### Probability Distributions

Probability distributions show league-wide win/loss rates (%) for a specific game-state (e.g., ‘home and trailing’) at the expiration of Period X. Example:
The figure to the left represents win/loss probabilities (%) for home teams that are trailing at the end of the 2nd period. This figure reveals that the league-wide win rate of said teams ranges between 0 and 23%, with a median value around 6%, whereas the league-wide loss rate of these teams ranges between 0 and 60% with a median value of roughly 28%.

Stated differently, home teams that are trailing at the end of the 2nd period are five times more likely to lose than win the game.

### Team-Period Probabilities

The below figure shows win/loss probabilities for each team as a function of categorical score (i.e., leading, tied, and trailing) at the end of a given period. The % probabilities of losing are shown in red, while those of winning are shown in blue. For aesthetics we chose to denote the losing % values as negative values.

NOTE: Each team’s win/loss probabilities are provided with respect to Category, i.e., Away or Home. For each Category, the absolute values of probabilities sum to 100% for each Team. Examples:

Let’s assume that the probabilities displayed in the above figure reflect those at the end of the 1st period for away games. Below are a few examples of how this figure is interpreted.

Anaheim Ducks (ANA) – The Ducks only lead their opponent 19.4% (6.5 + 12.9) of the time at the end of the 1st period. Conversely, they trail their opponent 48.4% (38.7+9.7) of the time at the end of the 1st period. Roughly 39% of all of the Ducks’ away games are accounted for by trailing their opponent at the end of the 1st period and eventually losing the game.

Boston Bruins (BOS) – The Bruins lead their opponents 41.3% (10.3 + 31) of the time at the end of the 1st period. They win 75% (31/41.3) of these games, and lose the other 25% (10.3/41.3).

Carolina Hurricanes (CAR) – The Hurricanes are undefeated when they lead their opponents at the end of the 1st period. Stated differently, when CAR has the lead at the end of the 1st period they win every single contest. Roughly 27% of all the Hurricanes’ away contests are accounted for by leading their opponent at the end of the 1st period and then going on to win the game.

### Markov Chain Team Probabilities:

White numbers located in colored boxes (nodes) display probabilities with respect to Period X. These probabilities directly map to those shown in the Team-Period probability Figures (above).

Black numbers located between the colored boxes display probabilities with respect to the node directly above them. For each node, these probabilities sum to 100%

Three distinct node colors are used to represent the categorical score of the respective team (see below figure). For rows denoted “END OF PERIOD X”, the colors represent whether the team is leading (blue), tied with (grey), or trailing (red) their opponent. For rows denoted “FINAL”, the colors represent whether the team won the game (blue), lost in overtime / shootout (grey), or lost in regulation (red). Example:

The figure above shows that our example team has a 39.3% chance of trailing their opponent at the end of the 1st period.

The probabilities that the example team will lead, be tied with, or trail their opponent at the end of the 2nd period after trailing at the end of the 1st period are 0%, 27.2%, and 72.8%, respectively. In other words, when the example team is trailing at the end of the 1st period, there’s a:

• 0% chance they’ll have the lead at the end of the 2nd period

• 27.2% chance they’ll be tied with their opponent at the end of the 2nd period

• 72.8% chance they’ll be trailing their opponent at the end of the 2nd period

If we look at the End of Period 2 row in the above figure, we can make statements like:

• 28.6% of our example team’s games are accounted for by the team trailing at the end of the 1st and 2nd periods

• There’s a 10.7% overall probability that our example team will trail their opponent at the end of the 1st period and then be tied with their opponent at the end of the 2nd period