Welcome back to our series on chess tournament tiebreaks! In Part 1, we introduced the three main tiebreak systems: Buchholz (TB2), Medi...
Welcome back to our series on chess tournament tiebreaks! In Part 1, we introduced the three main tiebreak systems: Buchholz (TB2), Median Buchholz (TB1), and Sonneborn-Berger (TB3). Now, let's follow our case study player, Finn Patel, through the "Royal Knights Open" to see exactly how his tiebreak scores were calculated.
Finn's Tournament Journey
Finn scored 3 points out of 6 rounds. Here's his round-by-round performance:
| Round | Opponent | Opponent's Final Score | Finn's Result |
|---|---|---|---|
| 1 | GM Diana King | 5.0 | Loss (Black) |
| 2 | Thomas Scholar | 1.5 | Loss (White) |
| 3 | Victor Novice | 2.0 | Win (White) |
| 4 | Brian Rookie | 1.0 | Win (Black) |
| 5 | Alex Champion | 4.0 | Loss (Black) |
| 6 | Ryan Tactician | 2.0 | Win (Black) |
As we can see, Finn faced a mix of strong and weak players. Now, let's calculate his tiebreak scores.
Calculating Buchholz (TB2)
The standard Buchholz score is the sum of the final scores of all of Finn's opponents. At first glance, this calculation seems straightforward:
5.0 + 1.5 + 2.0 + 1.0 + 4.0 + 2.0 = 15.5
However, Finn's official TB2 was recorded as 17.5. Why the discrepancy?
The Special Case: Unplayed Games
This is where we encounter an important tournament rule. One of Finn's opponents, Brian Rookie, withdrew from the tournament after playing against Finn in Round 4. Brian only played in one other round (where he received a bye worth 1 point) and forfeited or missed the other four rounds.
According to FIDE regulations (specifically the 2023 tiebreak rules), when an opponent has unplayed games, those games are counted as draws (0.5 points each) for tiebreak calculation purposes. This rule exists to prevent players from being unfairly penalized when their opponents don't complete the tournament.
Brian's Adjusted Score Calculation
Brian's actual tournament score: 1.0 point Brian's unplayed games: 4 rounds Each unplayed game counts as: 0.5 points Brian's adjusted score for tiebreak purposes: 1.0 + (4 × 0.5) = 3.0 points
Revised TB2 Calculation
When we replace Brian's actual score (1.0) with his adjusted score (3.0):
5.0 + 1.5 + 2.0 + 3.0 + 4.0 + 2.0 = 17.5
This matches Finn's official TB2 score of 17.5.
Calculating Median Buchholz (TB1)
The Median Buchholz removes the highest and lowest scoring opponents before summing. Using the original opponent scores, we would get:
Original opponent scores: 5.0, 1.5, 2.0, 1.0, 4.0, 2.0 Remove highest (5.0) and lowest (1.0) Sum remaining: 1.5 + 2.0 + 4.0 + 2.0 = 9.5
But Finn's official TB1 was 11.0. The key again is using the adjusted scores for opponents with unplayed games.
Revised TB1 Calculation
Adjusted opponent scores: 5.0, 1.5, 2.0, 3.0, 4.0, 2.0 Remove highest (5.0) and lowest (1.5) Sum remaining: 2.0 + 3.0 + 4.0 + 2.0 = 11.0
This matches Finn's official TB1 score of 11.0. Notice how the lowest score is now 1.5 (Thomas Scholar) instead of 1.0, because Brian's score was adjusted upward.
Why These Adjustments Matter
These adjustments ensure that players aren't unfairly penalized when their opponents don't complete the tournament. Without this rule, players who defeated opponents who later withdrew would be at a severe disadvantage in tiebreak calculations.
Consider two players who both scored 3 points:
- Player A defeated three players who completed the tournament with 2 points each
- Player B defeated three players, but one withdrew after their game and ended with 1 point
Without adjustments, Player B would have a lower Buchholz score through no fault of their own.
Visual Representation of Finn's Tiebreak Calculation
Here's a diagram showing the contribution of each opponent to Finn's tiebreak scores:
Diana King (5.0) ───────┐ │ Thomas Scholar (1.5) ─────┤ ├── Sum = 17.5 (TB2) Victor Novice (2.0) ─────┤ Without highest & lowest = 11.0 (TB1) │ Brian Rookie (3.0*) ────┤ * Adjusted from 1.0 │ Alex Champion (4.0) ──────┤ │ Ryan Tactician (2.0) ─────┘
In the next part of our series, we'll calculate Finn's Sonneborn-Berger score (TB3) and compare him with other players who scored 3 points to understand how tiebreaks determined their final rankings.
Stay tuned for Part 3: "Sonneborn-Berger and Tiebreak Comparisons"
Do you have questions about these calculations? Leave them in the comments, and I'll address them in future installments!
No comments