Actual vs. Expected Wins: Some Interesting Analysis

[Jangler]

poo poo

[pstall]

I'm serious. I love this kinda stuff.

[Chaos]

So, who will the Lions take with the #1 overall pick next year?

[Happy Panther]

So last night I decided to look at the effect of average margin of victory on win-loss records. Once you estimate the equation that includes the impact of average margin of victory on wins, you can estimate the expected number of wins for each team. Again, what I've done here is very basic, and I'm going to beef it up a lot in the coming months.

Not trying to poop on your party but I think you have regressed two very correlated variables. The MOV from the previous season and the win totals from the previous season are both measures of how good a team was. You could add in passing yards and number of feild goals and the result would be similar.

As for predictiveness, I agree there will be some predictive power but there has to be when you are modeling two variables that are linked to the same cause.

But I'm curious, are you going to run your regression after the first game of the season to predict the season win total?

[Happy Panther]

Out of curioisty, what is the Corr() of the two variables?

[mr beauxjangles]

Sorry for the delay in responding to all this. My best friend's are getting married this weekend in NY and I've got a lot of catching up to do to get ready. I'll try to respond to everyone's questions individually.

Let me be the dummy who asks this: how do you arrive at the margin of victory numbers? Take points against and points for and subtract PA from PF then divide by 16? Or do you use the scores of the games, take the point differentials, then average that?

Very interesting topic!

Margin of victory is simply the average margin of victory over 16 games. The two approaches you described would arrive at the same number.

i like it and i have some things i'd like to ask you about it but the first thing i want to know is what you used as the basis for expected wins?

Expected wins is the output of the model. In short, a regression works in the following way...and this a very oversimplified explanation:

You start with a dataset that includes a variety of indicators for multiple observations (teams). In this case, the indicators of interest were average margin of victory and wins. A regression model sets up an equation in the following way:

y=mx+b

where in this case:

y=actual wins

x=average margin of victory

m=effect of average margin of victory on actual wins

b=some constant (called the intercept)

The regression model estimates the effect of average margin of victory on actual wins, all other factors being held constant. A more complete model to predict wins would include far more variables, such as passing yards, running yards, turnover ratio, penalties, red zone effectiveness, and so on. In this more complete model (which I hope to run in the coming weeks) you will get separate effects for each variable, and each effect is interpreted with all other factors being held constant. That is to say, we can estimate the effect of turnover ratio on actual wins, with all other factors being held constant (assuming passing yards, running yards, etc are constant between all teams). This allows us to isolate the effect of just on variable on actual wins.

nice chart, did you factor recency bias at all?

Recency bias isn't something that I came across in my six years of education in econometrics. But I am familiar with the subject, I think....

If I understand what you're asking, you want to know if there is any bias resulting from using average margin of victory from one season to explain actual wins in the same season. Margin of victory in a previous season could be used as a proxy for a team's starting skill level at the beginning of the next season. I don't see any bias being entered into the model by using the current season's margin of victory; I think it's appropriate.

Glad you enjoy this stuff - more to come.

Not trying to poop on your party but I think you have regressed two very correlated variables. The MOV from the previous season and the win totals from the previous season are both measures of how good a team was. You could add in passing yards and number of feild goals and the result would be similar.

As for predictiveness, I agree there will be some predictive power but there has to be when you are modeling two variables that are linked to the same cause.

But I'm curious, are you going to run your regression after the first game of the season to predict the season win total?

YES! I am so glad someone on here clearly has some background in stats or econometrics and can scrutinize what I put up here (sounds like pstall has some stats background too). Here's where it gets technical and some of you will want to vomit.

First, let me say that there is no problem with having correlation between the dependent (wins) and the independent variable (MoV); in fact, you want them to be correlated otherwise you're including irrelevant variables in the model. A problem arises if you have multiple correlated independent variables - then you have to correct for multicollinearity.

I think what you're trying to say (and please correct me if I'm wrong) is that you are concerned that MoV predict wins, but that wins also predicts MoV - leading to autocorrelation. The number of points you score minus the number you allow, on average, definitely impacts total wins. But total wins (the outcome) does not impact the amount of points scored minus points scored against you. The outcome can't determine the inputs. Just to be sure, I ran a Durbin-Watson test for autocorrelation and it came up clean. And even if it was an issue, autocorrelation only biases the standard errors of the coefficients, not the coefficient estimates themselves. So our significance tests would be messed up, but the estimated equation would still be valid. Please jump in and correct me if I misinterpreted your question or if you think I'm wrong here. It's been four years since I left school studying econometrics, and I don't use regression analysis in my job.

I ran ordinary least squares for this - again, I just wanted to start with something very basic and gauge people's interest. I didn't want to spend a lot of time if other people weren't very interested. I will likely start running some nonlinear (logit or probit) regressions based on individual game statistics so I can get to predicted probability of winning for games next year.

Out of curioisty, what is the Corr() of the two variables?

Correlation is 0.9094

Thanks to everyone for chiming in.

[Jangler]

Oh poo.

[guyinchesapeake]

I admire anyone who has a grasp on stats, and how to analyze them, make them work, etc. However, I know that the networks and league utilize such tools themselves, to help 'predict' rankings, scenarios, and TV schedules. Yet, we know that they routinely fall short, because the teams don't perfom as 'predicted'. We know from the Panthers own history that a good season record-wise in one year will not automatically translate into them being good the next, in fact, betting on the opposite is much more of a sure thing.

