Your thoughts on how weeks 1, 2, 3, etc. (1 Viewer)

[Chase Stuart]

Looking for a formula here.

You project RBA to score W FP/G for the season. In week 1, RBA scores X FP. What will you project for him for the rest of the season?

In week 2, RBA scores Y FP. He's averaging (Y+W)/2 FP/G through two weeks. What will you project for him for the rest of the season?

In week 3, RBA scores Z FP. He's now averaging (Z+Y+W)/3 FP/G through three weeks. What will you project for him for the rest of the season?

If you're adverse to using letters, feel free to substitute whatever numbers you want for the letters. The goal here is to figure out exactly how much weight you put on each week of play, relative to your projections. I have an answer (or at least, an idea on how to get an answer) that I'm working on, but I wanted to get a consensus from the board first.

To be clear, I want to know your projections for the rest of the year. Obviously knowing how many FPs a RB has through three weeks will be a better indicator of his year end totals than his rest of year end totals.

 

[Maurile Tremblay]

Looking for a formula here.

You project RBA to score W FP/G for the season. In week 1, RBA scores X FP. What will you project for him for the rest of the season?

You've asked a question I happen to have done some work on recently, although in a different context.To really do this right, you should expand your projected W FP/G into a distribution with corresponding probabilities.

For example, let's say you project RBA to score 14.6 PPG, broken down into the following probabilities:

24 ppg 0.40%

23 ppg 0.81%

22 ppg 1.62%

21 ppg 2.43%

20 ppg 3.24%

19 ppg 4.86%

18 ppg 6.48%

17 ppg 8.50%

16 ppg 10.53%

15 ppg 12.96%

14 ppg 11.34%

13 ppg 9.72%

12 ppg 8.10%

11 ppg 6.48%

10 ppg 4.86%

9 ppg 3.24%

8 ppg 2.02%

7 ppg 1.21%

6 ppg 0.81%

5 ppg 0.40%

That's a weighted average of 14.6 PPG.

Now let's say he goes out and scores 22 points in his first game. Further, let's say you expect the standard deviation of his points from week to week to be around 9. What's your revised estimate for his PPG going forward?

This is a job for Bayes' theorem, which can be stated: P(A|B) = P(B|A)*P(A) / [P(B|A)*P(A) + P(B|Ā)* P(Ā)]

In this case, A = the chance that particular PPG in that row is the true one (a priori), and B = the chance of the observed PPG being observed. (Ā means "not A".)

What you want to know, for each possible PPG, is, what's the chance that that PPG is the true one given that we've observed a PPG of 22 points in the first game?

P(A), for each A, is the initial distribution of estimates given above.

P(B|A) is very tricky to work out. The way you can do it is, by using z-scores, figure the probability of getting between 0.1 points lower than the one listed in that row and 0.1 points higher than the one listed in that row. (This is why you need standard deviation -- your units will be converted to standard deviations rather than fantasy points before you use z-scores.)

P(B|Ā) will be the weighted average of the P(B|A) column excluding the current row. And P(Ā) is just 1 - P(A).

If you plug everything in, you'll get the revised probabilities that each PPG is the true one, and you can calculate expected PPG from there.

I know I didn't explain that fully -- particularly the step of getting P(B|A) -- but it would take a full article. It's one I've got half-written, but didn't finish in time to release this year. So it will be an FBG article in the 2008 preseason.

In the meantime, I'll give some examples of results.

If the RB scores 24 points in his first game, his revised PPG estimate goes to 15.8.

If the RB scores 8 points in his first game, his revised PPG estimate goes to 13.7.

If the RB scores 2 points in his first game, his revised PPG estimate goes to 12.9.

If the RB scores 35 points in his first game, his revised PPG estimate goes to 17.3.

In week 2, RBA scores Y FP. He's averaging (Y+W)/2 FP/G through two weeks. What will you project for him for the rest of the season?

If the RB averages 24 points in his first two games, his revised PPG estimate goes to 16.8.If the RB averages 8 points in his first two games, his revised PPG estimate goes to 13.0.

If the RB averages 2 points in his first two games, his revised PPG estimate goes to 11.6.

If the RB averages 35 points in his first two games, his revised PPG estimate goes to 19.3.

In week 3, RBA scores Z FP. He's now averaging (Z+Y+W)/3 FP/G through three weeks. What will you project for him for the rest of the season?

If the RB averages 24 points in his first three games, his revised PPG estimate goes to 17.6.If the RB averages 8 points in his first three games, his revised PPG estimate goes to 12.5.

If the RB averages 2 points in his first three games, his revised PPG estimate goes to 10.6.

If the RB averages 35 points in his first three games, his revised PPG estimate goes to 20.6.

 

[Maurile Tremblay]

You project RBA to score W FP/G for the season. In week 1, RBA scores X FP. What will you project for him for the rest of the season?

