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Sunday, April 08, 2012

Permutations and Combinations (aka The Draft lottery)

(Unfortunately this is one that I had multiple copies of in my files)

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 – Columbus-- 25.0%  (but they have a 48.2% chance of retaining first pick as teams can only move up four spots)
29th place team – Edmonton-- 18.8%
28th place team  -- Montreal-- 14.2%
27th place team – Islanders-- 10.7%
26th place team –Toronto-- 8.1%
25th place team –Anaheim-- 6.2%
24th place team –Minnesota-- 4.7%
23rd place team –Carolina-- 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%

So, the Isles have a 10.7% chance of winning the lottery and picking 1st.
If Toronto, Anaheim, Minnesota or Carolina win the lottery, the Isles will pick 5th (22.6%) -- this is what happened last year when Isles dropped from 4th to 5th when NJ won the lottery
Otherwise the Isles will pick 4th (65.7%)

The lottery will be held on Tuesday and televised beginning at 8:00 on NBC Sports Network and TSN.
 
Forever1940 is the nom de plume of Eric Hornick, statistician on Islander home telecasts since January 21, 1982. Visit my blog: NYISkinny.com and follow me on Twitter @ehornick

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