Math Question

[ted2019]

I was always curious on how some of you guys know on what type of math formulas to use in some of these studies. I find this fascinating, but hard to understand. I bought the book Stat Shot, but a lot of this just files over my head. I want to do some studies myself, but I'm not sure where to start at. Any help would be greatly appreciated.

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[LT]

What specific studies are you referring to?

Most of the time it's simpler than one would think. For things like metrics and all, some of it can just be "made up" as long as there's a good explanation for why one does what they do.

 

[Kane One]

What specific studies are you referring to?

Most of the time it's simpler than one would think. For things like metrics and all, some of it can just be "made up" as long as there's a good explanation for why one does what they do.

But how is it made up? Do people start with an agenda and then create a formula to back their agenda up?

 

[LT]

But how is it made up? Do people start with an agenda and then create a formula to back their agenda up?

Typically, no. For instance, Goal Differential is technically a made-up formula, albeit a very simple one.

You would never want to have an agenda and go hunting for data to back it up. What you should want is an idea, a question to answer, and then figure out what formula or stat would best answer it.

I don't do this for hockey very often, but I do it a lot with my work as a graduate student. I think most of the fundamentals should be the same.

 

[Doctor No]

Usually it's a variation of "I want to know the answer to this, and can't get there with what exists already", or "Many people claim this - how can I verify it with data?"

 

[Doctor No]

"Agenda" is a bit of a leading term. If you go out trying to prove something, you can run afoul of confirmation bias in your choices. For instance, I'd love to develop a metric that PROVES KIRK MCLEAN IS THE BEST GOALTENDER IN THE HISTORY OF WHATEVER. To do so, I'd probably have to look at it with a biased eye, and the result wouldn't make a lot of sense (sorry, Kirk!).

 

[Czech Your Math]

Off the top of my head:

1. Check your premises.
2. Your logic should be as coherent as possible.
3. When multiplying numbers, cancel out units and be sure your end result has the correct units.
4. You must understand your study or formula completely in order to even attempt to explain it to others.
5. Critique your own study (say, as a rough draft) and analyze (even better, recreate) some others' studies, once you understand the methodology. This will increase your knowledge and confidence of both the process and result.

 

[Doctor No]

Confirming the right units is a big one - and often overlooked.

 

[JackSlater]

I think what you're looking for is basic competency with statistics. I have years of math study from university, but none of it was statistics (or mathematical modeling), and thus very little of it relates to hockey studies. I don't know what your math level is but you will likely need to familiarize yourself with the basics of statistics, regression analysis and such. There are some quality studies that have been done by members on these boards however that are pretty basic mathematically but quite interesting. A lot of it is figuring out what you want to find, at its core, and finding what exactly measures the thing that it is you want to find. Becoming proficient in excel would also be helpful.

 

[ted2019]

where can I find some math formulas at?

 

[Doctor No]

I sent you some math formulas in my first response to your private message, then posted them in the "Studies Already Done" thread when you posted there asking the same question that you asked me.

They're still here:
Goaltending Statistics - Glossary of Terms

 

[Doctor No]

It would be helpful if you told us some ideas of what you're trying to do. "Math formulas" covers a very large spectrum.

What sorts of things do you want to explore further in hockey?

 

[abo9]

where can I find some math formulas at?

Outside of the very simple but creative formula most people come up with, what you could aim for is studying Forecasting analysis, Time Series, etc. I'm currently studying them and can see how they can be used in a regression analysis for hockey.

And in Stats Shot, if I remember correctly a lot of the formulas deal with de-seasonalizing the data which is what the study of Time Series are about.

There is no magic formula, like another poster said, you need to familiarize yourself with the theory of basic probabilities first, then regression and time series, which gives you the tools and techniques to develop statistical models.

Disclaimer: I'm doing an undergrad in statistics, but I am so busy with school that I only follow hockey analytics sparingly, although I'm pretty interested in applying what I learn at school to hockey analytics. ​

 

[ted2019]

Thank you for all the fantastic answers. I feel like I'm over my head a bit as i'm older (late 40's) and have memory problems.

 

[Hockey Outsider]

A few thoughts:

The majority of studies don't use complicated math - if you can add, subtract, multiply, divide and (maybe) use exponents, you should be able to understand the majority of hockey research.

For example, take a look at hockey-reference's point shares (Calculating Point Shares | Hockey-Reference.com). It's complex in the sense that there's a lot of calculations that go into it, but it's easy in the sense that the actual math is basic. What's more important (and interesting) is thinking through the logic behind all of the steps - one of the reasons that point shares isn't very useful is because there are a number of logical errors, which have been pointed out in other threads.

Being familiar with a basic stats program is also helpful. I use Microsoft Excel, which is as basic as it gets. I find that replicating something in Excel helps me understand the logic. (A good example, though unrelated to hockey - I have a giant Excel workbook that I use to prepare my personal tax return. When I first set it up many years ago, it really forced me to understand how different types of income, deductions and credits ultimately impact my refund/payable).

The biggest challenge with hockey analytics is just getting the data in a usable format. Things are much better now than they were ten or fifteen years ago. Still, once you have the data, a lot of times it needs to be edited and formatted, which can be painfully tedious and time-consuming. (For example, if you're trying to cross-refer scoring data and plus-minus data, and database has "Gordie Howe" and the other has "Howe, Gordie", you're either out of luck or may need to spent many hours editing one of them).

