Overview

Only players who place in an ABT event receive ABT points.  To place, a player must achieve a position or rank in the event specifically designated for recognition by the director.  Players entering ABT main events are segregated into skill divisions, with each division having an independent competition. ABT points are awarded independently for each such skill division within the main event. The total number of ABT points awarded shall always equal the number of unique players in the event (top skill division).

If the USBGF Ratings and Stats Committee considers the distribution of ABT points awarded for any ABT tournament to be inappropriately skewed compared to other ABT tournaments based on unusual features of that event, then the Committee may recommend a modification to the ABT points formula to be applied retroactively.  Alternatively, the Committee may recommend a one-time adjustment to the distribution of points for that specific event (including the number of positions awarded points).  The USBGF Board of Directors shall have final authority regarding any such deviation from the designated formulas set forth below.

In case of a dispute on how to award ABT points for a particular event, the USBGF Ratings and Stats Committee will review the facts and make the final interpretation on how the points are to be distributed in accordance with established ABT policy.

Skill Division Factor (DV)

For purposes of calculating ABT points, only the rank of the skill division from highest skill downward is relevant to assigning the Skill Divisional Factor. Common division names are given for example only.

Skill Divisional Factors shall be assigned as follows:

1. Division 1 / Highest skill: (Championship, Open, Championship/Open Overflow) DV = 1
2. Division 2 / Second highest skill: (Advanced, Intermediate) DV = 0.50
3. All remaining Lower Divisions: (Limited, Beginner, Novice and/or C Division) DV = 0.25

Attendance Factor

The number of unique players in attendance in a particular skill division is the only variable factor that determines the total number of ABT points to be awarded for a particular event. Reentries into a sanctioned ABT division are not included when determining the divisional attendance factor.

Attendance Factor = Number of unique players entered into this skill division

Total ABT Points Per Divisional Event

The total number of points to be awarded for an entire ABT skill division is the product of the attendance and the skill division factor:

Total Points = Attendance Factor * Skill Division Factor

Flight Factor (FL)

Typical ABT events contain multiple flights of play, wherein a player who is eliminated from play in a higher flight may continue to compete in order to win or place in a lower flight.  The Flight Factor is determined by the distance from the event’s Main flight (the one the produces the event winner), with each lower flight having a flight factor that is half that of the preceding flight. For example:

1. Main Flight: FL = 1
2. Consolation Flight: FL = 0.5
3. Last Chance Flight: FL = 0.25

Standardized Flight Shares (FS)

Standardized flight shares are awarded to all players who place in any flight and reflect the share of points awarded to a particular place within the flight relative to all other places in that flight. The method for assigning standardized flight shares depends upon the competition format used to rank the subset of players designated to place in that flight.  There are two methods: one used for a conventional elimination bracket format, and the other used for all other formats.

Elimination Bracket Format in Events Having At Least Two Flights

With an elimination bracket format, a 1st place win is always worth exactly double that of a 2nd place win. A 2nd place win is worth exactly double that of a semifinal finish, and so on for lower-ranking positions. Standardized flight shares are awarded to players placing within a flight as follows:

1. Winner: FS = 32
2. Finalist: FS = 16
3. Semi-finalist: FS = 8
4. For each previous round: FS = FS(next round) / 2

However, if a 3-way tie playoff is used to determine the top three places within a flight (where one of the three players receives a bye), the total award for places 1, 2 and 3 is FS = 32 + 16 + 8 = 56 shares. Those 56 shares are equitably awarded as follows:

• The two players who did not receive the bye shall each be awarded 1/10 of the 56 shares.
• The remaining 8/10 of the 56 shares shall be divided between places 1, 2, and 3 with ratios 3:2:1 respectively.

Other Formats (non-elimination), and Elimination Formats Having Exactly One Flight

The placing players within a flight may be ranked by means of a competition format other than a conventional elimination bracket, such as Swiss and Round Robin formats.  In such flights, or for any event that has exactly one flight, the players ranked 1 through 8 (to the extent applicable) shall be awarded standardized flight shares as follows:

FS = 32, 20, 13, 9, 7, 6, 5, 4

If more than eight places are ranked in the flight, their shares shall be calculated as 32/N where N is the place number. Thus, the ninth place would be 32/9, the tenth place would be 32/10, etc.

If the final ranking results in a tie among two or more players, the standardized flight shares for the tied places are added together and then divided by the number of players tied (the average FS). For example, with a three-way tie for second through fourth place, each tying player’s FS factor would be (20+13+9)/3 = 14.

However, if a 3-way tie playoff is used to determine the top three places within a flight (where one of the three players receives a bye), the total award for places 1, 2 and 3 is FS = 32 + 20 + 13 = 65 shares. Those 65 shares are equitably awarded as follows:

• The two players who did not receive the bye shall each be awarded 1/12 of the 65 shares.
• The remaining 10/12 of the 65 shares shall be divided between places 1, 2, and 3 with ratios 32:20:13 respectively.

