KRACH Explained
What is it? – KRACH is “Ken’s Rating for American College Hockey.” Ken is statistician Ken Butler and the mathematical model he used is known as the Bradley-Terry Rating System.
- KRACH combines the performance of each team with the strength of the opposition against which that performance was achieved and produces a value (“rating”) for each team. The higher the rating, the better the team.
- KRACH accounts for strength-of-schedule (SOS) as it ranks the teams.
- KRACH is calculated purely from game results (win/loss/tie).
- Overtime wins count as wins.
- Shootouts count as ties.
- The ratings can be interpreted as the team’s component of empirical odds. If the ratings for two teams are 200 and 100, that is equivalent to 200:100 odds (or 20:10 or 2:1). The scale is relative.
How is it used and why? – KRACH ratings are used only to determine Divisional seeding for Nationals and for selecting the Elite wild card team to fill out the 6-team Elite Nationals field. The rationale is as follows:
- Teams play an unbalanced schedule.
- Teams do not play every team in the Conference.
- Teams that play an empirically more difficult schedule should not be unduly undervalued.
- Teams that play an empirically weaker schedule should not be unduly overvalued.
How does it work? – The simplest example is a two-team system. If A plays 9 games vs B and wins 6 of them, KRACH A =666 and KRACH B=333. (or 6 & 3, OR 2 & 1, 0R 1398 & 699).
If you are asked what the probably is that A wins game #10 vs B, your answer is 2/3 based on empirical evidence. If B wins game #10, KRACH A=600 and KRACH B=400 and your empirical probability for A to win game #11 changes to 3/5.
When you add teams C, D, etc. and they all play or don’t play each other, the arithmetic gets more complicated very quickly.
The key is understanding that KRACH is calculated recursively. The ratings are such that if you take one team’s schedule to date, play a theoretical “game” for each game already actually played, using the KRACH ratings themselves in order to predict the winner, the end result would be a theoretical won-loss percentage that matches the team’s actual won-loss percentage. Thus the results are self-checking.
It is not possible to do any better than that with a completely objective method. Any other method introduces arbitrariness and/or subjectivity.
What is the process for the USPHL – The KRACH algorithm is built into an excel program for each Conference that takes the result from each game played as input and performs the iterative calculations of the model. Initially, a fictitious team is included that plays everyone once to a tie. This eliminates division by zero for teams without a loss or tie. Otherwise, a team with no losses has KRACH=infinity.
Iterations are set to 10,000 and are repeated as necessary until the difference in expected and actual values are less than 0.00001. Published results are scaled to an average KRACH of 100. The scale is arbitrary.
At some future point, when there are no unbeaten teams or teams without at least a shootout result, the fictitious team will be removed.
For more detail on the statistical calculations and the iterative process, Google KRACH.