Data organization tools in Excel (like vlookup and pivot tables) are extremely useful. I can answer obscure questions like "which player scored the most goals per game over their 3rd to 7th best seasons, from 1968 to 2019 only, minimum 40 games per season" in a matter of minutes because I know how manipulate & analyze the spreadsheets. (Not sure if there's a quick/easy way to teach this - a lot of my experience is because I'm doing this through work).

Some more advanced statistics that can be useful are ones that show the relationship between two (or more) sets of data - such as correlation coefficient and regression analysis. For example, I've found that face-offs, in general, seem to have a low correlation to winning, which was surprising. That's not to say they have no value (and it's also not the same as saying that they have negative value) - just that, in the grand scheme of things, they're drowned out by other, more important factors.

There are, of course, some studies are much more technical. Alan Ryder's excellent website comes to mind. But basic middle math is definitely enough for getting started.

 

[Fourier]

A few thoughts:

The majority of studies don't use complicated math - if you can add, subtract, multiply, divide and (maybe) use exponents, you should be able to understand the majority of hockey research.

For example, take a look at hockey-reference's point shares (Calculating Point Shares | Hockey-Reference.com). It's complex in the sense that there's a lot of calculations that go into it, but it's easy in the sense that the actual math is basic. What's more important (and interesting) is thinking through the logic behind all of the steps - one of the reasons that point shares isn't very useful is because there are a number of logical errors, which have been pointed out in other threads.

Being familiar with a basic stats program is also helpful. I use Microsoft Excel, which is as basic as it gets. I find that replicating something in Excel helps me understand the logic. (A good example, though unrelated to hockey - I have a giant Excel workbook that I use to prepare my personal tax return. When I first set it up many years ago, it really forced me to understand how different types of income, deductions and credits ultimately impact my refund/payable).

The biggest challenge with hockey analytics is just getting the data in a usable format. Things are much better now than they were ten or fifteen years ago. Still, once you have the data, a lot of times it needs to be edited and formatted, which can be painfully tedious and time-consuming. (For example, if you're trying to cross-refer scoring data and plus-minus data, and database has "Gordie Howe" and the other has "Howe, Gordie", you're either out of luck or may need to spent many hours editing one of them).

Data organization tools in Excel (like vlookup and pivot tables) are extremely useful. I can answer obscure questions like "which player scored the most goals per game over their 3rd to 7th best seasons, from 1968 to 2019 only, minimum 40 games per season" in a matter of minutes because I know how manipulate & analyze the spreadsheets. (Not sure if there's a quick/easy way to teach this - a lot of my experience is because I'm doing this through work).

Some more advanced statistics that can be useful are ones that show the relationship between two (or more) sets of data - such as correlation coefficient and regression analysis. For example, I've found that face-offs, in general, seem to have a low correlation to winning, which was surprising. That's not to say they have no value (and it's also not the same as saying that they have negative value) - just that, in the grand scheme of things, they're drowned out by other, more important factors.

There are, of course, some studies are much more technical. Alan Ryder's excellent website comes to mind. But basic middle math is definitely enough for getting started.

Your post illustrates an important point with respect to much of the most frequently quoted hockey analytics. The level of mathematical sophistication one needs to execute most of the studies is very basic. But what is often missing from those that use the stats is a basic sense of their limitations. This is where mathematical training can be of real value. Far too often on these boards people present "statistical evidence" that does not really do what it is purported to do or ignore evidence that actually is compelling. A good example of the latter case from you post is the face-off stats. The vast majority of people on these boards believe that a player with a 51% FO% would be much more valuable than the same player with a 45% FO% to the degree that they will ignore many other attributes. Who cares if a guy scores 25 goals and gets 50 points if he only wins 45% of his draws!!!! The reality is that while all things being equal winning more faceoffs is better, when assessing a players worth FO% might be one of the least important attributes for all but a very very select set of players.

 

[Canadiens1958]

Your post illustrates an important point with respect to much of the most frequently quoted hockey analytics. The level of mathematical sophistication one needs to execute most of the studies is very basic. But what is often missing from those that use the stats is a basic sense of their limitations. This is where mathematical training can be of real value. Far too often on these boards people present "statistical evidence" that does not really do what it is purported to do or ignore evidence that actually is compelling. A good example of the latter case from you post is the face-off stats. The vast majority of people on these boards believe that a player with a 51% FO% would be much more valuable than the same player with a 45% FO% to the degree that they will ignore many other attributes. Who cares if a guy scores 25 goals and gets 50 points if he only wins 45% of his draws!!!! The reality is that while all things being equal winning more faceoffs is better, when assessing a players worth FO% might be one of the least important attributes for all but a very very select set of players.

Good point, bad example.

NHL stats show face-offs as won or lost, black or white. Defensively the key is neutralizing the face-off so that the opposition cannot accomplish its objectives.

 

[Fourier]

Good point, bad example.

NHL stats show face-offs as won or lost, black or white. Defensively the key is neutralizing the face-off so that the opposition cannot accomplish its objectives.

But how does this make an individual's FO% more meaningful? We've had debates galore on the Oiler board about how much better player x would be if his FO% was 51% rather than 47%. People even believe that they can visually tell the difference between a player wins 51% of his faceoffs vs one who wins 47%.

 

[Canadiens1958]

As presented the NHL, FO%s are rather without substance. Individual teams break the data by the FO dots. Main concern and the value of a player on faceoffs is goals allowed - defensive and goals scored offensive.

 

[Junohockeyfan]

Thank you for all the fantastic answers. I feel like I'm over my head a bit as i'm older (late 40's) and have memory problems.

50% of the HF fan base consider themselves amateur mathematicians. The other 60% are not so brash.