[gvitaly]

I did the research about how many teams drafted in the top 3 in the last little while, or have players playing for them that were drafted in the top 3. You might find it interesting. I looked at all the drafts from 2003, with a couple of HMs.

Spoiler!

2003

1. Fleury - PIT -> VGK
2. Staal - CAR -> MTL
3. Horton - FLA -> Done

2004

1. Ovechkin - WSH
2. Malkin - PIT
3. Barker - CHI -> Done

2005

1. Crosby - PIT
2. Ryan - ANA -> DET
3. Johnson - CAR -> NYR

2006

1. Johnson - STL -> COL
2. Staal - PIT - CAR
3. Towes - CHI

2007

1. Kane - CHI
2. van Riemsdyk - PHI
3. Turris - ARI -> EDM

2008
1. Stamkos - TBL
2. Doughty - LAK
3. Bogosian – ATL(WPG) -> TOR

2009
1. Tavares – NYI -> TOR
2. Hedman – TBL
3. Duchene – COL -> NSH

2010
1. Hall – EDM -> BOS
2. Seguin – BOS -> DAL
3. Gudbranson – FLA – NSH

2011
1. Nugent-Hopkins – EDM
2. Landeskog – COL
3. Huberdeau – FLA

2012
1. Yakupov – EDM -> Done
2. Murray – CBJ -> NJD
3. Galchenyuk – MTL -> TOR

2013
1. MacKinnon – COL
2. Barkov – FLA
3. Drouin – TBL – MTL

2014
1. Ekblad – FLA
2. Reinhart – BUF
3. Draisaitl – EDM

2015
1. McDavid – EDM
2. Eichel – BUF
3. Strome – ARI – CHI

2016
1. Matthews – TOR
2. Laine – WPG -> CBJ
3. Dubois – CBJ -> WPG

2017
1. Hischier – NJD
2. Patrick – PHI
3. Heiskanen – DAL

2018
1. Dahlin – BUF
2. Svechnikov – CAR
3. Kotkaniemi – MTL

2019
1. Hughes – NJD
2. Kakko – NYR
3. Dach – CHI

2020
1. Lafreniere – NYR
2. Byfield – LAK
3. Stutzle – OTT

HM:
2001.2 Spezza – OTT -> TOR
1997.1 Thorton – BOS -> TOR
1997.2 Marleau – SJS

Just drafted in the top 3 - 26/31 teams.
Currently have a player that was drafted in the top 3 – 24/31 teams.
Either or – 29/31 teams.

As a result I don't think you can quantify that having a top 3 pick is a requirement. Chances are that one random team with a top 3 draft pick winning are 84%. Chances for a team that either has a top 3 pick or acquired one are 94%.