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Great Older Article on Fitzpatrick

Discussion in 'Miami Dolphins Forum' started by KeyFin, Jun 6, 2019.

  1. cbrad

    cbrad .

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    Yeah I think statistically these are the graphs (and equations) you want to go by, keeping in mind that we are talking about performance in a given year, not over a career. So THIS time you look at Dalton in 2015 separately from Dalton in 2016 for example.

    First, the x-axis is in z-scores or standard deviations above the mean. Now I know that brings up two issues: 1) most people don't calculate those, and 2) it might not be as intuitive. I can't help on #1 too much but I can help on #2. Go to this site:
    https://measuringu.com/pcalcz/

    Type in the z-score and make sure you click on "one-sided" not "two-sided", and that will convert z-scores to percentiles. In other words, we need to think in terms of percentiles NOT ranks (it's too important now.. can't keep this up with using rankings).

    Dalton in 2015 had a z-score of 1.8113 which by that link means he was top 3.5 percentile on average.

    OK, the graphs:
    [​IMG]

    I posted the right graph for SB winners before.. now you have the comparable graph for making the playoffs. So with Dalton's z-score in 2015 plugged into those equations (the "SD" is the z-score) you get a 84.8% probability of making the playoffs and a 12.5% probability of winning the SB. Goes to show you that even a QB "ranked #2" has such a low probability of winning it all, as you noticed. Just remember "ranked #2" translates to different z-scores in different years and this is in z-scores.

    If you do want to calculate z-scores yourself, go to pro-football-reference and look at "Passing Offense":
    https://www.pro-football-reference.com/years/2018/index.htm

    Copy the passer ratings, calculate the mean and standard deviation (they give you the mean at the bottom) and then calculate how many standard deviations above/below the mean a given QB's passer rating is. That's the z-score rating. QB ratings you can get here of course:
    https://www.pro-football-reference.com/years/2018/passing.htm

    As far as Conference Championships, obviously the curve will be between that of the playoff graph and SB graph, so it kind of gives you an idea how the probabilities change. I don't have the CC data for individual QB's (I have it only for teams) so I can't directly give you that result right now. But this should suffice for discussion purposes.
     
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  2. The Guy

    The Guy Well-Known Member

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    What's noteworthy about those graphs in my opinion is that a quarterback functioning in the average range gives a team about a 50% chance of making the playoffs, whereas the same quarterback gives a team almost no chance of winning a Super Bowl.

    The above isn't necessarily about Tannehill, but let's take him for example. We never experienced Tannehill in the playoffs, so it's easy to believe he could've done X, Y, or Z there, and that belief can't be refuted by anything we actually experienced with him. When something is irrefutable by actual experience in reality, then obviously it's easy to continue to believe it.

    But consider not only the above data (50% decreasing to almost 0% for any quarterback of that nature), and couple that with the fact that Tannehill played comparatively poorly against good competition and in clutch situations, which are ever-present factors in the playoffs, and I think you have to arrive at the conclusion that he would've given the team a near-zero probability of winning a Super Bowl.

    In my opinion that should pretty much close the book on any belief about what he could've done for the Miami Dolphins.
     
  3. The Guy

    The Guy Well-Known Member

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    I'm with you completely on the need for a team effort to win a Super Bowl. This is why my belief is that an elite quarterback, or an average one on a rookie salary, is necessary but not sufficient for a Super Bowl win in the present-day NFL. Having one doesn't guarantee a Super Bowl win -- i.e., other elements of a team are needed -- but not having one all but guarantees a team won't win a Super Bowl.

    The league essentially revolves around the passer, and there are two relatively simple formulas for success: 1) have an elite quarterback with at least an average pass defense, and/or 2) have at least an average quarterback, with an elite pass defense.

    You either have to beat teams with your own passer, or have a passer who won't lose the game for you while you stop the best passers in the league. It's really that simple anymore.
     