Point Shares

Each player placing in an event receives a standardized share of the ABT points to be awarded.

Point Shares = Standardized Flight Shares * Flight Factor

ABT Points Awarded

The number of ABT points awarded to each player that places in the tournament is a percentage of the fixed number of points to be awarded in the event. That percentage is calculated by considering the proportion of point shares earned by that player relative to the total number of point shares earned by all players. The number of points awarded to each placing player in an event shall be as follows:

ABT Points = Total Points * Point Shares / Total Point Shares

Alternative ABT Points Formula for Large Tournaments

An alternative calculation of ABT points shall be applied for ABT events having many players. It may be assumed that any ABT event having fewer than 100 unique players is not subject to this alternative.

To prevent the winner of a single extra-large ABT event from dominating the annual ABT points race and to prevent a player’s lifetime point total from being similarly skewed by any single win, a cap shall be imposed upon the number of points that the winner of an ABT event may be awarded. Any points that the winner does not receive because of this cap shall be redistributed to the other placing players such that the total number of points awarded remains equal to the number of unique players.

The method for determining the winner points cap and any redistribution of points when the cap is in effect is described below. This method describes the alternative calculations for the highest skill division. The division factor shall be applied as usual to all point awards in lower skill divisions.

Winner Points Cap (W)

W = 5 * Log2(Number of unique players in this skill division)

ABT points are first calculated using the standard (non-alternative) formula described above. If the number of points to be awarded to the event winner under the standard formula is less than or equal to W, then the cap shall not apply and the points shall be awarded as calculated, with no adjustments made. Otherwise, if the cap is exceeded, then the winner shall be awarded W ABT points, and the ABT point awards for all other placing players shall be recalculated as described below, depending upon the event format.

For Multi-flight Elimination Formats

Beyond the event winner, the standard Elimination Format points calculation awards each tier of finishers 0.5 times the number of points awarded to the next higher tier. When the winner’s points are capped at W, this 0.5 ratio between consecutive tiers shall be increased to the magic ratio value (R) that results in the number of points awarded for the event being exactly equal to the number of players. Thus:

1. Tier 1 finisher (Winner): T₁ = W
2. Tier 2 finishers (Finalist, Consolation winner): T₂ = T₁ * R
3. Tier N finishers (Distance from Winner of N-1): T_N = T_N-1 * R

Effectively, when the cap does not apply, by setting R = 0.5 this calculation method becomes equivalent to the standard method once the winner’s points have been determined. When the cap applies, as the event size increases, the value of R increases from 0.5 towards 1.

For Swiss/Other Formats

The Swiss/Other Format formula depends only upon the number of players in the event and the number of players who are to be awarded points. However, unlike the Elimination formula, the ratio of points to be awarded to consecutive places beyond the event winner is not the same from one place to the next. Nevertheless, the award for each specific place is a well-defined fraction of the award for the next higher place. The standard Swiss formula awards points to places 1 through N using the following point share ratios:

FS = 32, 20, 13, 9, 7, 6, 5, 4, … (32/N)

Let S_N = The Nth share term of FS (i.e. S₁ = 32; S₂ = 20, etc.)

Prior to adjustment, place N receives a fixed fraction (F_N) of the points awarded to place N-1:

F_N = S_N / S_N-1

Thus, if the winner receives W points, the unadjusted point awards for each place are as follows:

Winner: P₁ = W
Second place: P₂ = F₂ * P₁
Nth place: P_N = F_N * P_N-1

Equivalently, the award to Nth place may be expressed as a difference from place N-1:

P_N = P_N-1 – (P_N-1 – F_N * P_N-1)

To compensate for awarding fewer points to the winner because of the cap, more points are awarded to all other places by reducing the difference in points for each place from the place above it. The adjusted ABT points for the other players are computed as follows, using the magic Adjustment Factor (A) that results in the number of points awarded for the event being exactly equal to the number of players:

Winner: P₁ = W
Second place: P₂ = P₁ – (P₁ – F₂ * P₁) * A
Nth place: P_N = P_N-1 – (P_N-1 – F_N * P_N-1) * A

Effectively, when the cap does not apply, by setting A = 1 this calculation method becomes equivalent to the standard method once the winner’s points have been determined. When the cap applies, as the event size increases, the value of A decreases from 1.0 towards 0.

How to Obtain the Magic Numbers R or A

The magic numbers R (for Elimination) and A (for Swiss and other) depend on both the number of players in the event and the number of players who must be awarded ABT points. Both R and A are roots of a polynomial of many degrees. Thus, they cannot be calculated by simple arithmetic or algebra. But they can be calculated to arbitrary precision by software. The following web page enables the public to input the event size and payout structure and reports the magic number R or A as well as the number of ABT points to be awarded to each player:

                https://apps.usbgf.org/app/trn/view/?page=abt_points_calculator

Correctness of the magic value supplied by that web page may be verified by using it to calculate the ABT points as described above and verifying that the total number of points awarded equals the number of players in the event.