MY CALCULATIONS ABOUT THE MAPLE LEAFS' PLAYOFF CHANCES

  by Jeffrey S. Rosenthal (probability.ca/jeff), April 12, 2006

For the Toronto Sun newspaper article at:
http://torontosun.canoe.ca/News/Columnists/Strobel_Mike/2006/04/13/1532433.html


I assumed that in each game, each team has probability 45% of getting
two points, 10% of getting one point, and 45% of getting zero points.
(That is, I assumed that all teams have equal chance in the remaining
games, and furthermore I computed that about one game in ten ends with
an "OT" [one point] result.)

This leads to the following probabilities for final point counts for the
four different teams.  [* added later to show true final point count.]

TORONTO:
84:  4.1%
85:  3.7%
86: 17.6%
87: 11.1%
88: 27.0%
89: 11.1%
90: 17.6%  [*]
91:  3.7%
92:  4.1%

MONTREAL:
91:  4.1%
92:  3.7%
93: 17.6%  [*]
94: 11.1%
95: 27.0%
96: 11.1%
97: 17.6%
98:  3.7%
99:  4.1%

ATLANTA:
85:  4.1%
86:  3.7%
87: 17.6%
88: 11.1%
89: 27.0%
90: 11.1%  [*]
91: 17.6%
92:  3.7%
93:  4.1%

TAMPA BAY:
89:  9.1%
90:  6.1%
91: 28.7%
92: 12.2%  [*]
93: 28.7%
94:  6.1%
95:  9.1%

Those figures then lead to the following probabilities for Toronto to beat
or tie each of the various other teams (in total points at end of season):

Prob that Toronto beats Montreal = 0.17%  [didn't]
Prob that Toronto ties Montreal = 0.30%  [didn't]

Prob that Toronto beats Atlanta = 30.2%  [didn't]
Prob that Toronto ties Atlanta = 11.5%  [did]

Prob that Toronto beats Tampa Bay = 2.1%  [didn't]
Prob that Toronto ties Tampa Bay = 3.6%  [didn't]

OVERALL CONCLUSIONS:

 * It's virtually impossible for Toronto to beat or tie Montreal.  So,
let's ignore that possibility.

 * If Toronto beats Tampa Bay, then this means they did very well in
their last four games, so they will probably also beat Atlanta.  So,
let's not worry about Atlanta.

 * So, everything comes down to Toronto beating (or tying) Tampa Bay.

 * The probabilities are 3.6% to tie Tampa Bay, plus 2.1% to beat
Tampa Bay.  [they didn't]

 * This gives a total probability of 5.7% (about one chance in 17)
for Toronto to have a chance at the playoffs.  [they didn't]

 * Or, to be pessimistic, about 16 chances in 17 that they will miss out.
[they did]

Regards,

Jeffrey S. Rosenthal
Professor
Department of Statistics
University of Toronto
100 St. George Street, Room 6018
Toronto, Ontario
Canada  M5S 3G3

http://probability.ca/jeff/