10328 Posts
July 30 2011 08:42 GMT
#6
Ah these ELO formulae look familiar...
Writer
Primadog
Profile Blog Joined April 2010
United States4411 Posts
July 30 2011 08:45 GMT
#7
Yes, you can consider me as heyoka 2
Thank God and gunrun.
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