Delta of binary option - Quantitative Finance Stack Exchange

No gods, no kings, only NOPE - or divining the future with options flows. [Part 3: Hedge Winding, Unwinding, and the NOPE]

Hello friends!
We're on the last post of this series ("A Gentle Introduction to NOPE"), where we get to use all the Big Boy Concepts (TM) we've discussed in the prior posts and put them all together. Some words before we begin:
  1. This post will be massively theoretical, in the sense that my own speculation and inferences will be largely peppered throughout the post. Are those speculations right? I think so, or I wouldn't be posting it, but they could also be incorrect.
  2. I will briefly touch on using the NOPE this slide, but I will make a secondary post with much more interesting data and trends I've observed. This is primarily for explaining what NOPE is and why it potentially works, and what it potentially measures.
My advice before reading this is to glance at my prior posts, and either read those fully or at least make sure you understand the tl;drs:
https://www.reddit.com/thecorporation/collection/27dc72ad-4e78-44cd-a788-811cd666e32a
Depending on popular demand, I will also make a last-last post called FAQ, where I'll tabulate interesting questions you guys ask me in the comments!
---
So a brief recap before we begin.
Market Maker ("Mr. MM"): An individual or firm who makes money off the exchange fees and bid-ask spread for an asset, while usually trying to stay neutral about the direction the asset moves.
Delta-gamma hedging: The process Mr. MM uses to stay neutral when selling you shitty OTM options, by buying/selling shares (usually) of the underlying as the price moves.
Law of Surprise [Lily-ism]: Effectively, the expected profit of an options trade is zero for both the seller and the buyer.
Random Walk: A special case of a deeper probability probability called a martingale, which basically models stocks or similar phenomena randomly moving every step they take (for stocks, roughly every millisecond). This is one of the most popular views of how stock prices move, especially on short timescales.
Future Expected Payoff Function [Lily-ism]: This is some hidden function that every market participant has about an asset, which more or less models all the possible future probabilities/values of the assets to arrive at a "fair market price". This is a more generalized case of a pricing model like Black-Scholes, or DCF.
Counter-party: The opposite side of your trade (if you sell an option, they buy it; if you buy an option, they sell it).
Price decoherence ]Lily-ism]: A more generalized notion of IV Crush, price decoherence happens when instead of the FEPF changing gradually over time (price formation), the FEPF rapidly changes, due usually to new information being added to the system (e.g. Vermin Supreme winning the 2020 election).
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One of the most popular gambling events for option traders to play is earnings announcements, and I do owe the concept of NOPE to hypothesizing specifically about the behavior of stock prices at earnings. Much like a black hole in quantum mechanics, most conventional theories about how price should work rapidly break down briefly before, during, and after ER, and generally experienced traders tend to shy away from playing earnings, given their similar unpredictability.
Before we start: what is NOPE? NOPE is a funny backronym from Net Options Pricing Effect, which in its most basic sense, measures the impact option delta has on the underlying price, as compared to share price. When I first started investigating NOPE, I called it OPE (options pricing effect), but NOPE sounds funnier.
The formula for it is dead simple, but I also have no idea how to do LaTeX on reddit, so this is the best I have:

https://preview.redd.it/ais37icfkwt51.png?width=826&format=png&auto=webp&s=3feb6960f15a336fa678e945d93b399a8e59bb49
Since I've already encountered this, put delta in this case is the absolute value (50 delta) to represent a put. If you represent put delta as a negative (the conventional way), do not subtract it; add it.
To keep this simple for the non-mathematically minded: the NOPE today is equal to the weighted sum (weighted by volume) of the delta of every call minus the delta of every put for all options chains extending from today to infinity. Finally, we then divide that number by the # of shares traded today in the market session (ignoring pre-market and post-market, since options cannot trade during those times).
Effectively, NOPE is a rough and dirty way to approximate the impact of delta-gamma hedging as a function of share volume, with us hand-waving the following factors:
  1. To keep calculations simple, we assume that all counter-parties are hedged. This is obviously not true, especially for idiots who believe theta ganging is safe, but holds largely true especially for highly liquid tickers, or tickers will designated market makers (e.g. any ticker in the NASDAQ, for instance).
  2. We assume that all hedging takes place via shares. For SPY and other products tracking the S&P, for instance, market makers can actually hedge via futures or other options. This has the benefit for large positions of not moving the underlying price, but still makes up a fairly small amount of hedges compared to shares.