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  4. The Guy

    The Guy Well-Known Member

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    That's an interesting question, and I think the answer is that, as fans, it's easy to do so. Like the person who buys a lottery ticket with the idea that there was a winner last week, and so it's possible he or she can win this week. We know the odds are strongly stacked against us, but it's still possible.

    As fans we can easily think that way, and there's nothing wrong with it. But we can also think like the NFL GM who is making personnel decisions in the effort to stockpile the necessary talent to win a Super Bowl. That person, if he's shrewd, should be thinking in terms of probabilities, not possibilities.

    Certainly we want the GM of the Dolphins to think that way? I suspect none of us wants him to focus just on what's possible? Do we want him giving us just the possibility of a Super Bowl win, or do we want him acting in a way that makes it most probable?
     
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  5. cbrad

    cbrad .

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    Yeah let's get the numbers right first. Any number raised to 0 equals 1, so e^0=1. Solving those equations for SD=0 is therefore easy. The probability a QB that plays average in a given year makes the playoffs is 31.61*e^0 = 31.61%, and winning the SB is 2.719%.

    And if you think about it that's intuitive. 12/32 = 37.5% of teams make the playoffs each year and 1/32 = 3.12% of teams win the SB each year, and while the distribution above/below average is totally skewed (you can see that in those graphs) you'd still expect that for "average" it's close to randomly choosing the winner, and it is.

    Now.. that's for only a single year. What's more informative is to ask the probability that an average QB will make the playoffs at least once in X years, or win the SB at least once in X years because you're going to keep that QB for many years.

    This is what that looks like:
    [​IMG]

    So.. assuming you have a QB that plays average every year (SD=0), your chances of winning the SB at least once after 15 years is 33.87%. On the other hand you're fairly likely to make the playoffs even with an average playing QB after even several years. And we saw that here too, as Tannehill did help lead the team to the playoffs even though he didn't play in them.

    So I think the above graph is the type of graph you want to base judgments on. Obviously there is a different set of curves for every z-score. I guess I could create a 3-D graph to plot all of them at once but I doubt you can read off the values lol.
     
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  6. djphinfan

    djphinfan Season Ticket Holder Club Member

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    Easy solution..

    Wilson and Dalton are not fatally flawed..Dalton has weaknesses, but they can be managed.
     
  7. The Guy

    The Guy Well-Known Member

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    That's great information, thank you as always. Would it be possible to do the same graph and also incorporate pass defense? In other words, what is the likelihood that a team with an average quarterback, with anything other than an exceptionally good pass defense (i.e., opposing passer rating), would win a Super Bowl at least once in 15 years?

    What I'm trying to get at here is how, when it comes to winning a Super Bowl, having just an average quarterback necessitates an exceptionally good pass defense, or the probability of winning a Super Bowl at least once in 15 years (probably) plummets from roughly 34% to some very low number.
     
  8. The Guy

    The Guy Well-Known Member

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    Wilson is far from fatally flawed. Right now he has the second-highest career passer rating of all time in the NFL.
     
  9. djphinfan

    djphinfan Season Ticket Holder Club Member

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    Yes I know, I was just acknowledging the comparison that was presented, Wilson is very easy to build around, you know he’s going to out perform what you need..
     
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  10. The Guy

    The Guy Well-Known Member

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    And that's pretty rough info by itself, by the way, for teams with average QBs. If you have an average QB who has a 15-year career, there is roughly a two-thirds chance you aren't winning a Super Bowl, even once, during that period of time. That's pretty startling.

    Who knows whether they had this information or not, but given the above, is it any wonder the Cardinals moved on from Rosen in favor of Murray, if indeed they believed Rosen would become no better than average, whereas Murray on the other hand would become exceptional?

    This is certainly a reason to give up on a QB you believe can be no better than average, even after just one year with him, if you have the opportunity to land one you believe can be exceptional.
     
    Last edited: Jun 16, 2019
  11. cbrad

    cbrad .

