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Saturday, April 09, 2011

Permutations and Combinations (aka the Draft Lottery)

Quick: what's 14 x 13 x 12 x 11? It's 24,024.

What's that have to do with the Draft Lottery? Well, everything.


The lottery is conducted with the selection of four balls from a pool of 14. Once a ball is chosen, it is not replaced (so each ball can be selected only once). As if turns out, there are 24,024 possible "permutations" that can be chosen. However, when you change it to combinations (ie 1-2-3-4 is the same result as 4-3-2-1 or 2-3-4-1.... or 21 other permutations), there are only (24,024 divided by 24 = ) 1,001 possible results.


One of those 1,001 is thrown out (I don't believe that the NHL has ever identified which one it is) and the others are assigned to each of the teams.


Here are the odds of winning the lottery:

30th place team – Edmonton -- 25.0%  (but they have a 48.2% chance of retaining first pick as teams can only move up four spots)
29th place team – Colorado -- 18.8%
28th place team  -- Florida -- 14.2%
27th place team – 10.7% --currently NYI
26th place team – 8.1% -- NYI, if Isles beat Philadelhpia
25th place team – 6.2%
24th place team – 4.7%
23rd place team – 3.6%
22nd place team – 2.7%
21st place team – 2.1%
20th place team – 1.5%
19th place team – 1.1%
18th place team – 0.8%
17th place team – 0.5%

If the Isles beat Philadelphia tonight, they will finish 26th, and have an 8.1% chance of winning the lottery (about 1/12.5); if the lose (in regulation, overtime or shootout), they will finish 27th, and have almost a 1 in 9 shot of winning the lottery.

Forever1940 is the nom de plume of Eric Hornick, statistician on Islander home telecasts since 1982. Visit my blog: forever1940.blogspot.com and follow me on Twitter @ehornick



From: Eric <forever1940@yahoo.com>
To: forever1940@yahoo.com
Sent: Mon, April 12, 2010 12:47:31 PM
Subject: [Notes From Forever1940] Permutations and Combinations (aka the Draft Lottery)

Quick: what's 14 x 13 x 12 x 11? It's 24,024.

What's that have to do with the Draft Lottery? Well, everything.

The lottery is conducted with the selection of four balls from a pool of 14. Once a ball is chosen, it is not replaced (so each ball can be selected only once). As if turns out, there are 24,024 possible "permutations" that can be chosen. However, when you change it to combinations (ie 1-2-3-4 is the same result as 4-3-2-1 or 2-3-4-1.... or 21 other permutations), there are only (24,024 divided by 24 = ) 1,001 possible results.

One of those 1,001 is thrown out (I don't believe that the NHL has ever identified which one it is) and the others are assigned to each of the teams.

Having watched last year's lottery, I think that the NHL could do a better job with building excitement during the drawing itself -- updating the odds after each of the numbers are drawn. Perhaps former Ranger announcer Monty Hall, or fellow Canadian Alex Trebek could host.

81 of those 1,000 combinations belong to the Isles, meaning that by chance the Isles should win the lottery every 12.345 years. Perhaps this is the one.

Forever1940 is the nom de plume of Eric Hornick, statistician on Islander home telecasts since 1982. Visit my blog: forever1940.blogspot.com and follow me on Twitter @ehornick

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Posted By Eric to Notes From Forever1940 at 4/12/2010 12:47:00 PM

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