Doctor No
Registered User
Part of it's home-ice (just having an extra game) - apples to apples would be (sort of) looking at the sweep probabilities for each team, since there the number of home games is the same.
SRS algorithm (2016 Stanley Cup playoffs)
- Thread starter Doctor No
- Start date
Ohashi_Jouzu*
Registered User
Or a six game series:
Pit: 38.1%
SJ: 30.8%
Draw: 31.1%
I'm prepping for a seesaw ride, myself.
Doctor No
Registered User
Doctor No
Registered User
Pens take a nice lead in the series to start:
Outcome
|
Prob
PIT in 4 games|13.1%
PIT in 5 games | 21.5%
PIT in 6 games|18.2%
PIT in 7 games|17.1%
SJS in 7 games|13.4%
SJS in 6 games|11.7%
SJS in 5 games|5.0%
PIT wins | 69.9%
SJS wins|30.1%
PIT in 4 games|13.1%
PIT in 5 games | 21.5%
PIT in 6 games|18.2%
PIT in 7 games|17.1%
SJS in 7 games|13.4%
SJS in 6 games|11.7%
SJS in 5 games|5.0%
PIT wins | 69.9%
SJS wins|30.1%
Hank Chinaski
Registered User
But remember: there's no profit to be had if your probability measurement is only "as good" as the Vegas line.
Doctor No
Registered User
True - and if you assume that discrepancies are because of Vegas' error half the time, and because of your own error half the time (perhaps generous, perhaps not), then you have to identify gaps at least twice the size of the vigorish just to break even.
Doctor No
Registered User
Penguins up 2-0 at home:
Outcome
|
Prob
PIT in 4 games|23.7%
PIT in 5 games | 28.2%
PIT in 6 games|17.7%
PIT in 7 games|13.7%
SJS in 7 games|10.6%
SJS in 6 games|6.0%
PIT wins | 83.4%
SJS wins|16.6%
PIT in 4 games|23.7%
PIT in 5 games | 28.2%
PIT in 6 games|17.7%
PIT in 7 games|13.7%
SJS in 7 games|10.6%
SJS in 6 games|6.0%
PIT wins | 83.4%
SJS wins|16.6%
Tim Calhoun
#11
- May 31, 2006
- 10,457
- 1,319
Doctor No
Registered User
Good question! Both get to a similar place, but do so differently.
An SRS algorithm looks at a team's body of work all at once (evenly weighted, or weighted per the developer's preferences once "tuned"). The SRS looks at your average margin of victory (in total) and your average schedule strength (in total), and that's its measure of your strength. Order doesn't matter (unless you program it in afterwards).
An ELO algorithm adjusts each team's strength based on each individual matchup Order does matter.
Ultimately, they both get to similar places, if tuned properly.
One advantage of the SRS is that the end units are intuitive - goals per game. For an ELO, that's not the case.
An SRS algorithm looks at a team's body of work all at once (evenly weighted, or weighted per the developer's preferences once "tuned"). The SRS looks at your average margin of victory (in total) and your average schedule strength (in total), and that's its measure of your strength. Order doesn't matter (unless you program it in afterwards).
An ELO algorithm adjusts each team's strength based on each individual matchup Order does matter.
Ultimately, they both get to similar places, if tuned properly.
One advantage of the SRS is that the end units are intuitive - goals per game. For an ELO, that's not the case.
Doctor No
Registered User
Sharks win on home ice:
Outcome
|
Prob
PIT in 5 games
|
27.0%
PIT in 6 games|24.4%
PIT in 7 games|20.4%
SJS in 7 games|16.4%
SJS in 6 games|11.9%
PIT wins | 71.8%
SJS wins|28.2%
PIT in 6 games|24.4%
PIT in 7 games|20.4%
SJS in 7 games|16.4%
SJS in 6 games|11.9%
PIT wins | 71.8%
SJS wins|28.2%
hatterson
Registered User
So I think it'd be interesting to see how much of the odds change in the algorithm is due to modified ratings of the teams and how much is simply due to certain situations being eliminated as possibilities.
For example, in the first run, the Pens had a 55.4% chance to win the series. They won the first game and their odds jumped to 69.9%. Part of that is due to the Pens being rated stronger (due to winning) and part of it is due to the fact that a Sharks sweep is no longer possible or, more generally, the "new" series is a 6 game series with equal home games where the Pens only have to get to 3 before the Sharks have to get to 4.
To think of it another way. If the odds of the single game for game 1 were Pens 60% Sharks 40% and then the Pens win, you're essentially throwing out 40% of all the possible trails the series could take that led to the initial 55.4% winning chance which will obviously change the odds.
Are you able to (easily) run the odds while keeping the team strengths the same after each game? Would be interesting to see, especially if done to past series/years, if the model has higher accuracy when updating team strengths during a series or if it's more accurate when the team strength is fixed constant and the only variable is the state of the series.
In general, if a team wins game 1 and 2 do they actually have a higher chance to win game 3 than this system would have predicted at the beginning of the series or is the series purely a weighted random walk between two static opponents?
Edit: To give a concrete example.
If we assume we have two perfectly even teams and home ice advantage doesn't exist, then the probability of each team winning any given game is 50%. Also the probability of each team winning a 7 game series is 50%. Now, if absolutely nothing changes with the teams other than that team 1 won the coin flip in game 1 suddenly the odds of the series aren't 50% any more, team 1 suddenly has a 65.625% chance to win the series. That doesn't mean that team 1 is significantly stronger than team 2, they still only have a 50% chance in every game, but the win in game 1 added information to our prediction in and of itself (not just as an update to team strengths).
