Snooker Player Data Analytics

New ELO-inspired scoring to reflect latest forms and strength

Visualization and Interactive Dashboard available at HERE

Method A

In this approach, apart from typical ELO, recent abilities to make 70+ breaks are taken into consideration. Average score for all players is 1500.

ELO is handled on frame level

For a Match between player1 and player2, we have expected frame win rate for player1 as:

$$P_{1,2} = \frac{1}{1+e^{(S_1-S_2)/400}}$$

Where $S_1$ and $S_2$ are the scores of player1 and player2 respectively. After a match, the scores are updated as:

$$S_1’ = S_1 + K \cdot (F_1 - T_{1,2} \cdot P_{1,2})$$

$$S_2’ = S_2 + K \cdot (F_2 - T_{2,1} \cdot P_{2,1})$$

Where:

• $F_1$ and $F_2$ are the actual frame wins for player1 and player2 respectively
• $T_{1,2} = T_{2,1} = F_1 + F_2$ is the total frames played in the match
• $P_{2,1} = 1 - P_{1,2}$ is the expected frame win rate for player2 against player1
• $K$ is a constant that determines the sensitivity of score updates

This so far is standard frame-wise ELO, satisfying the Zero-Sum property, meaning the total score of both players remains constant after a match, because:

$$T_{1,2} = T_{2,1} = F_1 + F_2$$
$$P_{2,1} + P_{1,2} = 1$$

Count of 70+ breaks is introduced

$$S_1’’ = S_1’ + M \cdot (B_1 - G \cdot F_1) $$
$$S_2’’ = S_2’ + M \cdot (B_2 - G \cdot F_2) $$

Where:

• $B_1$ and $B_2$ are the counts of 70+ breaks for player1 and player2 respectively
• $G$, usually around 0.31-0.33, is the season global average of 70+ breaks per frame, calculated as total 70+ breaks divided by total frames in the season
• $M$ is a constant that determines the weight of 70+ breaks in the score

Now the Zero-Sum property is no longer satisfied on the match level, since two players could play both well (many 70+) or bad and therefore have both positive or negative changes in scores.

However, on a season level, the average score of all players remains constant, because we compared player’s match performance against the seasonal average 70+ breaks per frame, and the total 70+ breaks and total frames are fixed for the season, and therefore the total score change from 70+ breaks across all players will sum to zero.

Method A score prior to 2026 World Open last 64:

Rank	Player Name	Latest Score
1	Zhao Xintong	2406.340808642514
2	Mark Selby	2378.5029682660784
3	Judd Trump	2328.046582784832
4	Wu Yize	2323.810588553531
5	Chang Bingyu	2293.6605320392305
6	John Higgins	2264.31645446841
7	Kyren Wilson	2236.3574342426523
8	Mark Allen	2228.2852619426403
9	Barry Hawkins	2191.193175970828
10	Zhou Yuelong	2187.0799682827574
11	Shaun Murphy	2178.3587654488315
12	Ronnie O’Sullivan	2123.3886251770477
13	Xiao Guodong	2109.266799325858
14	Jack Lisowski	2109.135987267064
15	Elliot Slessor	2092.8455557749594
16	Neil Robertson	2083.49485922483

A demonstration of Score evolution since 2022/2023 season for Judd Trump, Zhao Xintong and Mark Selby:

Method B

The main problem for Method A is that the number of total frames in a match is not fixed.

Expected Number of Frames won

Method B calculates the expected number of frames won by players. For a scenario when player 1 wins k frames and player 2 wins r frames, the probability of this scenario is calculated as:

$$P(F_1=k,F_2=r,k \gt r) = \binom{k+r-1}{r} \cdot P_{1,2}^k \cdot P_{2,1}^r$$

$$P(F_1=k,F_2=r,k \lt r) = \binom{k+r-1}{k} \cdot P_{1,2}^k \cdot P_{2,1}^r$$

Where $P_{1,2}$ and $P_{2,1}$ are the expected frame win rates for player1 and player2 respectively, calculated as in Method 1.

Considering all scenarios, the expected number of frames won by player1 and player 2 are:

$$E[F_1] = \sum_{k}{} \sum_{r}^{} k \cdot P(F_1=k,F_2=r)$$
$$E[F_2] = \sum_{k}{} \sum_{r}^{} r \cdot P(F_1=k,F_2=r)$$

Then the score updates are calculated as:

$$S_1’ = S_1 + K \cdot (F_1-E[F_1])$$
$$S_2’ = S_2 + K \cdot (F_2-E[F_2])$$

In this case, there is no match level zero-sum property. Take example of a match where Zhao Xintong best an amateur player 4-3:

• Method A would deduct Zhao’s score because he has about 90+% expected frame win rate but only won 4 out of 7
• Method B would increase Zhao’s score slightly because he won more frames than expected (but very close to 4)
• Both Methods would increase the amateur player’s score significantly because he won much more frames than expected

Therefore, we need a solution to balance out the inflation of scores caused by Method B, introducing:

Score Decay and Recovery

For a match on day $t$ for a player. Check their last match’s date $t’$, if $\Delta t=t-t’>7$, it triggers decay or recovery before we evaluate the matches expected number of frames won by players.

• if the player’s current score is below 1500 and their historical highest score, we “recover” their score by an amount proportional to $\Delta t$ and the difference between current score and historical highest, with a maximum cap.
• else, if the player’s current score is above its historical average score, we “decay” their score by an amount proportional to $\Delta t$ and the difference between the current score and the historical average, with a maximum cap.

By adjusting the hyperparameters of decay and recovery, we can control the overall inflation of scores caused by Method B, keeping the overall average around 1500.

This “decay and recovery” mechanism also helps to reflect players’ current forms more accurately, as elite players who have been inactive for a while will have their skills regressed towards their average, and players with lower scores will recover from the break.

A important note to this method is that an initialization of players’ estimated scores are recommended (or a burn-in period), otherwise the historical average would not be accurate.

Method B score prior to 2026 World Open last 64:

Rank	Player Name	Latest Score
1	Mark Selby	2960.1461099128837
2	Zhao Xintong	2753.019490099193
3	Wu Yize	2546.3414952509206
4	John Higgins	2426.842646091861
5	Mark Allen	2391.3486734734875
6	Judd Trump	2333.2611272735026
7	Barry Hawkins	2284.461814312875
8	Ronnie O’Sullivan	2235.531035051619
9	Xiao Guodong	2234.5004336109746
10	Elliot Slessor	2213.436021451588
11	Jack Lisowski	2210.7400483689507
12	Kyren Wilson	2191.188032900559
13	Zhang Anda	2176.361755067192
14	Shaun Murphy	2159.3051323349814
15	Chang Bingyu	2128.725427902105
16	Chris Wakelin	2116.705502290573

A demonstration of Score evolution since 2022/2023 season for Judd Trump, Zhao Xintong and Mark Selby:

Prediction for 2026 World Open last 64:

source:

• For rankings: snooker.org
• For matches results: cuetracker.net

sourcecode:

• My Github