Win Probability Added (WPA) - playoff point scoring

[overpass]

I created a WPA model with a Poisson scoring distribution for NHL playoff scoring. Briefly, the model calculates the team's probability of winning before the goal, after the goal, and assigns a value to the goal based on the difference.

Win probability is calculated using the assumption that a team is equally likely to score at any time throughout the game (i.e. a Poisson distribution), with a scoring frequency equal to the average of team GF and opponent GA.

No difference is made between goals and assists, and a player gets full credit for a goal on which he receives a point (just as he does with the points statistic).

Here are the top WPA point scoring playoff seasons since 1980.

1. Evgeni Malkin 2009 - 7.88 WPA
2. Joe Sakic 1996 - 7.08 WPA
3. Doug Gilmour 1993 - 6.77 WPA
4. Nikita Kucherov 2020 - 6.53 WPA
5. Brayden Point 2020 - 6.39 WPA
6. Connor McDavid 2024 - 6.38 WPA
7. Mario Lemieux 1991 - 6.38 WPA
8. Mark Recchi 1991 - 6.27 WPA
9. Wayne Gretzky 1993 - 6.24 WPA
10. Peter Forsberg 2002 - 6.23 WPA

I think it's interesting to see a playoff scoring leaderboard that isn't dominated by Gretzky and Lemieux, although they are present.

Here are the top WPA per game playoff seasons since 1980 (minimum 15 GP)
1. Leon Draisaitl 2022 - 0.372 WPA/GP
2. Connor McDavid 2022 - 0.354 WPA/GP
3. Mario Lemieux 1992 - 0.342 WPA/GP
4. Wayne Gretzky 1988 - 0.333 WPA/GP
5. Evgeni Malkin 2009 - 0.328 WPA/GP
6. Doug Gilmour 1993 - 0.323 WPA/GP
7. Joe Sakic 1996 - 0.322 WPA/GP
8. Wayne Gretzky 1985 - 0.312 WPA/GP
9. Peter Forsberg 2002 - 0.312 WPA/GP
10. Matthew Tkachuk 2023 - 0.298 WPA/GP

And here are the top WPA per point playoff seasons since 1980 of the seasons I've calculated (which is far from all of them).
This shows whose points were the most valuable, on average. It favours players in lower scoring eras, as well as players who frequently scored key points and rarely scored meaningless points.

1. Joe Nieuwendyk 1999, 0.258 WPA/P
2. Jarome Iginla 2004, 0.252 WPA/P
3. Matthew Tkachuk 2023, 0.248 WPA/P
4. Patrick Kane 2013, 0.231 WPA/P
5. Peter Forsberg 2002, 0.231 WPA/P
6. Evgeni Malkin 2009, 0.219 WPA/P
7. Joe Sakic 1996, 0.208 WPA/P
8. Daniel Briere 2010, 0.206 WPA/P
9. David Krejci 2013, 0.206 WPA/P
10. Sidney Crosby 2008, 0.203 WPA/P

And the lowest WPA per point (higher scoring eras, more meaningless points). Playing for dominant teams also lends itself to lower WPA.

1. Mike Bossy 1981, 0.115 WPA/P
2. Wayne Gretzky 1985, 0.119 WPA/P
3. Steve Yzerman 1998, 0.127 WPA/P
4. Wayne Gretzky 1984, 0.128 WPA/P
5. Rick Middleton 1983, 0.130 WPA/P

 

[Bear of Bad News]

I like this a lot - it's also consistent with the knowledge that in high-scoring eras, it takes more goals to "buy" a victory.

 

[overpass]

I like this a lot - it's also consistent with the knowledge that in high-scoring eras, it takes more goals to "buy" a victory.

Yeah, the scoring era adjustment is built in.

The scoring level of goals/game can be compared with the inverse of WPA/game. Both could be considered the number of goals to buy a victory.

 

[Hockey Outsider]

Thanks for sharing. This is exactly what I was planning to get to (at some point). Do you have a summary of the highest career scorers under this method? (Obviously that favours players who played in more playoff games, but curious to see how Gretzky looks compared to Crosby/Sakic/Yzerman).

 

[ScottyMascotty]

 

[overpass]

Thanks for sharing. This is exactly what I was planning to get to (at some point). Do you have a summary of the highest career scorers under this method? (Obviously that favours players who played in more playoff games, but curious to see how Gretzky looks compared to Crosby/Sakic/Yzerman).

I do not. I'm going to play around with automating the calculation more and I'll see if I can get complete numbers.

 

[MadLuke]

Not sure i get this comments:
Given that it's very unlikely that any 3rd period goal changes the probability of the game even a fraction of a percent...
Here's the final* Win Probability Added for skaters in the 2023 Playoffs.

Also it seem's like 7 Panthers added 20.13 games (so I imagine some panthers were in the negative win added to balance, for how much they did not score ?)