BTW, the way that I gave is not the way I would do it in real life.First, I would not use a strictly mathematical formula, because I have eyes to watch the games with and I like to use those as well.

Second, I would not use PPG directly. I would use yards per carry, touchdowns per carry, receptions per target, yards per reception, touchdowns per reception, number of carries, and number of targets. I'd project all those separately, and build expected PPG from there.

The main point that the numbers above show, however, is that you should not completely throw out your preseason projections based on week one performance, or even weeks 1-3 performance. In the grand scheme of things, your initial expectations are still quite relevant in comparison to actual performance over a small sample of games. The more games he plays, the more his actual performance rises in importance and your initial expectations shrink in importance . . . but it takes a while before you should make huge revisions to your initial projections. (Unless it becomes evident that your initial projections were based on factually incorrect assumptions, which you can now correct.)

 

[-OZ-]

Duh, you take their first game and multiply by 16.

Take their first two, multiply by 8

 

[avoiding injuries]

It's obviously easier to forecast with a larger sample size, so after a couple weeks you may be able to predict. I think a lot of factors can affect the production of just a couple games to throw off a forecast. Strong run defense, score of the game, one long run, 3 td's for a combined 1yd, etc. I'll pay attention more to how they were used and how they looked while being used over their FP's to make a season prediction.

 

[Bracie Smathers]

Looking for a formula here.

You project RBA to score W FP/G for the season. In week 1, RBA scores X FP. What will you project for him for the rest of the season?

In week 2, RBA scores Y FP. He's averaging (Y+W)/2 FP/G through two weeks. What will you project for him for the rest of the season?

In week 3, RBA scores Z FP. He's now averaging (Z+Y+W)/3 FP/G through three weeks. What will you project for him for the rest of the season?

If you're adverse to using letters, feel free to substitute whatever numbers you want for the letters. The goal here is to figure out exactly how much weight you put on each week of play, relative to your projections. I have an answer (or at least, an idea on how to get an answer) that I'm working on, but I wanted to get a consensus from the board first.

To be clear, I want to know your projections for the rest of the year. Obviously knowing how many FPs a RB has through three weeks will be a better indicator of his year end totals than his rest of year end totals.

I think you skipped to the production rather than the reason for an unsuspected increase in production. If a player's situation changes where the number of touches they see increased to a point where previous projections were based on lower touches than those long term projections would need to be changed.But if a player just has a large bump in production without any increase in touches then I'd look at individual cases. Is their a previous history for the RB starting out hot and fading? Was their a change to a new offense? If this a rookie with no previous history? Is this a RB coming off an injury with a high ceiling? Etc, et, el.

In other words instead of looking at the bottom line and going straight to a formula, I'd first look at the variables to the formula:

X - could be projected touches

Y - could be if this is a rookie or veteran

Z - previuos history of starting hot and fading etc.

Once you covered basic situation variables then I think your formula for bottom line production (with variables) would be of more value.

Jes my humble-O.

 

[Jeff Pasquino]

IBT -5^2=25 reference.

 

[Jeff Tefertiller]

I think I remember a Drinen article on this and that week one was a predictor, a decent predictor, for success in the rest of the season. to Drinen for the stats/history lessons

 

[az_prof]

You project RBA to score W FP/G for the season. In week 1, RBA scores X FP. What will you project for him for the rest of the season?

BTW, the way that I gave is not the way I would do it in real life.First, I would not use a strictly mathematical formula, because I have eyes to watch the games with and I like to use those as well.

Second, I would not use PPG directly. I would use yards per carry, touchdowns per carry, receptions per target, yards per reception, touchdowns per reception, number of carries, and number of targets. I'd project all those separately, and build expected PPG from there.

The main point that the numbers above show, however, is that you should not completely throw out your preseason projections based on week one performance, or even weeks 1-3 performance. In the grand scheme of things, your initial expectations are still quite relevant in comparison to actual performance over a small sample of games. The more games he plays, the more his actual performance rises in importance and your initial expectations shrink in importance . . . but it takes a while before you should make huge revisions to your initial projections. (Unless it becomes evident that your initial projections were based on factually incorrect assumptions, which you can now correct.)

I can think of a lot of examples where players got off to a slow start and owners gave up on them. I put more faith in my original projections and don't start downgrading my players for several weeks. I remember one years CJ didn't get it going until like week 8.

 

[Chase Stuart]

Good responses so far. Would love to hear more thoughts.

E.g., let's say you drafted QB10 and QB14, according to your rankings. You've got QB10 projected at 18FP/G, and QB14 at 17 FP/G. Assuming they always play an average defense, how long do you wait until you start QB14 over QB10? If QB14 beats him by 20 points in week 1? If QB14 beats him by 3 FPs a week for the first three weeks? What if QB10 scores 20, 10 and 30 FPs, and QB14 scores 30, 20 and 20 FPs....who do you start the next week?