NHL Standings and Magic Numbers

Answers to Anticipated Questions

• Stuff about magic numbers
  • What is a magic number?
  • OK, so what does a magic number mean?
  • How do you calculate a magic number?
• About these tables in particular
  • What do the headings mean?
  • What do the other numbers or symbols mean?
  • How are the tables generated?
  • How often are the tables updated?
  • Is there anything the tables don't take into consideration?
  • Why aren't all the numbers shown?
  • How long have you been doing this?
• Future plans

In general, you have two teams A and B, with a magic number N. In the games that the two teams have left, you add the points that A earns and the points that B fails to earn (by tying or losing). If this sum exceeds N, then A is guaranteed to finish higher than B in the standings.

Magic numbers are simpler in, say, baseball, because one game equals one point, and there is only one playoff spot per division (ignoring the wild card slot). If A is in first place and B is in second, then A will clinch first place after any combination of A's wins and B's losses that add up to more than N.

Things are more complicated in hockey because of the 2-1-0 win-tie-loss system, and the fact that there are 7 extra playoff spots. The bottom line is:

• For every subsequent game that A wins, subtract 2 from N
• For every subsequent game that A ties or loses in overtime, subtract 1 from N
• For every subsequent game that B ties or loses in overtime, subtract 1 from N
• For every subsequent game that B loses in regulation, subtract 2 from N

If N is 0 (indicated here with ===, it means A can do no worse than tie with B even if A loses all its remaining games and B wins all its remaining games.

If N is negative (indicated here with ***), it means A is guaranteed to finish higher than B.

If N is some number, like 4, it means A is guaranteed to finish higher than B if it earns 4 points.

If it appears with an equal sign, such as =4, it means A can clinch a tie with B if it earns 4 points.

Thus, a team has clinched a playoff spot (barring ties, and the other details below) when its row has 7 or more ***'s. A team is mathematically eliminated when its column has 8 or more ***'s.

In some cases, the number N may be greater than two times the number of games remaining. In that case, A is not guaranteed to finish above B, unless B "helps out" -- B must lose or tie some games to reduce A's magic number. See also the question about why all the numbers aren't shown.

Take the current number of points that B has. Add the maximum number of points that B could possibly gain in its remaining games. Subtract the current point total for A to get A's magic number with respect to B.

Adjusting for ties: Next you see how many wins B would have if it won all its remaining games. If A can't achieve the magic number without exceeding that number of wins, then in reaching the magic number A will automatically win the first tie-breaker and no adjustment is necessary. Otherwise, add one to the magic number. See also the item on things these tables don't take into account for more about ties.

About these tables in particular

GP = games played, W = wins, L = losses, T = ties, OTL = overtime loss, PTS = points, PTS/G = points per game, PRJ = final points the team will have if it continues to earn points at its current rate. Overtime losses and ties are distinct, so a record of 26-11-8-3 means 26 wins, 11 losses, 8 ties, and 3 overtime losses for a total of 49 games.

The row for each team shows its current number of games played, wins, losses, etc., followed by its magic number for the other teams in the same conference. If the row for team A and the column for team B has a number, for example 4, that means if team A earns 4 more points in the standings, it is guaranteed to finish higher than team B. If the number is prefaced by an = sign, such as =4, then it means team A can clinch a tie with team B by earning 4 points.

Why would the table ever show a number like 4, instead of just saying =3? Suppose team A has 40 wins, 100 points and 3 games left, while team B has 39 wins, 99 points, and 2 games left. Team B can finish with a maximum of 41 wins and 103 points. Team A only needs 3 points to tie team B in points, but if it gets those 3 points via three OTLs, then it will finish with 40 wins and 103 points, losing the tie-breaker. In this case the table would say 4 instead of =3. (If team A goes on to win its next game, resulting in 41 wins, 102 points, and 2 games left, then the magic number will in fact say =1, instead of 2.)

If, instead of a number, it shows ===, then team A has already clinched a tie with team B. If it shows *** then team A is guaranteed to finish higher than team B. If it shows ... then team A cannot guarantee a higher finish than team B by itself; it needs "help" from team B in order to be assured of a higher finish (this generally means team B has games in hand).