 

[Bear of Bad News]

Not sure i get this comments:
Given that it's very unlikely that any 3rd period goal changes the probability of the game even a fraction of a percent...
Here's the final* Win Probability Added for skaters in the 2023 Playoffs.

The score was 6-1, Vegas, going into the third period, so the premise was that nothing that happened in the third period was likely to change Vegas's near-100% win probability at that point so he may as well post the tables.

 

[MadLuke]

A that the kind of context reading something 2 years after easily lost, make sense...

 

[Hockey Outsider]

Also it seem's like 7 Panthers added 20.13 games (so I imagine some panthers were in the negative win added to balance, for how much they did not score ?)

This is an interesting issue. The win probability added doesn't necessarily add up to 100% in each game.

Let's say a team takes a 1-0 lead five minutes into the first period. Their goalie gets a shutout. The player who scored that goal might get 0.10 (ie the win probability went from 50% to say 60%). Who does the remaining 40% get allocated to? There are no other "events" aside from the passage of time.

On the other hand, there could be a game that ends up being 6-5 in overtime. The teams keep alternating 1-goal leads. The goal that makes it 1-0 five minutes into the first would still be worth 0.10. Then when the opponent ties it five minutes later, that goal would be worth slightly more (maybe 0.12). As the game progresses into the second and third, these go-ahead and tying goals might start being worth 0.2 or even 0.3. The OT winner, by definition, is worth 0.5. So the winning team could easily end up with a 150% win probability (50% for the OT goal and then perhaps 20% for each of its five goals).

The only way the system "works" (ie each game adds up to 100%) is if the skaters get credit for the goals scored, and the opposing goalie gets penalized for the decrease in win probability. That doesn't seem fair (or informative) because goalies would only have negative values.

 

[Hockey Outsider]

Here's a theoretical discussion about how the framework might work. I have some ideas for how to incorporate goaltending into it, but I'll save that for another time.

Let's take game 7 of the 2001 Stanley Cup finals as an example:

• the game starts 50-50. After the first several scoreless shifts, the game's still tied, and the probability remains 50-50. Each shift by each player is worth zero.
• Alex Tanguay scores at 7:58 of the first period. The probability is now (hypothetically) 60-40 for the Avalanche. The five skaters on the ice would get the +0.1 shared between them (ie 50% to 60% = 10%, or 0.1 as a decimal). (We can debate how that gets allocated - presumably Tanguay would get the biggest portion. Hinote, with the only assist, would get a bit less. But arguably the other three skaters - Sakic, Bourque, and Foote - deserve something. Maybe it's +0.04 for Tanguay, +0.03 for Hinote, and +0.01 for the other three). The five Devils on the ice (Stevens, Holik, etc) would get equal blame for the goal against (ie they get -0.02 each). The system "balances" so both sides still add up to zero.
• The rest of the period passes. By the end of the period, the win probability might now be 70-30 in favour of Colorado. With each scoreless shift, each Avalanche gets a very small plus, and each Devil gets a very small minus. At the end of the first period, Colorado's players are collectively +0.20 (of which +0.10 is from the goal, and +0.10 is from the passage of time). Tanguay might be up to +0.041, Bourque at +0.012, Blake (who wasn't on the for the goal, but who played lots of minutes) at +0.002, etc. New Jersey's players are collectively -0.20 (of which -0.10 is from the goal, and -0.10 is from the passage of time).
• Colorado scored two goals at approx the five and six minute marks of the second period. By that point, up 3-0 close to halfway through the game, they probably had a 90% chance of winning. Tanguay, with two goals, a secondary assist, and several zero-event shifts, might now be up to +0.20. Sakic, with a goal and an assist, might be +0.10. The scoreless Ray Bourque (who was on the ice for at least two of these goals) might be something like +0.05. Add everything up and the team would be +0.40 overall (reflecting an increase in win probability from 50% to 90%). Similarly, Holik and Stevens would be something like -0.08 each.
• the Devils score midway through the second. Sykora scores a big goal (cutting the probability from say 90-10 to 75-25) - but he was also on the ice for a goal against. My guess is he probably ends the game on the positive side, but not by much.
• with each passing shift in the third period, the probability of Colorado winning increases. It might have been 80-20 at the start of the third (with a two goal lead), but by the end it's 100-0. So there's an extra +0.2 to allocate to Colorado players, and -0.2 to allocate to New Jersey players (reflecting that a scoreless shift in the third period when the Avalanche are up 3-1, is a good thing for the winning team and a bad thing for the losing team).
• ultimately, all Colorado skaters end up at +0.5 and all New Jersey skaters end up at -0.5.

Obviously this is a theoretical discussion, but I think the framework makes sense conceptually.

 

[Bear of Bad News]

I've done something similar to what you describe with just the goalies (using a Poisson approximation). It ascribes all credit for "nothing happening" to the leading goaltender (for instance).