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Thursday, April 26, 2018

Permutations & Combinations (aka the NHL's 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 (it is the combination 11-12-13-14) and the others are assigned to each of the teams.

Here are the odds of winning the lottery:


31st: Buffalo Sabres: 18.5%
30th: Ottawa Senators: 13.5% (*)
29th: Arizona Coyotes: 11.5%
28th: Montreal Canadiens: 9.5%
27th: Detroit Red Wings: 8.5%
26th: Vancouver Canucks: 7.5%
25th: Chicago Blackhawks: 6.5%
24th: New York Rangers: 6.0%
23rd: Edmonton Oilers: 5.0%
22nd: New York ISLANDERS: 3.5%
21st: Carolina Hurricanes: 3.0%
20th: New York ISLANDERS (from CGY): 2.5%
19th: Dallas Stars: 2.0%
18th: St. Louis Blues: 1.5% (**)
17th: Florida Panthers: 1.0%
(*) Ottawa owes either this year's 1st round pick or next year's 1st round pick to Colorado
(**) If the Blues win one of the lottery picks (and thus move into the top 10) they can retain this pick and send Philadelphia next year's 1st round pick.  Otherwise this pick goes to the Flyers.

While last year the Isles' odds were 99:1, their odds are slightly better than 16:1 that they will win the lottery with either their pick or the pick they acquired from Calgary in the Travis Hamonic deal.

For the second time, the first three picks are determined via lottery so if you want to dream, the Isles have a remotely small chance of ending up with the first two picks.

The Isles have won the lottery twice, moving from 4th to 1st in 2000 (DiPietro) and retaining the first pick in 2009 (Tavares).

Last year, the Devils (5th seed) won the lottery, and then selected Nico Hischier; the Flyers moved from 13th to 2nd and chose Nolan Patrick; Dallas moved up from 8th to 3rd and picked Finnish defenseman Miro Heiskanen.  (The Isles enter this year's lottery with the 10th and 12th seeds).

The Isles have picked 1st overall four times:  Harris (1972), Potvin (1973), DiPietro (2000), Tavares (2009)

So what are the Isles' lucky numbers?  Here are the combinations that will win the lottery for the Isles.

(Isles' own pick)

1-2-3-13
1-2-4-10
1-3-4-10
1-3-5-12
1-3-7-12
1-3-9-13
1-4-6-8
1-4-11-13
1-5-7-8
1-5-7-14
1-5-9-13
1-5-12-13
1-6-7-13
1-6-10-14
1-8-11-12
1-8-12-14
2-3-7-12
2-3-8-13
2-6-9-11
3-5-6-10
3-6-7-9
3-6-10-14
3-12-13-14
4-5-13-14
4-7-11-12
4-10-13-14
5-6-11-13
5-7-8-11
5-8-11-13
6-7-10-13
6-7-11-12
6-8-10-13
6-9-11-12
7-11-12-14
8-10-12-13

(Calgary's pick)
1-4-6-10
1-7-8-11
1-7-11-13
1-8-11-13
1-10-11-12
1-10-11-14
2-3-4-11
2-3-5-10
2-3-6-10
2-3-10-13
2-4-10-13
2-5-7-9
2-6-8-11
2-8-10-14
2-8-11-14
2-9-10-13
3-7-8-12
3-7-9-14
3-9-11-14
4-6-7-9
4-6-8-10
4-7-8-14
4-8-13-14
7-8-10-14
8-10-11-12

Each lottery ball appears in exactly 286 combinations (although the 11-12-13-14 combination would be thrown out).  

The number 1 is the most common winning number for the Isles, appearing 22 times; number 9 is the least common, appearing only 10 times.

The lottery losers will be revealed between 7:30 and 8:00 on Saturday (NBCSN); the winning three teams will be revealed during the second intermission of that night's San Jose - Vegas game (NBC).

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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