1. Buchholz and Sonneborn-Berger coefficients in hockey
Fine evaluation of mid-season standings and remaining strength schedule
Roman Parparov –

2. Personal background Chess master Chess arbiter Hockey stats aficionado
Morehockeystats.com founder
Chess statistics applications in hockey

3. Buchholz and Sonneborn-Berger coefficients
Used in chess tournaments for tie-breaks
Based on scores of the participant’s opponents

4. The Buchholz Coefficient
Applicable to situations with varying opposition
Original formula: sum of scores of the opponents
B= 1 𝑛 𝑆 𝑛
Not as useful in a regular round robin (e.g. soccer)

5. Buchholz for NHL 𝐵 𝑁𝐻𝐿 = 𝑖=1 𝑁 𝑆 𝑖 𝑁 𝑖 𝑁
Varying number of games at any point
Varying number of games of opponents at any point!
The formula:
𝐵 𝑁𝐻𝐿 = 𝑖=1 𝑁 𝑆 𝑖 𝑁 𝑖 𝑁
Excellent indicator of the strength of opponents played so far.

6. 2017/18, 640 games

7. Remaining Schedule Strength
Buchholz can be applied the same way to remaining games:
𝐵𝑟𝑒𝑚= 𝑖 𝑆 𝑖 𝑁 𝑖 82−𝑁
At the end of the season indicates the strength of divisions.

8. Rem. Str 03/12/2017

9. The Sonneborn-Berger coefficient
Used as a round-robin main tiebreaker
Indicates how well the participant played:
𝑆𝐵= 𝑖=1 𝑁 𝑟 𝑖 ∗ 𝑆 𝑖
where 𝑟 𝑖 is the result in the round I (1, 0.5, 0)
Beating tougher opposition gets rewarded

10. SB coefficient for the NHL
Again, the formula needs an adjustment:
𝑆𝐵 𝑁𝐻𝐿 = 𝑖=1 𝑁 𝑟 𝑖 ∗ 𝑆 𝑖 𝑁 𝑖 𝑁
But 𝑟 𝑖 also changes:
𝑟 𝑖 = 1 𝑖𝑓 𝑅𝑒𝑔𝑊 𝑖𝑓 𝑂𝑇𝑊/𝑆𝑂𝑊 𝑖𝑓 𝑂𝑇𝐿/𝑆𝑂𝐿 &0 𝑖𝑓 𝑅𝑒𝑔𝐿

11. Meaning of SB in the NHL Shows where the team gets its points:
High SB: a lot of upsets, good against peers, loses to bottom feeders
Normal SB: mostly from peers, or from a few upsets and bottom feeders
Low SB: from bottom feeders, cannon fodder for the top
Normal SB: 𝑆𝐵𝑛𝑜𝑟= 1 3 ∗𝑆𝐵𝑚𝑎𝑥+ 2 3 ∗𝑆𝐵𝑚𝑖𝑛
Indication of the coach’s usage of the roster?

12. 2016/17 season

14. Summary Chess has some useful tools for hockey!
Buchholz coeff. is good for schedule strength evaluation.
Sonneborn-Berger may be good for performance evaluation.
Performance? Progressive?
Descriptive, not predictive!
Predictive is … Elo!

15. More at https://morehockeystats.com/teams/buchberg Thank You!