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    Well.. without writing an extra program for that, a good approximation is to interpret "z-score" in those graphs as the sum of passer rating z-score and passer rating allowed z-score. The reason that should be a good approximation is because the correlation between passer rating and win% across NFL history is 0.633 while it's -0.593 for passer rating allowed. In other words they're nearly identical, though as you'll often see offense is a tad more important than defense, on average of course.

    So for z=0 you might be talking about a QB that plays at z = +0.7 with a pass defense of z = -0.7 as an example, or vice versa.

    And to be technical, the ratio should be 8:7 for offensive passer rating over defensive passer rating (ratio of square of correlations). So 0.8 z-score on defense is equivalent to 0.7 z-score on offense.
     
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  12. The Guy

    The Guy Well-Known Member

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    So essentially there is about a 34% chance the average QB will have the pass defense necessary to win a Super Bowl at least once during a 15-year period?
     
  13. cbrad

    cbrad .

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    Yup.

    What I can't answer without writing a separate program is how much the passer rating z-score is affected by the passer rating allowed z-score. The calculations are easy but writing the program is a bit tedious since the data aren't formatted to easily match up a QB with that QB's pass defense.. those data exist for teams but aren't linked by who the QB was.
     
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  14. resnor

    resnor Derp Sherpa

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    I think one of the issues is one side is looking at how the QB can raise his rating, so that it correlates with winning. The other side is looking at how other parts of the team can raise their level of play, which will also raise the QBs rating, so that it correlates with winning.
     
  15. djphinfan

    djphinfan Season Ticket Holder Club Member

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    The only issue I see Res is most have now seen enough to say he isn’t good enough to Lead your team to a champ, and few others still think he could.
     
  16. Surfs Up 99

    Surfs Up 99 Team Flores & Team Tua

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    Sorry if I am not remembering this correctly, but I think cbrad said that a QB rated tops will contribute about 1/3 towards a win. I can’t remember how much a top defense does. I am not sure what’s harder, to find a franchise QB or build a top flight defense. Obviously we are trying to do both. However, we might find ourselves with a defense much better than the starting QB we eventually will have.
     
  17. cbrad

    cbrad .

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    Oh.. from that graph on the right in post #281 you can see that the maximum a QB could be responsible for IF passer rating were completely due to the QB is 1/3 for winning a SB. So not a single game. To get an estimate for a single game, note that average correlation between passer rating and win% is 0.633 so the square of that tells you the maximum a QB could affect a game, on average, IF passer rating were completely due to the QB, and that's 40.07%.

    Of course that's if passer rating has nothing to do with the coach or surrounding cast. I once estimated contribution of the QB is more like 15% but that's a guesstimate.

    As far as defense vs. everything affecting passer rating, absolutely no question defense is more influential. Average correlation between points allowed and win% is -0.7342 so the square of that is maximum 53.9% due to the defense. Obviously some of "points allowed" is influenced by the offense which is why that number is greater than 50%. Similarly, the maximum due to offense is 56.58% so offense is on average slightly more influential on win%.

    None of this on its own answers the question is which is harder of course: find an elite QB or build an elite defense. Too many unknowns to answer that question, including the larger spread among QB abilities than defense abilities (so it's not necessarily the case you have the same number of "elite" QB's as "elite" defenses), the number of players you need that are above average at different positions to have an "elite" offense or defense, and of course the probabilities of finding the players.

    All I know is that with rare exceptions you need to be good on both sides of the ball so whether we are "elite" or not, we absolutely need that franchise QB (if you play the odds) AND we need one of the better defenses in the league. Easy right?
     
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  18. The Guy

    The Guy Well-Known Member

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    Essentially it’s passer rating differential. The worse your passer, the better the pass defense you need, and vice-versa.

    And of course the converse of that is true as well. The better your passer, the worse your pass defense can be, and vice-versa.