Winding and Unwinding

I briefly touched on this in a past post, but two properties of NOPE seem to apply well to EER-like behavior (aka any binary catalyst event):
  1. NOPE measures sentiment - In general, the options market is seen as better informed than share traders (e.g. insiders trade via options, because of leverage + easier to mask positions). Therefore, a heavy call/put skew is usually seen as a bullish sign, while the reverse is also true.
  2. NOPE measures system stability
I'm not going to one-sentence explain #2, because why say in one sentence what I can write 1000 words on. In short, NOPE intends to measure sensitivity of the system (the ticker) to disruption. This makes sense, when you view it in the context of delta-gamma hedging. When we assume all counter-parties are hedged, this means an absolutely massive amount of shares get sold/purchased when the underlying price moves. This is because of the following:
a) Assume I, Mr. MM sell 1000 call options for NKLA 25C 10/23 and 300 put options for NKLA 15p 10/23. I'm just going to make up deltas because it's too much effort to calculate them - 30 delta call, 20 delta put.
This implies Mr. MM needs the following to delta hedge: (1000 call options * 30 shares to buy for each) [to balance out writing calls) - (300 put options * 20 shares to sell for each) = 24,000 net shares Mr. MM needs to acquire to balance out his deltas/be fully neutral.
b) This works well when NKLA is at $20. But what about when it hits $19 (because it only can go down, just like their trucks). Thanks to gamma, now we have to recompute the deltas, because they've changed for both the calls (they went down) and for the puts (they went up).
Let's say to keep it simple that now my calls are 20 delta, and my puts are 30 delta. From the 24,000 net shares, Mr. MM has to now have:
(1000 call options * 20 shares to have for each) - (300 put options * 30 shares to sell for each) = 11,000 shares.
Therefore, with a $1 shift in price, now to hedge and be indifferent to direction, Mr. MM has to go from 24,000 shares to 11,000 shares, meaning he has to sell 13,000 shares ASAP, or take on increased risk. Now, you might be saying, "13,000 shares seems small. How would this disrupt the system?"
(This process, by the way, is called hedge unwinding)
It won't, in this example. But across thousands of MMs and millions of contracts, this can - especially in highly optioned tickers - make up a substantial fraction of the net flow of shares per day. And as we know from our desk example, the buying or selling of shares directly changes the price of the stock itself.
This, by the way, is why the NOPE formula takes the shape it does. Some astute readers might notice it looks similar to GEX, which is not a coincidence. GEX however replaces daily volume with open interest, and measures gamma over delta, which I did not find good statistical evidence to support, especially for earnings.
So, with our example above, why does NOPE measure system stability? We can assume for argument's sake that if someone buys a share of NKLA, they're fine with moderate price swings (+- $20 since it's NKLA, obviously), and in it for the long/medium haul. And in most cases this is fine - we can own stock and not worry about minor swings in price. But market makers can't* (they can, but it exposes them to risk), because of how delta works. In fact, for most institutional market makers, they have clearly defined delta limits by end of day, and even small price changes require them to rebalance their hedges.
This over the whole market adds up to a lot shares moving, just to balance out your stupid Robinhood YOLOs. While there are some tricks (dark pools, block trades) to not impact the price of the underlying, the reality is that the more options contracts there are on a ticker, the more outsized influence it will have on the ticker's price. This can technically be exactly balanced, if option put delta is equal to option call delta, but never actually ends up being the case. And unlike shares traded, the shares representing the options are more unstable, meaning they will be sold/bought in response to small price shifts. And will end up magnifying those price shifts, accordingly.