In any case where you see an =, whether it's === or =4, you will need to look up the head-to-head record, and possibly the goal differential, to determine how to resolve the tie, since as mentioned below, these tables do not account for the latter tie-breakers.

The intent is for the tables to show what numbers guarantee a higher finish or tie. Due to schedule dependencies and numbers of wins, there are often scenarios where a team could clinch a higher finish or tie while earning fewer points than are show in this table. So these numbers represent an upper bound.

I wrote a program that takes as input the list of team records. It computes the magic numbers and outputs the standings. Standings information is taken from ESPN's NHL standings page. So the information you see here is at best as accurate and up-to-date as the information on that page (though if I notice and/or people point out errors in their standings, I'll usually correct the standings by hand until ESPN fixes them).

Every 15 minutes. Which is a mild waste of bandwidth during the day (if there are no day games) but it's just a drop in the bucket compared to all the people downloading pr0n. (Actually I think this is a poor rationalization but at the moment I'm too lazy to do anything about it.)

There are a few things:

• reality -- these are only mathematical computations. A team may have a mathematical chance at a playoff spot long after any realistic hope has passed.
• ties -- the program does know how to break ties by number of wins, but it does not have info about head-to-head records or goal differentials, etc. The program assumes that a team will win all tie-breakers that it doesn't know about. So in fact if two teams are tied and have the same number of games remaining and the same number of wins, the program will report the magic number for each team over the other (and it will be the same number). If they have no games remaining, it will report that each has eliminated the other. You'll have to apply the remaining tie-breaking criteria yourself to determine which team actually finished higher. The tie-breaking criteria are, in order:
  1. Greater number of games won by the club.
  2. Higher number of points earned in games against each other. If two teams are tied and have not played an equal number of home games against each other, points earned in the first game played in the city that had the extra home game shall not be included. If more than two teams are tied, the higher percentage of available points earned in games among those teams shall be used to determine the standing.
  3. The greater differential between goals scored for and against for the entire regular season.
  Source: http://www.nhl.com/news/mar/033099playoffs.htm (a document which no longer exists, but a similar one will probably be recreated as playoff time nears -- it's a real pain to search for stuff on the NHL web site...)
• schedules -- the program has no knowledge about scheduling impossiblities -- for example, this year ('98-'99) after Vancouver had already been eliminated by 7 teams, Calgary and Edmonton had magic numbers of 2 and 3 over the Canucks so they showed up as not eliminated yet. However Calgary and Edmonton had 3 games remaining against each other, which means 6 points have to be divided up between Calgary and Edmonton somehow (and with the new overtime system, it would be 6 or more points this year), and there's no way to do that without giving Calgary at least 2 or Edmonton at least 3, so Vancouver was in fact mathematically eliminated at that point, even though the tables showed otherwise (I might have the teams or the numbers wrong but it illustrates the point anyway).

In some cases, a team's magic number will be greater than the number of points available to them in their remaining games. For example, they might have a magic number of 10 but only have 4 games left to play. Since they can only win 8 of those 10 points on their own, they need the other team's "help" in achieving the magic number. Thus, the outcome depends on another team's performance, so I've decided to leave the numbers out in this case and only print out the cases where a team has direct control of its own destiny.

Note that in some cases, it is the lower-ranked team that has control of the situation, when it has "games in hand." In the simplest case, the higher-ranked team might have one more point in the standings, but no games left to play, while the lower-ranked team still has one or more games left to play. In that case the lower-ranked team actually has a magic number of 2 over the higher-ranked team (or possibly 1 depending on the tie-breaking conditions).

Originally I always displayed the magic number for the higher-ranked team over the lower-ranked team, even if the lower-ranked team had control. Then Arik Florimonte asked why I don't show all the magic numbers, which (after a couple months' delay) got me to thinking about the whole situation, which led to the change described in the first paragraph.

Since the '94-'95 playoff run.

Future Plans

• Fix bug wherein the program currently does not recognize that if 7 playoff spots have been clinched exclusively by teams in 2 of the 3 divisions in a conference, the last spot has to go to the leader of the 3rd division, so all remaining teams in the first two divisions are eliminated.
• Account for head-to-head records and goal differentials when breaking ties (see above, "Is there anything the tables don't take into consideration?")
• Account for scheduling quirks (see above)
• Show projected performance based on last 10 games (as suggested by Chuq Von Rospach)