Probability, Statistics for Sports

[fletch]

The impetus for this thread is a math error that I made in another thread.  Contributions on use of probability/statistics/modeling for sports, especially for hockey, are welcome.

 

I'm using as sources (to check my math)

https://www.calculator.net/probability-calculator.html

https://www.omnicalculator.com/statistics/probability-three-events

 

Ultimately, any errors are my own fault for not double-checking, rather than glitches in web resources

[fletch]

Probability of two events, equally likely (ex. theoretically fair coin flip), that are independent events (no correlation).

P(A) = heads = 0.5

P(B) = tails = 0.5

Four possibilities are possible from the two coin flips (HH, HT, TH, TT).

2 heads = 0.5 * 0.5 = 0.25

1 head, 1 tail = (0.5*0.5) + (0.5*0.5) = 0.5

2 tails = 0.5 * 0.5 = 0.25

[fletch]

Probability of three events, equally likely (ex. theoretically fair coin flip), that are independent events (no correlation).

P(A) = heads = 0.5

P(B) = tails = 0.5

8 possibilities are possible from the three coin flips (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).

1 possibility for 3 heads = 0.5*0.5*0.5 = 0.125

3 possibilities for 2 heads, 1 tail = 3*0.5*0.5*0.5 = 0.375

3 possibilities for 1 head, 2 tails = 3*0.5*0.5*0.5 = 0.375

1 possibility for 3 tails = 0.5*0.5*0.5 = 0.125

 

 

[fletch]

Probability of two events, not equally likely (ex. biased coin flip), that are independent events (no correlation).

P(A) = heads = 0.6

P(B) = tails = 0.4

Four possibilities are possible from the two coin flips (HH, HT, TH, TT).

2 heads = 0.6 * 0.6 = 0.36

1 head, 1 tail = 2*(0.4*0.6) = 0.48

2 tails = 0.4 * 0.4 = 0.16

[SaveByRichter35]

[Albatrosss]

wtf happened to fletch?  

 

hey fletch, do you need to know how many ranger fans wore blue jerseys at the game and how many wore white?

[siddious]

6 minutes ago, CCCP said:

wtf happened to fletch?  

 

hey fletch, do you need to know how many ranger fans wore blue jerseys at the game and how many wore white?

first thing I thought of lol 

[Ozzy]

We did shots during the second period too...That's gotta count for something!

[fletch]

7 hours ago, CCCP said:

wtf happened to fletch?  

 

hey fletch, do you need to know how many ranger fans wore blue jerseys at the game and how many wore white?

just jotted down some notes before work.  corsi, fenwick all are important tools for analysis.  if there are folks on the site that know how they are calculated, this is the place to discuss.  understanding the math and assumptions allows you to better interpret what the stats tell you, instead of letting someone tell you what they mean.

[fletch]

Summary of some advanced statistics for hockey.  I like natural stat trick site.  There are other good sites. The abbreviations appear (relatively) consistent among sites.  Note there are player stats and team stats.

https://www.naturalstattrick.com/glossary.php?players

• Corsi - Any shot attempt (goals, shots on net, misses and blocks) outside of the shootout. Referred to as SAT by the NHL.
  • CF - Count of Corsi for that player's team while that player is on the ice.
  • CA - Count of Corsi against that player's team while that player is on the ice.
  • CF% - Percentage of total Corsi while that player is on the ice that are for that player's team. CF*100/(CF+CA)
• Fenwick - any unblocked shot attempt (goals, shots on net and misses) outside of the shootout. Referred to as USAT by the NHL.
  • FF - Count of Fenwick for that player's team while that player is on the ice.
  • FA - Count of Fenwick against that player's team while that player is on the ice.
  • FF% - Percentage of total Fenwick while that player is on the ice that are for that player's team. FF*100/(FF+FA)
• Shots - any shot attempt on net (goals and shots on net) outside of the shootout.
  • SF - Count of Shots for that player's team while that player is on the ice.
  • SA - Count of Shots against that player's team while that player is on the ice.
  • SF% - Percentage of total Shots while that player is on the ice that are for that player's team. SF*100/(SF+SA)
• Goals - any goal, outside of the shootout.
  • GF - Count of Goals for that player's team while that player is on the ice.
  • GA - Count of Goals against that player's team while that player is on the ice.
  • GF% - Percentage of total Goals while that player is on the ice that are for that player's team. GF*100/(GF+GA)