NOPE and Earnings

So we have a new shiny indicator, NOPE. What does it actually mean and do?
There's much literature going back to the 1980s that options markets do have some level of predictiveness towards earnings, which makes sense intuitively. Unlike shares markets, where you can continue to hold your share even if it dips 5%, in options you get access to expanded opportunity to make riches... and losses. An options trader betting on earnings is making a risky and therefore informed bet that he or she knows the outcome, versus a share trader who might be comfortable bagholding in the worst case scenario.
As I've mentioned largely in comments on my prior posts, earnings is a special case because, unlike popular misconceptions, stocks do not go up and down solely due to analyst expectations being meet, beat, or missed. In fact, stock prices move according to the consensus market expectation, which is a function of all the participants' FEPF on that ticker. This is why the price moves so dramatically - even if a stock beats, it might not beat enough to justify the high price tag (FSLY); even if a stock misses, it might have spectacular guidance or maybe the market just was assuming it would go bankrupt instead.
To look at the impact of NOPE and why it may play a role in post-earnings-announcement immediate price moves, let's review the following cases:
  1. Stock Meets/Exceeds Market Expectations (aka price goes up) - In the general case, we would anticipate post-ER market participants value the stock at a higher price, pushing it up rapidly. If there's a high absolute value of NOPE on said ticker, this should end up magnifying the positive move since:
a) If NOPE is high negative - This means a ton of put buying, which means a lot of those puts are now worthless (due to price decoherence). This means that to stay delta neutral, market makers need to close out their sold/shorted shares, buying them, and pushing the stock price up.
b) If NOPE is high positive - This means a ton of call buying, which means a lot of puts are now worthless (see a) but also a lot of calls are now worth more. This means that to stay delta neutral, market makers need to close out their sold/shorted shares AND also buy more shares to cover their calls, pushing the stock price up.
2) Stock Meets/Misses Market Expectations (aka price goes down) - Inversely to what I mentioned above, this should push to the stock price down, fairly immediately. If there's a high absolute value of NOPE on said ticker, this should end up magnifying the negative move since:
a) If NOPE is high negative - This means a ton of put buying, which means a lot of those puts are now worth more, and a lot of calls are now worth less/worth less (due to price decoherence). This means that to stay delta neutral, market makers need to sell/short more shares, pushing the stock price down.
b) If NOPE is high positive - This means a ton of call buying, which means a lot of calls are now worthless (see a) but also a lot of puts are now worth more. This means that to stay delta neutral, market makers need to sell even more shares to keep their calls and puts neutral, pushing the stock price down.
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Based on the above two cases, it should be a bit more clear why NOPE is a measure of sensitivity to system perturbation. While we previously discussed it in the context of magnifying directional move, the truth is it also provides a directional bias to our "random" walk. This is because given a price move in the direction predicted by NOPE, we expect it to be magnified, especially in situations of price decoherence. If a stock price goes up right after an ER report drops, even based on one participant deciding to value the stock higher, this provides a runaway reaction which boosts the stock price (due to hedging factors as well as other participants' behavior) and inures it to drops.

NOPE and NOPE_MAD

I'm going to gloss over this section because this is more statistical methods than anything interesting. In general, if you have enough data, I recommend using NOPE_MAD over NOPE. While NOPE in theory represents a "real" quantity (net option delta over net share delta), NOPE_MAD (the median absolute deviation of NOPE) does not. NOPE_MAD simply answecompare the following:
  1. How exceptional is today's NOPE versus historic baseline (30 days prior)?
  2. How do I compare two tickers' NOPEs effectively (since some tickers, like TSLA, have a baseline positive NOPE, because Elon memes)? In the initial stages, we used just a straight numerical threshold (let's say NOPE >= 20), but that quickly broke down. NOPE_MAD aims to detect anomalies, because anomalies in general give you tendies.
I might add the formula later in Mathenese, but simply put, to find NOPE_MAD you do the following:
  1. Calculate today's NOPE score (this can be done end of day or intraday, with the true value being EOD of course)
  2. Calculate the end of day NOPE scores on the ticker for the previous 30 trading days
  3. Compute the median of the previous 30 trading days' NOPEs
  4. From the median, find the 30 days' median absolute deviation (https://en.wikipedia.org/wiki/Median_absolute_deviation)
  5. Find today's deviation as compared to the MAD calculated by: [(today's NOPE) - (median NOPE of last 30 days)] / (median absolute deviation of last 30 days)
This is usually reported as sigma (σ), and has a few interesting properties:
  1. The mean of NOPE_MAD for any ticker is almost exactly 0.
  2. [Lily's Speculation's Speculation] NOPE_MAD acts like a spring, and has a tendency to reverse direction as a function of its magnitude. No proof on this yet, but exploring it!