Game 2 can then go one of two ways. 50% of the time team A wins and then has an 81.25% chance to take the series. 50% of the time team B wins and then the series is back to dead even at 50% each.
If we apply that to this series, a 52.5% chance to win each individual game to the Pens (assuming home ice doesn't exist, which is a false assumption but done to provide an example) that results in a ~55.4% chance to win the overall series. In such a scenario, Pens winning game 1 would turn the overall odds from 55.4-44.6 into 70.2-29.8. Winning game 2 turns it into 82.2-17.8. Sharks winning game 3 turns it into 72.4-27.6 Interestingly enough, those are very close to the final numbers, which does imply that most of the variation is simply due to added information about the state of the series as opposed to the quality of the teams. Although I'm not sure how much that will change once home ice is taken into account.
I also like the coin example because it shows that a jump from 50/50 odds to 81% chance to win isn't automatically a case of an algorithm suffering from any form of recency bias or overrating a team after a couple wins, it's just due to the odds of the modified series state.
For example, in the first run, the Pens had a 55.4% chance to win the series. They won the first game and their odds jumped to 69.9%. Part of that is due to the Pens being rated stronger (due to winning) and part of it is due to the fact that a Sharks sweep is no longer possible or, more generally, the "new" series is a 6 game series with equal home games where the Pens only have to get to 3 before the Sharks have to get to 4.
To think of it another way. If the odds of the single game for game 1 were Pens 60% Sharks 40% and then the Pens win, you're essentially throwing out 40% of all the possible trails the series could take that led to the initial 55.4% winning chance which will obviously change the odds.
Are you able to (easily) run the odds while keeping the team strengths the same after each game? Would be interesting to see, especially if done to past series/years, if the model has higher accuracy when updating team strengths during a series or if it's more accurate when the team strength is fixed constant and the only variable is the state of the series.
In general, if a team wins game 1 and 2 do they actually have a higher chance to win game 3 than this system would have predicted at the beginning of the series or is the series purely a weighted random walk between two static opponents?
Edit: To give a concrete example.
If we assume we have two perfectly even teams and home ice advantage doesn't exist, then the probability of each team winning any given game is 50%. Also the probability of each team winning a 7 game series is 50%. Now, if absolutely nothing changes with the teams other than that team 1 won the coin flip in game 1 suddenly the odds of the series aren't 50% any more, team 1 suddenly has a 65.625% chance to win the series. That doesn't mean that team 1 is significantly stronger than team 2, they still only have a 50% chance in every game, but the win in game 1 added information to our prediction in and of itself (not just as an update to team strengths).
Game 2 can then go one of two ways. 50% of the time team A wins and then has an 81.25% chance to take the series. 50% of the time team B wins and then the series is back to dead even at 50% each.
If we apply that to this series, a 52.5% chance to win each individual game to the Pens (assuming home ice doesn't exist, which is a false assumption but done to provide an example) that results in a ~55.4% chance to win the overall series. In such a scenario, Pens winning game 1 would turn the overall odds from 55.4-44.6 into 70.2-29.8. Winning game 2 turns it into 82.2-17.8. Sharks winning game 3 turns it into 72.4-27.6 Interestingly enough, those are very close to the final numbers, which does imply that most of the variation is simply due to added information about the state of the series as opposed to the quality of the teams. Although I'm not sure how much that will change once home ice is taken into account.
I also like the coin example because it shows that a jump from 50/50 odds to 81% chance to win isn't automatically a case of an algorithm suffering from any form of recency bias or overrating a team after a couple wins, it's just due to the odds of the modified series state.
Last edited:
Doctor No
Registered User
You've got it exactly right - I'd elaborate, but you said it better and probably more concisely than I would have.
It's pretty easy to do the algorithm without adjusting the NPI values for each game - I just need to not run that part. Of course, at this point I have to undo some of the updates.
It's pretty easy to do the algorithm without adjusting the NPI values for each game - I just need to not run that part. Of course, at this point I have to undo some of the updates.
Doctor No
Registered User
Penguins on the Cup cusp:
Outcome
|
Prob
PIT in 5 games
|
56.7%
PIT in 6 games|21.2%
PIT in 7 games|12.5%
SJS in 7 games|9.6%
PIT wins | 90.4%
SJS wins|9.6%
EDIT: And here's what the same table would currently look like if I had left the power ratings (and home ice advantage estimate) unchanged from the start of the series:
Outcome
|
Prob
PIT in 5 games
|
55.7%
PIT in 6 games|21.4%
PIT in 7 games|12.8%
SJS in 7 games|10.2%
PIT wins | 89.8%
SJS wins|10.2%
PIT in 6 games|21.2%
PIT in 7 games|12.5%
SJS in 7 games|9.6%
PIT wins | 90.4%
SJS wins|9.6%
EDIT: And here's what the same table would currently look like if I had left the power ratings (and home ice advantage estimate) unchanged from the start of the series:
PIT in 6 games|21.4%
PIT in 7 games|12.8%
SJS in 7 games|10.2%
PIT wins | 89.8%
SJS wins|10.2%
Doctor No
Registered User
Sharks hold on:
Outcome
|
Prob
PIT in 6 games
|
48.4%
PIT in 7 games|28.5%
SJS in 7 games|23.1%
PIT wins | 76.9%
SJS wins|23.1%
PIT in 7 games|28.5%
SJS in 7 games|23.1%
PIT wins | 76.9%
SJS wins|23.1%
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