Chess Tournament Tiebreaks Explained - Part 3: Sonneborn-Berger and Tiebreak Comparisons

 Welcome to the third installment of our chess tournament tiebreaks series! So far, we've explored Buchholz (TB2) and Median Buchholz (T...

 Welcome to the third installment of our chess tournament tiebreaks series! So far, we've explored Buchholz (TB2) and Median Buchholz (TB1) calculations using Finn Patel's tournament as our case study. Today, we'll tackle the final major tiebreak system—Sonneborn-Berger (TB3)—and see how tiebreaks determine final rankings among players with equal points.

Calculating Sonneborn-Berger (TB3)

The Sonneborn-Berger score rewards players who beat stronger opponents. It's calculated by:

• Adding the final scores of opponents you defeated
• Adding half the final scores of opponents you drew with

Since Finn had no draws, his TB3 calculation focuses only on the opponents he defeated:

Initial Calculation

Finn won against:

• Victor Novice (final score: 2.0 points)
• Brian Rookie (final score: 1.0 point)
• Ryan Tactician (final score: 2.0 points)

Raw TB3 calculation: 2.0 + 1.0 + 2.0 = 5.0

However, Finn's official TB3 was recorded as 7.0. By now, you might suspect the reason—Brian Rookie's adjusted score due to unplayed games.

Revised TB3 Calculation

Using Brian's adjusted score for tiebreak purposes (3.0 instead of 1.0):

2.0 (Victor) + 3.0 (Brian) + 2.0 (Ryan) = 7.0

This matches Finn's official TB3 score of 7.0. The +2.0 difference comes entirely from counting Brian's adjusted score rather than his actual score.

Tiebreak Comparisons: Why Finn Ranked 15th

In the "Royal Knights Open," seven players finished with 3 points (ranks 10-16). Let's see how tiebreaks determined their final standings:

Final Rank
Player
Points
TB1
TB2
TB3
10
Peter Scholar
3.0
14.5
21.5
10.0
11
Meera Grandmaster
3.0
14.0
21.0
8.0
12
Adam Silverking
3.0
12.0
18.5
7.25
13
Mohammed Youngstar
3.0
11.5
16.5
5.0
14
Gregory Smartmove
3.0
11.0
18.5
7.0
15
Finn Patel
3.0
11.0
17.5
7.0
16
Sara Rookmaster
3.0
9.5
14.0
4.5

Analyzing this table:

1. First, players are ranked by TB1 (Median Buchholz):
   • Peter (14.5) > Meera (14.0) > Adam (12.0) > Mohammed (11.5) > Gregory & Finn (11.0) > Sara (9.5)
2. When TB1 scores are equal (Gregory and Finn both have 11.0), TB2 is used as the next tiebreaker:
   • Gregory (18.5) > Finn (17.5)
3. If TB2 scores were also equal, TB3 would be the final tiebreaker (though it wasn't needed in this specific comparison)

This explains why Finn ranked 15th while Gregory ranked 14th despite both having the same TB1 score of 11.0. Gregory's TB2 score (18.5) was higher than Finn's (17.5).

Real-World Application: The Gregory vs. Finn Comparison

Let's examine why Gregory ranked higher than Finn:

Gregory's Opponents and Their Scores:

• Round 1: Lost to Diana King (5.0)
• Round 2: Won against Lucas Beginner (2.0)
• Round 3: Lost to James Mastermind (3.0)
• Round 4: Won against Victor Novice (2.0)
• Round 5: Lost to Olivia Queenmaster (3.5)
• Round 6: Won against William Knight (3.0)

Gregory's TB2 calculation:

5.0 + 2.0 + 3.0 + 2.0 + 3.5 + 3.0 = 18.5

Finn's Opponents and Their Scores (including adjustments):

• Round 1: Lost to Diana King (5.0)
• Round 2: Lost to Thomas Scholar (1.5)
• Round 3: Won against Victor Novice (2.0)
• Round 4: Won against Brian Rookie (3.0 adjusted)
• Round 5: Lost to Alex Champion (4.0)
• Round 6: Won against Ryan Tactician (2.0)

Finn's TB2 calculation:

5.0 + 1.5 + 2.0 + 3.0 + 4.0 + 2.0 = 17.5

The 1-point difference in TB2 scores determined their final rankings. Gregory faced opponents with slightly higher overall scores than Finn, giving him a small but decisive edge in the tiebreak calculation.

Visualizing Tiebreak Hierarchies

The tiebreak hierarchy works like this:

Points (Primary)
   │
   ├── Equal Points? → Check TB1 (Median Buchholz)
   │                     │
   │                     ├── Equal TB1? → Check TB2 (Buchholz)
   │                     │                   │
   │                     │                   └── Equal TB2? → Check TB3 (Sonneborn-Berger)
   │                     │
   │                     └── Different TB1? → Higher TB1 ranks better
   │
   └── Different Points? → Higher points rank better

This ensures that players with equal points are ranked fairly based on the strength of their competition and their performance against stronger opponents.

Conclusion

Understanding tiebreak systems helps players appreciate the importance of who they play against, not just their personal results. In Finn's case, a single opponent who withdrew from the tournament (Brian Rookie) had a significant impact on his tiebreak scores, adding 2 points to both his TB2 and TB3 values due to FIDE's rules for handling unplayed games.

In the next part of our series, we'll explore special cases in tiebreak calculations, including how byes, forfeits, and unusual tournament situations are handled according to official FIDE regulations.

Stay tuned for Part 4: "Special Cases in Tiebreak Calculations: Byes, Forfeits, and Edge Cases"

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Have questions about your own tournament tiebreak experiences? Share them in the comments!