# BoxRec Ratings Description

## Introduction

**BoxRec.com** provides *Active* (Current) and *Active and Inactive* (All Time) boxer ratings, as calculated daily by its computer. These ratings are not influenced by subjective views or opinions but are wholly dependent upon the bouts contained in the BoxRec database.

The *Active* ratings include only those boxers who have fought a bout within the past 365 days. After a year of not fighting, a boxer is automatically designated "Inactive" by the BoxRec computer. A boxer is also designated "Inactive" if he has announced his retirement, even if he may have had a bout within the past 365 days. Every boxer in the database is rated--even those with an 0-1 record.

The BoxRec computer re-calculates the ratings instantly with every bout entered or changed. So a boxer may gain or lose ratings points with every of his bouts entered or changed in the database by a BoxRec Editor. A boxer may also gain or lose points if bouts are added to any of his opponents' records, or to their opponents' records--even if the boxer himself has not had a fight since the last BoxRec computer calculation.

There admittedly are inaccuracies and anomalies, especially in the *All Time* ratings, mostly because of incomplete records in the BoxRec database. Although a boxer’s own record may be complete, his opponents’ records may not be complete. Pre-World War II boxers in particular are at somewhat of a disadvantage, vis-à-vis modern boxers. Their opponents’ records often are quite incomplete--because of the scarcity of source material or Editors' time--while the records of opponents of more current boxers may be quite complete. So, for example, while Mike Tyson's own record, and those of his opponents, may be complete--thereby earning Tyson a certain number of points and thus giving him a high ranking among the *All Time* Heavyweights--the records of Young Stribling’s opponents may be extremely lacking, thereby giving Stribling fewer points and a much-lower *All Time* rating. And it may appear to the casual BoxRec visitor that Stribling had fought many boxers making their professional debuts or having had only a handful of career bouts, when the truth is that not all of his opponents’ total career bouts have been entered into the database. (Too many of those old-time bouts are forever lost in history because they were not reported by a newspaper or similar source, or the source was later destroyed.) However, as BoxRec Editors continue to research older resources and enter “new” historical bouts into the database, or correct bouts/boxers previously entered, the rating of an old-time boxer like Stribling may gradually move up or down, even if his own record is considered complete, if bouts are added to his opponents’ records, or to their opponents' records, and so on.

Finally, because of the very few women presently boxing professionally, with some weight divisions having only a handful of active female boxers, a woman with an 0-1 record will appear “world ranked” by BoxRec. This is simply an anomaly due to the few female entries in the database.

## The BoxRec Ratings Algorithm

### Whole-History Rating Algorithm

The ratings are build upon the Whole-History Rating (WHR) algorithm (Remi Coulom) described in the paper Whole-History Rating.

Abstract. Whole-History Rating (WHR) is a new method to estimate the time-varying strengths of players involved in paired comparisons. Like many variations of the Elo rating system, the whole-history approach is based on the dynamic Bradley-Terry model. But, instead of using incre- mental approximations, WHR directly computes the exact maximum a posteriori over the whole rating history of all players. This additional ac- curacy comes at a higher computational cost than traditional methods, but computation is still fast enough to be easily applied in real time to large-scale game servers (a new game is added in less than 0.001 second). Experiments demonstrate that, in comparison to Elo, Glicko, TrueSkill, and decayed-history algorithms, WHR produces better predictions.

- All boxers have a rating at the time of all of their bouts.
- Boxers are rated by the results of bouts between 2 opponents a and b.
- The result may be a win or a loss.
- The probability of a win of boxer a with rating r_a against a boxer b with rating r_b is: r_a / (r_b + r_b).
- The likelihood of all wins is the product of all the bout win probabilities,

'All boxers shall start with rating 1.

- For that it is assumed, that all boxers have a virtual loss and a virtual win against a virtual opponent with rating 1 at time of their first bout.

Let's look at the situation after the first real bout of 2 boxers a and b resulting in a win for a.

- We have 5 results then:

- a defeated v with probability r_a / (r_a + r_v) (the v represents the virtual opponent with rating 1)
- v defeated a with probability r_v / (r_v + r_a)
- b defeated v with probability r_b / (r_b + r_v)
- v defeated b with probability r_v / (r_v + r_b)
- a defeated b with probability r_a / (r_a + r_b)

- For all ratings assumed to be still 1 this would give a joint probability for all bouts (likelihood) of:
- Likelihood = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.0312

- But boxers a and b should be rated different now after a defeating b.

- Let's look now, what likelihood would result for rating a higher with 1.1 and rating b lower with 0.9.
- Likelihood = 1.1/(1.1+1) * 1/(1+1.1) * 0.9/(0.9+1) * 1/(1+0.9) * 1.1/(1.1+0.9) = 0.0342
- Oops, this likelihood is higher than for rating all boxers with 1.

- Let's look further, what likelihood would result for rating a even higher with 1.2 and rating b even lower with 0.8.
- Likelihood = 1.2/(1.2+1) * 1/(1+1.2) * 0.8/(0.8+1) * 1/(1+0.8) * 1.2/(1.2+0.8) = 0.0367
- Oops, this likelihood is even higher than for rating a with 1.1 and rating b with 0.9.

The WHR algorithm provides a way to find the optimised ratings by maximising the likelihood for all bout wins.

- r_a = 1.70 and r_b = 0.59 give a maximum likelihood of 0.0404.

This is equivalent to maximising the sum of all logarithms of the bout win probilities.

But the ratings of a boxer may vary from r1 at time t1 of bout1 to r2 at time t2 of bout2.