Using the NOPE to predict ER

So the last section was a lot of words and theory, and a lot of what I'm mentioning here is empirically derived (aka I've tested it out, versus just blabbered).
In general, the following holds true:
  1. 3 sigma NOPE_MAD tends to be "the threshold": For very low NOPE_MAD magnitudes (+- 1 sigma), it's effectively just noise, and directionality prediction is low, if not non-existent. It's not exactly like 3 sigma is a play and 2.9 sigma is not a play; NOPE_MAD accuracy increases as NOPE_MAD magnitude (either positive or negative) increases.
  2. NOPE_MAD is only useful on highly optioned tickers: In general, I introduce another parameter for sifting through "candidate" ERs to play: option volume * 100/share volume. When this ends up over let's say 0.4, NOPE_MAD provides a fairly good window into predicting earnings behavior.
  3. NOPE_MAD only predicts during the after-market/pre-market session: I also have no idea if this is true, but my hunch is that next day behavior is mostly random and driven by market movement versus earnings behavior. NOPE_MAD for now only predicts direction of price movements right between the release of the ER report (AH or PM) and the ending of that market session. This is why in general I recommend playing shares, not options for ER (since you can sell during the AH/PM).
  4. NOPE_MAD only predicts direction of price movement: This isn't exactly true, but it's all I feel comfortable stating given the data I have. On observation of ~2700 data points of ER-ticker events since Mar 2019 (SPY 500), I only so far feel comfortable predicting whether stock price goes up (>0 percent difference) or down (<0 price difference). This is +1 for why I usually play with shares.
Some statistics:
#0) As a baseline/null hypothesis, after ER on the SPY500 since Mar 2019, 50-51% price movements in the AH/PM are positive (>0) and ~46-47% are negative (<0).
#1) For NOPE_MAD >= +3 sigma, roughly 68% of price movements are positive after earnings.
#2) For NOPE_MAD <= -3 sigma, roughly 29% of price movements are positive after earnings.
#3) When using a logistic model of only data including NOPE_MAD >= +3 sigma or NOPE_MAD <= -3 sigma, and option/share vol >= 0.4 (around 25% of all ERs observed), I was able to achieve 78% predictive accuracy on direction.

Caveats/Read This

Like all models, NOPE is wrong, but perhaps useful. It's also fairly new (I started working on it around early August 2020), and in fact, my initial hypothesis was exactly incorrect (I thought the opposite would happen, actually). Similarly, as commenters have pointed out, the timeline of data I'm using is fairly compressed (since Mar 2019), and trends and models do change. In fact, I've noticed significantly lower accuracy since the coronavirus recession (when I measured it in early September), but I attribute this mostly to a smaller date range, more market volatility, and honestly, dumber option traders (~65% accuracy versus nearly 80%).
My advice so far if you do play ER with the NOPE method is to use it as following:
  1. Buy/short shares approximately right when the market closes before ER. Ideally even buying it right before the earnings report drops in the AH session is not a bad idea if you can.
  2. Sell/buy to close said shares at the first sign of major weakness (e.g. if the NOPE predicted outcome is incorrect).
  3. Sell/buy to close shares even if it is correct ideally before conference call, or by the end of the after-market/pre-market session.
  4. Only play tickers with high NOPE as well as high option/share vol.
---
In my next post, which may be in a few days, I'll talk about potential use cases for SPY and intraday trends, but I wanted to make sure this wasn't like 7000 words by itself.
Cheers.
- Lily
submitted by the_lilypad to thecorporation [link] [comments]