[fletch]

For Corsi:

https://en.wikipedia.org/wiki/Corsi_(statistic)

'Corsi numbers provide an indication of the time a team spends in the offensive zone, versus time spent in their defensive zone. Positive Corsi numbers indicate the team spends more time in the offensive zone than the defensive zone, while negative Corsi shows the opposite. This makes Corsi a proxy for "puck possession,"'

• Corsi For (CF) = Shot attempts for at even strength: Shots + Blocks + Misses
• Corsi Against (CA) = Shot attempts against at even strength: Shots + Blocks + Misses
• Corsi (C) = CF - CA
• Corsi For % (CF%) = CF / (CF + CA)
• Corsi For % Relative (CF% Rel) = CF% - CFOff%
• Corsi Per 60 Minutes at Even Strength (C/60) = (CF - CA) * 60 / TOI
• Relative Corsi per 60 Minutes at Even Strength (Crel/60) = CF/60 - CFoff/60 = On-Ice Corsi For / 60 Minutes - Off-Ice Corsi For / 60 Minutes

[fletch]

For Fenwick:

https://en.wikipedia.org/wiki/Fenwick_(statistic)#:~:text=Fenwick is an advanced statistic,(USAT) by the NHL.

'Fenwick is an indicator of how much a team controls the puck offensively throughout the course of a game.'

Fenwick = (Shots on goal FOR + missed shots FOR) – (Shots on goal AGAINST + missed shots AGAINST)

 

 

[fletch]

So Corsi and Fenwick are different ways of using shot totals to look at offensive zone versus defensive zone time and puck possession.

Edited December 8, 2022 by fletch

[fletch]

Additional statistics

https://www.naturalstattrick.com/glossary.php?players

 

Includes scoring chances, high danger scoring chances, high danger saves

 

https://www.naturalstattrick.com/glossary.php?teams

Includes Corsi, Fenwick, Scoring Chance Goals, High Danger Scoring Chances

 

'Scoring Chances - A scoring chance, as originally defined by War-on-Ice'

'Each shot attempt (Corsi) taken in the offensive zone is assigned a value based on the area of the zone in which it was recorded (see graphic on site).

Attempts from the yellow areas are assigned a value of 1, attempts from the red areas are assigned a value of 2, and attempts in the green area are assigned a value of 3....Add 1 to this value if the attempt is considered a rush shot or a rebound...Decrease this value by 1 if it was a blocked shot...Any attempt with a score of 2 or higher is considered a scoring chance.'

 

Naturalstattrick is explaining the rational for when a shot is considered a scoring chance, and when it is not considered a scoring chance.

[Albatrosss]

just FYI, there were 38% of all rangers fans wearing white jerseys at the T-Mobile arena last night; 42% were wearing blue ranger jerseys; 16% were not wearing any jersey; and 4% were undecided. 

 

 

[fletch]

9 hours ago, CCCP said:

just FYI, there were 38% of all rangers fans wearing white jerseys at the T-Mobile arena last night; 42% were wearing blue ranger jerseys; 16% were not wearing any jersey; and 4% were undecided. 

 

 

Let's not talk about the breakdown by jersey.  Let's look at the female dataset by outfit choice.  Let me know.

Edited December 9, 2022 by fletch

[fletch]

Useful distinction for me to remember about statistics versus probability.  Statistics reflect actual game data.  Probability involves modeling/simulation, or parsing historical data for likelihood of an event.

 

Statistics can be collected by observer or tracking data for player location on ice for event.

https://www.naturalstattrick.com/glossary.php?players

 

'Scoring Chances - A scoring chance, as originally defined by War-on-Ice'

'Each shot attempt (Corsi) taken in the offensive zone is assigned a value based on the area of the zone in which it was recorded (see graphic on site).