- The logarithm for the rating change may be proportional to the absolute difference of the logarithm of the ratings.
- The logarithm for the rating change may be inversely proportional to the time difference.
- This term is added to the sum of all logarithms of the bout win probilities for all pairs of bouts and opponents.

So the WHR algorithm finally also provides a way to find the time-varying ratings by maximizing the likelihood of all results of all boxers.

### BoxRec Algorithm as a Generalised Whole-History Rating Algorithm

Boxing not always results in a clear decision for one of the opponents. There are draws, and furthermore there are close decisions. So BoxRec assigns a bout result value to every outcome of a bout, varying from 0 to 1. Where 1 represents a clear win for the a-side boxer, 0 represents a clear win for the b-side boxer and 0.5 represents a draw. Values between 0.5 and 1 represent a close win for the a-side boxer. Values between 0 and 0.5 represent a close win for the b-side boxer.

In the generalised Whole-History Rating:

- A close win with result of 0.7 is represented by 0.7 wins for the a-side boxer and 0.3 wins for the b-side boxer.
- A draw with result 0.5 is represented by 0.5 wins for the a-side boxer and 0.5 wins for the b-side boxer.
- A close loss with result 0.2 is represented by 0.2 wins for the a-side boxer and 0.8 wins for the b-side boxer.

### BoxRec Ratings Special Additions for Professional Boxing

BoxRec is obliged to provide ratings with the best winner prediction rate available. Currently the yielded ratio is 86.38 percent for professional boxing.

Boxing requires some special additions to the generalised WHR ratings and the additional parameter values are found by maximising the winner prediction ratio.

#### Seeding the boxers at start of their career is a critical task

The standard WHR rating seeds a boxer by 1 prior win and 1 prior loss against an opponent with rating 1.

BoxRec seeds the boxers depending on being connected to other connected boxer by at least 1 result > 0.16.

- BoxRec seeds a boxer by 3 prior bouts with result 0.05 against
- an opponent with rating of 1 for connected boxers.
- an opponent with rating of 1/6 for boxer with at least 1 win.
- an opponent with rating of 1/20 else.

#### Bout Result

- There are the decisions KO (knockout), TKO (technical knockout), RTD (retired), PTS (on points), UD (unanimous decision), MD (mixed decision), SD (split decision), D (draw), DQ (disqualification).
- The extent of a win is represented by the clear decision factor cd.
- KO, TKO, RTD have cd = 1.
- Decisions on points (with score points unknown) have a cd of:
- PTS, UD = 0.875
- MD = 0.55
- SD = 0.45

- Decisions on points with score points known have a cd of:
- Take the average score difference scd per judge and per round boxed.
- If scd <= 0.5, cd = 1.75 * scd.
- If scd <= 1, cd = 0.875 + 0.25*(scd-0.5).
- If scd > 1, cd = 1.
- For MD cd cannot be higher than 0.55.
- For SD cd cannot be higher than 0.45.

- The bout result finally is (1+cd)/2.

#### Weighting the Importance of a Bout

- A stopped bout is weighted with factor 1.
- A result on points is devaluated if there are less than 12 rounds boxed: factor = (rounds_boxed / 12) ** 2; rounds_boxed > 12 is treated as rounds_boxed = 12
- A bout between not connected opponents is devaluated with a factor of 1/20.

### Current Ratings

The current rating of a boxer is derived from the BoxRec ratings at time of his last fights.

Winner above loser:

- For the last 18 months a winner of a fight is kept above the loser.
- This can be overcome by the loser having success in the future over a higher-rated opponent

### All-time Ratings

All-time Ratings are based on the career peak rating of a boxer and the top defeated opponents - at least.

(0.67 * average_5_top_defeated_opponents + 0.33 * career_top_rating) * division_factor * 10

For lower weight divisions the points are converted with the cube of Heavyweight upper weight reference in relation to the upper weight reference of the Boxer's weight division.

The best boxers can get a higher all-time rating, if

- their points for their best 10 wins against p4p top 1000 opponents
- their points for their best 10 annual rankings in the p4p top 1000

are higher.

### Bout Star Ratings

All bouts are rated with 0 to 5 stars. The rating points are converted with the cube of Heavyweight upper weight reference in relation to the upper weight reference of the bout weight division.

Men

- 5 stars = both opponents have 20.1 rating points at least ~ best 100 boxers
- 4 stars = both opponents have 9.12 rating points at least ~ best 300 boxers
- 3 stars = both opponents have 2.94 rating points at least ~ best 900 boxers
- 2 stars = both opponents have 0.724 rating points at least ~ best 2700 boxers
- 1 stars = both opponents have 0.153 rating points at least = best 8100 boxers
- 0 stars = one opponents has not even 0.017 rating points at least = not rated boxers

Women

- 5 stars = both opponents have 54.4 rating points at least ~ best 10 boxers
- 4 stars = both opponents have 22.6 rating points at least ~ best 30 boxers
- 3 stars = both opponents have 8.90 rating points at least ~ best 90 boxers
- 2 stars = both opponents have 3.85 rating points at least ~ best 270 boxers
- 1 stars = both opponents have 0.970 rating points at least = best 810 boxer
- 0 stars = one opponents has not even 0.150 rating points at least = not rated boxers

## Links

- Whole-History Rating: [1]
- BoxRec's Ratings: [2]
- BoxRec Forum Discussion of Ratings Formula: [3]
- BoxRec History & Description
- BoxRec's Annual Ratings Men, BoxRec's Annual Ratings Women