Look at how many recent Super Bowl losers have had poor seasons after appearing there (us included). The true rarities are the teams like the Steelers, Pats, and Colts who seem to be in the playoff hunt every season of late. Most teams don't build 'programs', they build to a season nowdays.

[mr beauxjangles]

So help me out here cuz I r stoopid when it comes to this stuff...

How does MoV convert into Expected Wins?

How you came to MoV is self evident but I cant figure out how you used that number to come to the Est Wins number.

It's hard to explain and hard to understand, so don't worry. I left out the part about arriving at expected wins in my last reply.

As I said before, you start with a data set that includes the variable that you want to explain (total wins) and the variables that should explain total wins (in this case, only margin of victory). You estimate the equation that I mentioned before:

y=mx+b

where in this case:

y=actual wins

x=average margin of victory

m=effect of average margin of victory on actual wins

b=some constant (called the intercept)

The regression model estimates the effect of average margin of victory on actual wins (m in the above equation), all other factors being held constant. It also estimates the intercept (b above). So once this equation is defined and the data is run through the computer program that estimates the parameters of the equation, these previously unknown values (m and are known. The result in this case is as follows:

total wins = 0.451431*(average margin of victory) + 7.96875

Once this equation is estimated, you can plug in the actual values for average margin of victory for each team and solve the equation. This solution gives you the expected or predicted wins for each team. These results are what's included in the column "expected wins" in the table I posted.

I hope that helps.

[mr beauxjangles]

I admire anyone who has a grasp on stats, and how to analyze them, make them work, etc. However, I know that the networks and league utilize such tools themselves, to help 'predict' rankings, scenarios, and TV schedules. Yet, we know that they routinely fall short, because the teams don't perfom as 'predicted'. We know from the Panthers own history that a good season record-wise in one year will not automatically translate into them being good the next, in fact, betting on the opposite is much more of a sure thing.

Look at how many recent Super Bowl losers have had poor seasons after appearing there (us included). The true rarities are the teams like the Steelers, Pats, and Colts who seem to be in the playoff hunt every season of late. Most teams don't build 'programs', they build to a season nowdays.

I completely agree. The networks do have statisticians that do this kind of stuff all day to try to predict teams records in the following year. And yes, they are never perfect. This analysis was a little bit different though. It didn't try to predict teams records next year based on this past years performance. It tried, at a very basic level, to get some estimate of which teams underachieved and overachieved last year based on their margin of victory. So it's a little different. It isn't intended to predict the future, but rather, to provide some insights on what happened in the past.

[Darth Bobo]

Margin of Victory is an interesting statistic. There is one problem with using it, from my perspective and that is, that sometimes when an individual game's margin is high, the Panthers in particular seem to go into "coast" mode. In coast mode, they allow the other team to reduce the margin of victory at the expense of eating up the game clock. This method is designed to ensure the victory, but without regard to the margin of victory. In that regard, the Panthers have little respect for the Margin of Victory.

The opposite is true for teams like Indianapolis, which is in perpetual scoring mode, due to the relatively weak performance of their defense as it compares to their offensive performance. With Indianapolis, the margin of victory is the key to the victory itself, and they seem keen to "run up the score".

Maybe I'm off. I'm sure someone can make a good case against what I said.

I think to get a good feel for how strong a team really is, you have to look at both which teams have been beaten, and by how much. You have to treat all 256 games of a season as distinct, because in fact, they are.

I think you also have to throw out the last 32 games of the season, because the outcome of those games is predetermined by each team's prospects to enter the playoffs, and are thus statisitcally unreliable. So really, we're talking about 224 games.

I think you need more covariates. Strength of Schedule is one. Strength of Victory is another. Margin of Victory is a part of all of that. But I don't think a statistician needs to look back further than say 10 games to be able to estimate the strength of an opponent. But knowing the strength of an opponent relative to the teams they beaten is important to knowing the value of beating the opponent.

It goes back to who you've beaten and by how much.

[jkeough]

my head hurts

[mr beauxjangles]

Margin of Victory is an interesting statistic. There is one problem with using it, from my perspective and that is, that sometimes when an individual games margin is high, the Panthers in particular seem to go into coast mode. In coast mode, they allow the other team to reduce the margin of victory at the expense of eating up the time clock. This method is designed to ensure the victory, but without regard to the margin of victory. In that regard, the Panthers have little respect for the Margin of Victory.

The opposite is true for teams like Indianapolis, which is in perpetual scoring mode, due to the relatively weak performance of their defense as it compares to their offensive performance. With Indianapolis, the margin of victory is the key to the victory itself, and they seem keen to nurture it.

Maybe I'm off. I'm sure someone can make a good case against what I said.

I think the strength of schedule (SoS) for each year is also a good covariate to consider, because it assumes some level of consistency for teams, which I think is generally a fair assumption.

All very good points. Since this is based on aggregated data over an entire season, it would be difficult to incorporate the "coast mode" into an analysis that uses aggregated stats for an entire season. But if I did this, or any other analysis, using individual game statistics, that would be something you might be able to capture. Good thought.

[mr beauxjangles]

I'm leaving tonight for a friend's wedding this weekend and won't be back until Tuesday; if anyone else has questions I won't be able to respond until then. Appreciate the interest.