Standard Deviation of Player Scoring (1 Viewer)

[tombonneau]

Just gave a look around, and was wondering if there was anywhere on the premium site that offers up the standard deviation of players scoring along with the typical ppg totals.

Was thinking in regards to kickers, this might be a interesting way to evaluate a player vs simple ppgs. For instance, I have Akers, who is avg 6.8 a game, but whose stdev is only 0.98. Whereas a guy like Carney, ranked much higher has a 9.2ppg avg but a stdev of 3.65.

For marginal positions like kickers, I think its more valuable to have a guy who is consistant vs. a guy who is going to sprinkle in a few 1 or 3 point games but has an inflated average due to one outlier 15pt game. Ergo, the need to look at the stdev of scoring.

I think this also might be of use looking at WRs; big difference btwn how Santana Moss gets to to 13ppg to and Marvin Harrison gets there. I think most people would prefer Marvin's steady production vs. Moss' 3 blah games with 1 WOW game.

I don't know, I mean the sample size obv. is very small in-season, so not sure how relevant stdev would even be when looking at ppg stats, but I think it adds another potentially releveant facet for certain positions.

 

[Doug Drinen]

Kicker G AVG StDev--------------------------------------Robbie Gould 6 12.0 3.2Nate Kaeding 5 11.0 3.0Jeff Wilkins 6 10.8 4.7John Carney 6 8.8 3.0Mike Vanderjagt 4 8.5 1.5Ryan Longwell 5 8.2 1.6John Kasay 6 8.2 3.5Josh Scobee 5 8.0 3.6Shayne Graham 5 7.8 2.5Jay Feely 5 7.4 3.4Morten Andersen 3 7.3 6.8Josh Brown 5 7.2 3.1John Hall 5 7.2 3.4Jeff Reed 4 7.0 1.9David Akers 6 6.8 0.9Matt Stover 6 6.7 4.3Lawrence Tynes 5 6.6 3.9Dave Rayner 5 6.6 3.4Neil Rackers 6 6.5 3.4Jason Elam 5 6.4 1.7Joe Nedney 6 6.3 3.3Jason Hanson 6 6.0 2.8Rian Lindell 6 5.7 2.8Stephen Gostkowski 5 5.6 2.6Phil Dawson 5 5.4 3.7Olindo Mare 6 5.0 2.8Rob Bironas 6 4.8 3.7Kris Brown 5 4.4 1.9Mike Nugent 6 4.3 2.4Sebastian Janikowski 5 4.0 2.8Martin Gramatica 3 4.0 2.2Matt Bryant 5 2.8 1.9Michael Koenen 5 2.6 2.9I've gotta run, but two quick thoughts:1. Guys with higher averages will naturally have higher standard deviations.

2. I don't have any evidence one way or the other, but I am VERY skeptical of the notion that past consistency is a predictor of future consistency. Longwell has been more consistent than Kasay so far, but I would not bet one thin dime that he will be more consistent going forward.

 

[JayMan]

1. Guys with higher averages will naturally have higher standard deviations. 2. I don't have any evidence one way or the other, but I am VERY skeptical of the notion that past consistency is a predictor of future consistency. Longwell has been more consistent than Kasay so far, but I would not bet one thin dime that he will be more consistent going forward.

Very ... consistency should not be looked at with Standard Deviation... just look at a guy that scores 0 point every week - he'll have a StDev of 0 - he's consistently poor...You should look at a "threshold" (was he good enough to be a starter at his position this week?) kind of value to look at consistent player...But even doing so, like Doug mentioned - intra-year consistency or even extra-year consistency is not statistically significant... no statistical evidence showing that: a guy that scored 10 points the last few weeks will have better chance to score 10 points the upcoming week than an equivalent player who scored only 5 points the last few weeks...

 

[tombonneau]

Thanks, Drinen. Good to see I was right in my thinking that Akers was thus far the most consistant kicker. But you're probably both dead right that past performance of consistancy is not a solid indicator of future consistancy.

BTW, is that info available somewhere on the site Doug, or is it just part of your own personal data stash?

Would be interested to see what it looks like for wrs as well....

 

[Ditka is God]

But you're probably both dead right that past performance of consistancy is not a solid indicator of future consistancy.

Yeah, just ask Neil Rackers! Seriosuly, though, you're on the right track IMO. "Boom/bust" guys can kill you.

 

[Ditka is God]

1. Guys with higher averages will naturally have higher standard deviations.

Not necessarily.Kaeding has the second highest ppg yet there are 14 Ks who have a higher std dev than he does.

