Buchholz and Sonneborn-Berger coefficients in hockey Fine evaluation of mid-season standings and remaining strength schedule Roman Parparov – MoreHockeyStats, @morehockeystats

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

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

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)

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.

2017/18, 640 games

Remaining Schedule Strength Buchholz can be applied the same way to remaining games: 𝐵𝑟𝑒𝑚= 𝑖+1 82 𝑆 𝑖 𝑁 𝑖 82−𝑁 At the end of the season indicates the strength of divisions.

Rem. Str 03/12/2017

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

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 2 3 𝑖𝑓 𝑂𝑇𝑊/𝑆𝑂𝑊 1 3 𝑖𝑓 𝑂𝑇𝐿/𝑆𝑂𝐿 &0 𝑖𝑓 𝑅𝑒𝑔𝐿

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?

2016/17 season

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? http://www.swissperfect.com/tiebreak.htm Descriptive, not predictive! Predictive is … Elo!

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