MAME 0.222

MAME 0.222

MAME 0.222, the product of our May/June development cycle, is ready today, and it’s a very exciting release. There are lots of bug fixes, including some long-standing issues with classics like Bosconian and Gaplus, and missing pan/zoom effects in games on Seta hardware. Two more Nintendo LCD games are supported: the Panorama Screen version of Popeye, and the two-player Donkey Kong 3 Micro Vs. System. New versions of supported games include a review copy of DonPachi that allows the game to be paused for photography, and a version of the adult Qix game Gals Panic for the Taiwanese market.
Other advancements on the arcade side include audio circuitry emulation for 280-ZZZAP, and protection microcontroller emulation for Kick and Run and Captain Silver.
The GRiD Compass series were possibly the first rugged computers in the clamshell form factor, possibly best known for their use on NASA space shuttle missions in the 1980s. The initial model, the Compass 1101, is now usable in MAME. There are lots of improvements to the Tandy Color Computer drivers in this release, with better cartridge support being a theme. Acorn BBC series drivers now support Solidisk file system ROMs. Writing to IMD floppy images (popular for CP/M computers) is now supported, and a critical bug affecting writes to HFE disk images has been fixed. Software list additions include a collection of CDs for the SGI MIPS workstations.
There are several updates to Apple II emulation this month, including support for several accelerators, a new IWM floppy controller core, and support for using two memory cards simultaneously on the CFFA2. As usual, we’ve added the latest original software dumps and clean cracks to the software lists, including lots of educational titles.
Finally, the memory system has been optimised, yielding performance improvements in all emulated systems, you no longer need to avoid non-ASCII characters in paths when using the chdman tool, and jedutil supports more devices.
There were too many HyperScan RFID cards added to the software list to itemise them all here. You can read about all the updates in the whatsnew.txt file, or get the source and 64-bit Windows binary packages from the download page.

MAME Testers Bugs Fixed

New working machines

New working clones

Machines promoted to working

Clones promoted to working

New machines marked as NOT_WORKING

New clones marked as NOT_WORKING

New working software list additions

Software list items promoted to working

New NOT_WORKING software list additions

submitted by cuavas to emulation [link] [comments]

MAME 0.222

MAME 0.222

MAME 0.222, the product of our May/June development cycle, is ready today, and it’s a very exciting release. There are lots of bug fixes, including some long-standing issues with classics like Bosconian and Gaplus, and missing pan/zoom effects in games on Seta hardware. Two more Nintendo LCD games are supported: the Panorama Screen version of Popeye, and the two-player Donkey Kong 3 Micro Vs. System. New versions of supported games include a review copy of DonPachi that allows the game to be paused for photography, and a version of the adult Qix game Gals Panic for the Taiwanese market.
Other advancements on the arcade side include audio circuitry emulation for 280-ZZZAP, and protection microcontroller emulation for Kick and Run and Captain Silver.
The GRiD Compass series were possibly the first rugged computers in the clamshell form factor, possibly best known for their use on NASA space shuttle missions in the 1980s. The initial model, the Compass 1101, is now usable in MAME. There are lots of improvements to the Tandy Color Computer drivers in this release, with better cartridge support being a theme. Acorn BBC series drivers now support Solidisk file system ROMs. Writing to IMD floppy images (popular for CP/M computers) is now supported, and a critical bug affecting writes to HFE disk images has been fixed. Software list additions include a collection of CDs for the SGI MIPS workstations.
There are several updates to Apple II emulation this month, including support for several accelerators, a new IWM floppy controller core, and support for using two memory cards simultaneously on the CFFA2. As usual, we’ve added the latest original software dumps and clean cracks to the software lists, including lots of educational titles.
Finally, the memory system has been optimised, yielding performance improvements in all emulated systems, you no longer need to avoid non-ASCII characters in paths when using the chdman tool, and jedutil supports more devices.
There were too many HyperScan RFID cards added to the software list to itemise them all here. You can read about all the updates in the whatsnew.txt file, or get the source and 64-bit Windows binary packages from the download page.