 

[Jeff Pasquino]

A few quick thoughts in general....

The lower the average score, say for a RB or WR, the more an "unlikely" even such as a TD will cause irregularities in their scoring and create a larger standard deviation. This is more of a reflection of the ups and downs of getting the TD than a testament to inconsistent play.

PPR will smooth out standard deviation.

 

[bobspruill]

I've been looking into this question some recently and don't have what I'd call an "answer." As indicated above, the tradeoff is between production and variance, but the question is how to weight these two things, and how to measure them.

In the case of the kicker numbers above, the sample sizes are so small that the sample stdev's are essentially meaningless. I was futzing just this morning with the 2005 QB numbers and trying to see what effect variance in score has on value. I got a decent fit from a gamma distribution and decided to use that to model production.

In 2005, under the scoring system in the league from which information was drawn, the average PPW for top-30 QB performances was 27.8, with a stdev of 12.3. The median performance was 27 points--note that the shape of the gamma agrees that the mean and median points performances should be different.

I used the gamma assumption and some Monte Carlo simulation (about 2500 trials) to compare two hypothetical QBs, each with average PPW's of 30. I gave one a stdev of 12 points, the other a stdev of 13. A couple tidbits:

The QB with the lower stdev outscored the QB with the higher stdev about 51-52% of the time.

The QB with the higher stdev had a greater margin of victory in the weeks he won, as expected, than did the QB with the lower stdev: about 0.1 PPW.

The mean value of the difference in scores was about 0.2 PPW in favor of QB1.

Obviously this isn't master's thesis material--you have to make assumptions when you do simulation--but a back-of-the-envelope look convinces me that even slightly less consistent players at QB aren't as valuable as consistent ones even when they score the same on average.

If you give the QB with the higher stdev a higher scoring average as well--31 to the other QB's 30--here's what you find:

The QB with higher scoring average and higher stdev now wins more often than the other, but the frequency isn't as large--it looks like the advantage is just over 0.5%.

The mean value of the difference in scores is about 0.8 PPW in favor of the higher-scoring QB.

Of course, average score is still the thing we care most about. But volatility does diminish the value of a player and should be taken into account. The question, of course, is how you develop a good estimate of volatility and use it to adjust the player's average production....

 

[JayMan]

Of course, average score is still the thing we care most about. But volatility does diminish the value of a player and should be taken into account. The question, of course, is how you develop a good estimate of volatility and use it to adjust the player's average production....

Very good analysis... well thought process...The only problem I see is that: being previously consistent won't mean that you'll be consistent in the future... I have looked at a few players that were very consistent in year n - only to find that they weren't "more consistent" in year n+1 in comparison to guys that were inconsistent in year n... Same concept is applicable to weeks instead of year...

 

[Archie Bunker]

1. Guys with higher averages will naturally have higher standard deviations.

Not necessarily.Kaeding has the second highest ppg yet there are 14 Ks who have a higher std dev than he does.

Generally speaking, Doug is correct. Higher averages usually, not always mean higher std deviations. The coefficient of variation may be a better measurement. It is the ratio of the std. deviation to the mean. I have played with this data before when trying to rank players. There is some value to it. If nothing else, it debunks myths such as "Sean Alexander doesn't score consistently." How many threads have there been on that topic over the past 3 years?I think kickers might be the most difficult to apply this to because there are so many other variables that can affect their output. A change in QB, injury to a RB or OL, could be the difference between lots of FGs @ 3 pts each and PATs @ 1 pt each. Also, with the exception of a few, steady kickers, they tend to be hot & cold. Someone mentioned Rackers. Up until last year, Rackers was considered a marginal kicker, at best. For RBs & WRs, especially WRs, I can see where it could be beneficial. Santana Moss is notorious for having a couple of huge games a year that account for much of his fantasy scoring. In 2005, he had 9 TDs across 5 games. Larry Fitzgerald, who finished tied with Moss in my league's scoring system, had 1 td each in 10 different games. I'm not saying it is 100% accurate in predicting consistency, but it is another tool in trying to differentiating players who, on the surface, are projected to score a comparable # of points across an entire season.

 

[dgreen]

1. Guys with higher averages will naturally have higher standard deviations.

Not necessarily.Kaeding has the second highest ppg yet there are 14 Ks who have a higher std dev than he does.