    Blowouts in Super Bowls are rare. The last time it happened was when a team had a quarterback with a very high passer rating, combined with one of the best pass defenses of all time in terms of passer rating surrendered. That was the 2013-2014 Seahawks. That team had an absolutely monstrous regular season passer rating differential of 39.
     
    Last edited: Jun 16, 2019
  19. Pauly

    Pauly Season Ticket Holder

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    Just to build on the first two paragraphs. When I ran the numbers there is essentially zero correlation between passer rating made and passer rating allowed in the salary cap era. It doesn't have to be an either or situation. You can improve your offense without hurting your defense and vice versa.
    Based on the better correlation between offensive stats and win% the smart thing is to prioritize improving your passing offense, but if because of circumstances you can get better bang for buck building your pass defense then that isn’t wrong. Ideally you want to improve both.

    The only correlation I found was that having a really bad (-2 std devs below average) passer rating made correlates with a reduced passer rating allowed.
     
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  20. The Guy

    The Guy Well-Known Member

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    The only two formulas I would pursue in the present-day NFL are to have an average quarterback who protects the ball extremely well (Alex Smith, for example), while trying to compile an elite pass defense, or an elite quarterback coupled with at least an average pass defense. Anything other than that is a waste of time in my opinion.
     
  21. djphinfan

    djphinfan Season Ticket Holder Club Member

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    Check out play at 4:47 this is one of the many examples of what “ fatally flawed” looks like.
     
  22. KeyFin

    KeyFin Well-Known Member

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    My cold turned into bronchitis and I've been in bed since Sunday (meaning I skipped Father's Day and my b-day on Monday...YAY for me). Just wanted to let you know that I wasn't ignoring you any more than I've ignored the rest of the world these past few days.

    I still think the run game is a crucial 3rd factor in that equation and it's been the secret ingredient for NE, Philly and several recent SB champs. A great passing game may be the biggest factor for wins on paper, but I think that's misleading to some extent since the real #1 priority is extending drives. The 3 and outs have decimated our offense in recent years and I really think you have to have a balanced attack that keeps LB's/DE's honest.

    I've noticed in recent years a lot of the better teams will just keep running the football until you convince them not to. It seems like we only ran on 1st and 10 or 3rd and 19...LOL. Hopefully that changes this upcoming season.
     
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  23. AGuyNamedAlex

    AGuyNamedAlex Well-Known Member

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    This might be a dumb question but once the playoffs start wouldn't the % chance of winning the Superbowl change entirely based upon which other QB are still competing? If not, why?
     
  24. cbrad

    cbrad .

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    Yes it definitely does. That's called a "conditional probability": a probability given that some condition is satisfied. Those graphs only tell you the probability of an outcome given QB performance over the regular season.

    However.. you can derive the solution to the problem you pose from those two equations if you're interested in historical probabilities of success. Let's represent p(SB) = probability of winning the SB, p(PL) = probability of making the playoffs, and p(SB|PL) = probability of winning the SB given that you made the playoffs. These probabilities are related as follows: p(SB) = p(PL)*p(SB|PL). The equations in those two graphs give you p(SB) and p(PL) so you can solve for p(SB|PL) = 8.06*e^(0.2965*SD) if you report things in percent probability (if it's just in probabilities that 8.06 becomes 0.0806).

    So consider a QB that plays average in a given year so that SD = 0. That equation is saying that IF that QB makes the playoffs he has an 8.06% probability of winning the SB based on historical data. Compare that to the chance you'd win 3 games in a row if all teams are on average of equal strength: 12.5%. Or if it's 4 games in a row (Wild Card) that's 6.25%. So the 8.06% fits intuitively too.

    Now you're definitely right that every season is different, every set of QB's and teams in the playoffs in each year are different, etc.. So the solution I just gave tells you historical probabilities. It's obviously not good enough to predict exactly what will happen in the unique circumstances you always find yourself in at any moment in time (true with all statistics). But then again no non-statistical method can either.
     
    Last edited: Jun 19, 2019
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