On Tuesday night, Flyers general manager Chuck Fletcher will pray to the ping pong ball gods as the Flyers look to land the No. 1 overall selection in the 2022 NHL draft.

All 16 teams who didn’t make the playoffs this year (or the teams that acquired the positions of those non-playoff teams) will have their first-round fates decided when the draft lottery from NHL Network’s Secaucus, N.J., studio airs on Tuesday beginning at 6:30 p.m. on ESPN.

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The odds at landing that No. 1 overall pick, however, aren’t in the Flyers’ favor.

By finishing with the fourth-worst record in the league (25-46-11), the Flyers possess the fourth-best odds at earning the top pick in the draft. The Flyers have a 9.5% chance at getting the top selection. The Montreal Canadiens lead the way with a 25.5% likelihood, followed by the Arizona Coyotes (13.5%), and the Seattle Kraken (11.5%).

The expansion Kraken, led by former Flyers head coach Dave Hakstol, just edged out the Flyers for the third-worst record in the league by dropping their their final game of the season to the Winnipeg Jets.

The Flyers odds at drawing picks No. 2, 4, 5 and 6 are greater than their odds at No. 1 — 9.8% at the second selection, 15.4% at the fourth, 44.9% at the fifth, and 20.5% at the sixth.

The NHL instituted a new format for the 2022 lottery that limits the number of spots a team can move up if it wins one of the draws to 10 places. So, only the teams with the 11 worst records (or the teams that acquired those spots) can receive the first-overall pick. Given there are only two draws in the new format, the Flyers cannot be awarded the No. 3 overall pick.

Only once before have the Flyers selected first in the NHL draft. In 1975, after the Flyers won back-to-back Stanley Cups, general manager Keith Allen traded Bill Clement, Don McLean, and the No. 18 pick to the Washington Capitals in exchange for the top choice. He used that pick on center Mel Bridgman, who played 462 games for the Flyers over the course of seven years, registering 324 points (119 goals, 205 assists).

The Flyers have only selected No. 2 overall twice — once in 2007 and again in 2017.

While the Flyers finished the 2006-07 season with the league’s worst record (22-48-12) and the Chicago Blackhawks finished with the fifth-worst (31-42-9), the Blackhawks won the draft lottery. They selected winger Patrick Kane, who now ranks second in franchise history in points (1,180) and assists (750), and third in goals (430).

With the No. 2 pick in the 2007 draft, the Flyers selected winger James van Riemsdyk. He played three seasons for the Flyers before he was traded to the Toronto Maple Leafs in exchange for defenseman Luke Schenn on June 23, 2012. After spending six years in Toronto, van Riemsdyk returned to the Flyers via free agency in 2018 when he signed a five-year, $35 million deal.

In seven seasons overall with the Flyers, van Riemsdyk has posted 268 points (134 goals, 134 assists) in 466 games. He led the 2021-22 Flyers with 24 goals.

While they Flyers had greater luck in the 2017 draft lottery than they did in 2007, they were not luckier in terms of the success of their eventual pick.

The Flyers finished the 2016-17 season with the league’s 19th-best record of 39-33-10. In the lottery, the Flyers were awarded the No. 2 pick — moving up 13 spots in the draft lottery despite having just a 2.4% shot at landing it. After the New Jersey Devils selected center Nico Hischier with the top pick in the 2017 draft, the Flyers picked center Nolan Patrick second overall.

Patrick played 170 games in three seasons for the Flyers (30 goals and 40 assists for 70 points). However, injuries and a migraine disorder marred his time in Philadelphia. On July 17, 2021, the Flyers traded Patrick and defenseman Phil Myers to the Nashville Predators in exchange for defenseman Ryan Ellis. The Predators then flipped Patrick to the Vegas Golden Knights for forward Cody Glass.

In hindsight, the Flyers passed over 2019-20 Calder Trophy winner and 2021-22 Norris Trophy finalist defenseman Cale Makar (No. 4 overall to the Colorado Avalanche), top-pairing defenseman Miro Heiskanen (No. 3 to the Dallas Stars) and center Elias Pettersson (No. 5 to the Vancouver Canucks), who scored 32 goals in 2021-22, to draft Patrick.

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Earlier this year, Flyers legend Bobby Clarke criticized former general manager Ron Hextall for allegedly going against scouts’ wishes and selecting Patrick. Clarke claimed the scouts wanted to take Makar. Regardless of the team’s internal discussions, Hischier and Patrick were the consensus top-two picks going into the draft.

This year, the Flyers are the favorites to earn the No. 5 overall draft pick. They have selected there once before in franchise history. On the day after the June 6, 1967 expansion draft, the Flyers used the No. 5 overall selection on right winger Serge Bernier.