Generally speaking, Doug is correct. Higher averages usually, not always mean higher std deviations. The coefficient of variation may be a better measurement. It is the ratio of the std. deviation to the mean.

Just using the above 33 kickers, the R-squared is only 0.05. More data might change that some.

 

[Keg]

call me rain man but for the most part i dont need a formula to tell me who is gonna be more consistent then someone else...

between my rain man tendencies and all the pasta i throw on the wall I do pretty well

 

[tombonneau]

I've been looking into this question some recently and don't have what I'd call an "answer." As indicated above, the tradeoff is between production and variance, but the question is how to weight these two things, and how to measure them.In the case of the kicker numbers above, the sample sizes are so small that the sample stdev's are essentially meaningless. I was futzing just this morning with the 2005 QB numbers and trying to see what effect variance in score has on value. I got a decent fit from a gamma distribution and decided to use that to model production.In 2005, under the scoring system in the league from which information was drawn, the average PPW for top-30 QB performances was 27.8, with a stdev of 12.3. The median performance was 27 points--note that the shape of the gamma agrees that the mean and median points performances should be different.I used the gamma assumption and some Monte Carlo simulation (about 2500 trials) to compare two hypothetical QBs, each with average PPW's of 30. I gave one a stdev of 12 points, the other a stdev of 13. A couple tidbits:The QB with the lower stdev outscored the QB with the higher stdev about 51-52% of the time.The QB with the higher stdev had a greater margin of victory in the weeks he won, as expected, than did the QB with the lower stdev: about 0.1 PPW.The mean value of the difference in scores was about 0.2 PPW in favor of QB1.Obviously this isn't master's thesis material--you have to make assumptions when you do simulation--but a back-of-the-envelope look convinces me that even slightly less consistent players at QB aren't as valuable as consistent ones even when they score the same on average.If you give the QB with the higher stdev a higher scoring average as well--31 to the other QB's 30--here's what you find:The QB with higher scoring average and higher stdev now wins more often than the other, but the frequency isn't as large--it looks like the advantage is just over 0.5%.The mean value of the difference in scores is about 0.8 PPW in favor of the higher-scoring QB.Of course, average score is still the thing we care most about. But volatility does diminish the value of a player and should be taken into account. The question, of course, is how you develop a good estimate of volatility and use it to adjust the player's average production....

Thanks, Bob. Always enjoy getting thoughtful responses like this from people who are waaaaaaaaaaaaaaaaaaaaay smarter than me.

 

[radballs]

I've been looking into this question some recently and don't have what I'd call an "answer." As indicated above, the tradeoff is between production and variance, but the question is how to weight these two things, and how to measure them.In the case of the kicker numbers above, the sample sizes are so small that the sample stdev's are essentially meaningless. I was futzing just this morning with the 2005 QB numbers and trying to see what effect variance in score has on value. I got a decent fit from a gamma distribution and decided to use that to model production.In 2005, under the scoring system in the league from which information was drawn, the average PPW for top-30 QB performances was 27.8, with a stdev of 12.3. The median performance was 27 points--note that the shape of the gamma agrees that the mean and median points performances should be different.I used the gamma assumption and some Monte Carlo simulation (about 2500 trials) to compare two hypothetical QBs, each with average PPW's of 30. I gave one a stdev of 12 points, the other a stdev of 13. A couple tidbits:The QB with the lower stdev outscored the QB with the higher stdev about 51-52% of the time.The QB with the higher stdev had a greater margin of victory in the weeks he won, as expected, than did the QB with the lower stdev: about 0.1 PPW.The mean value of the difference in scores was about 0.2 PPW in favor of QB1.Obviously this isn't master's thesis material--you have to make assumptions when you do simulation--but a back-of-the-envelope look convinces me that even slightly less consistent players at QB aren't as valuable as consistent ones even when they score the same on average.If you give the QB with the higher stdev a higher scoring average as well--31 to the other QB's 30--here's what you find:The QB with higher scoring average and higher stdev now wins more often than the other, but the frequency isn't as large--it looks like the advantage is just over 0.5%.The mean value of the difference in scores is about 0.8 PPW in favor of the higher-scoring QB.Of course, average score is still the thing we care most about. But volatility does diminish the value of a player and should be taken into account. The question, of course, is how you develop a good estimate of volatility and use it to adjust the player's average production....

Very nice work with this. You should submit an article next year. I love statistical anaylsis and I used to do a lot of work with SD. Unfortunately, it just seems impossible to forecast players having approximate week to week consistency throughout and across different seasons.