Attempts from the yellow areas are assigned a value of 1, attempts from the red areas are assigned a value of 2, and attempts in the green area are assigned a value of 3....Add 1 to this value if the attempt is considered a rush shot or a rebound...Decrease this value by 1 if it was a blocked shot...Any attempt with a score of 2 or higher is considered a scoring chance.'

 

High Danger Scoring Chances - a scoring chance with a score of 3 or higher

High Danger Goals - goals generated from High Danger Scoring Chances

Medium Danger Scoring Chances - a scoring chance with a score of exactly 2

Low Danger Scoring Chances - a scoring chance with a score of 1 or less. Does not include any attempts from the attacking team's neutral or defensive zone.

LDCF - Count of Low Danger Scoring Chances for that player's team while that player is on the ice.

SH% - Percentage of Shots for that player's team while that player is on the ice that were Goals. GF*100/SF

SV% - Percentage of Shots against that player's team while that player is on the ice that were not Goals. GA*100/SA

PDO - Shooting percentage plus save percentage. (GF/SF)+(GA/SA)

[siddious]

@Keirik @Phil y’all gonna ban fletch? His account has clearly been hacked 

[Ozzy]

54 minutes ago, siddious said:

@Keirik @Phil y’all gonna ban fletch? His account has clearly been hacked 

 

...by my accountant!

Edited December 10, 2022 by Ozzy

[Keirik]

2 hours ago, siddious said:

@Keirik @Phil y’all gonna ban fletch? His account has clearly been hacked 

[fletch]

Good stuff!

4 hours ago, siddious said:

@Keirik @Phil y’all gonna ban fletch? His account has clearly been hacked 

 

3 hours ago, Ozzy said:

 

...by my accountant!

 

1 hour ago, Keirik said:

 

 

https://www.imdb.com/title/tt0119217/characters/nm0000354

Good Will Hunting was awesome.  Will was a helluva lot tougher than me.

 

Try A Beautiful Mind about John Nash, played by Russell Crowe.

https://en.wikipedia.org/wiki/A_Beautiful_Mind_(film)

https://en.wikipedia.org/wiki/John_Forbes_Nash_Jr.

 

You don't need a degree in math to learn about statistics or probability.  Just takes an interest.   Over the years, for particular projects, I've had to learn enough of the assumptions in order to use calculations for particular datasets.  Wasn't always easy, and I leaned heavily on statisticians and mathematicians who do the various analyses on a regular basis.   But if I can do it, there are smarter people than me on BSBH, that can do it better than I can.

[siddious]

[Keirik]

5 hours ago, fletch said:

Good stuff!

 

 

 

 

https://www.imdb.com/title/tt0119217/characters/nm0000354

Good Will Hunting was awesome.  Will was a helluva lot tougher than me.

 

Try A Beautiful Mind about John Nash, played by Russell Crowe.

https://en.wikipedia.org/wiki/A_Beautiful_Mind_(film)

https://en.wikipedia.org/wiki/John_Forbes_Nash_Jr.

 

You don't need a degree in math to learn about statistics or probability.  Just takes an interest.   Over the years, for particular projects, I've had to learn enough of the assumptions in order to use calculations for particular datasets.  Wasn't always easy, and I leaned heavily on statisticians and mathematicians who do the various analyses on a regular basis.   But if I can do it, there are smarter people than me on BSBH, that can do it better than I can.

I have a masters degree in biochemistry. I’m not bad at numbers, but thank you. I will say, some of us did refer to some of the advanced classes as cal-clueless lol

 

Yes, a Beautiful Mind was good albeit a bit boring.  

 

 

I think people are just joking with you my man. 

[Ozzy]

3 hours ago, Keirik said:

I have a masters degree in biochemistry. I’m not bad at numbers, but thank you. I will say, some of us did refer to some of the advanced classes as cal-clueless lol

 

Yes, a Beautiful. I d was good albeit a bit boring.  

 

 

I think people are just joking with you my man. 

 

Yeah, that! 

[Keirik]

41 minutes ago, Ozzy said:

 

Yeah, that! 

It’s too bad I slept through typos 101 in college