MAME Testers Bugs Fixed

New working machines

New working clones

Machines promoted to working

Clones promoted to working

New machines marked as NOT_WORKING

New clones marked as NOT_WORKING

New working software list additions

Software list items promoted to working

New NOT_WORKING software list additions

submitted by cuavas to MAME [link] [comments]

MAME 0.222

MAME 0.222

MAME 0.222, the product of our May/June development cycle, is ready today, and it’s a very exciting release. There are lots of bug fixes, including some long-standing issues with classics like Bosconian and Gaplus, and missing pan/zoom effects in games on Seta hardware. Two more Nintendo LCD games are supported: the Panorama Screen version of Popeye, and the two-player Donkey Kong 3 Micro Vs. System. New versions of supported games include a review copy of DonPachi that allows the game to be paused for photography, and a version of the adult Qix game Gals Panic for the Taiwanese market.
Other advancements on the arcade side include audio circuitry emulation for 280-ZZZAP, and protection microcontroller emulation for Kick and Run and Captain Silver.
The GRiD Compass series were possibly the first rugged computers in the clamshell form factor, possibly best known for their use on NASA space shuttle missions in the 1980s. The initial model, the Compass 1101, is now usable in MAME. There are lots of improvements to the Tandy Color Computer drivers in this release, with better cartridge support being a theme. Acorn BBC series drivers now support Solidisk file system ROMs. Writing to IMD floppy images (popular for CP/M computers) is now supported, and a critical bug affecting writes to HFE disk images has been fixed. Software list additions include a collection of CDs for the SGI MIPS workstations.
There are several updates to Apple II emulation this month, including support for several accelerators, a new IWM floppy controller core, and support for using two memory cards simultaneously on the CFFA2. As usual, we’ve added the latest original software dumps and clean cracks to the software lists, including lots of educational titles.
Finally, the memory system has been optimised, yielding performance improvements in all emulated systems, you no longer need to avoid non-ASCII characters in paths when using the chdman tool, and jedutil supports more devices.
There were too many HyperScan RFID cards added to the software list to itemise them all here. You can read about all the updates in the whatsnew.txt file, or get the source and 64-bit Windows binary packages from the download page.

MAME Testers Bugs Fixed

New working machines

New working clones

Machines promoted to working

Clones promoted to working

New machines marked as NOT_WORKING

New clones marked as NOT_WORKING

New working software list additions

Software list items promoted to working

New NOT_WORKING software list additions

submitted by cuavas to cade [link] [comments]

[OC] Building an NFL Draft Model using Machine Learning

Happy Sunday nfl. Like most of the users here, I get draft-obsessed every February when the Combine comes around. Well, this year I decided to do something about it by building a draft model. If you're not interested in the details, you can stop right here and click the links below.
 
Model outputs from validation can be viewed here: https://docs.google.com/spreadsheets/d/1-ooQ4UTafyFOTWDtbYGmPgdHfspY8bci45tUS6I5-LU/edit?usp=sharing
Album of select draft prospect profiles: https://imgur.com/a/SCdkLj1
I've created some simple player visual dashboards which present position-specific percentile rankings in performance and athleticism. Each of these refer to either neutralized statistics, or engineered features, so "Tackles" is more accurately "Neutralized Tackles per Game" and "Speed" is actually "Speed Score". If anyone has requests to see other players, let me know and I'll try to cover all of them.

Research Goal

To build an NFL draft model capable of producing meaningful player predictions. I had originally planned to do so using a fuzzy Random Forest trained on NFL Combine and Pro Day physical measurements, individual and team college statistics, and engineered features. The model produced superior results when treating physical measurements as crisp rather than fuzzy, which was surprising but nonetheless forced me to change my approach.
Random Forest model is appropriate for this dataset because of the relatively small number of observations (roughly 250-300 players per draft class) and the highly non-linear relationship between the input and output variables. Random Forests are fairly robust against overfitting, which is a concern when modelling noisy data.
Player performance is impacted by round and team selection in the draft - first-round selections receive more opportunities than seventh-round selections, different schemes fit some players better. Because of this the model performance can be greatly improved by including some regression to draft selection or, in the case of test data, public rankings.

Model Output

I've decided to take the novel approach of using player ratings from EA Sports' Madden video game franchise as a proxy for player production, skill, and value. This is beneficial for a number of reasons. The first is that these ratings provide continuous output on a consistent scale across both years and positions; a player rated 99 overall is considered to be elite at their position, regardless of the unique responsibilities or challenges in quantifying performance specific to that position. The second reason is that Madden ratings predate modern quantitative evaluative metrics like those provided by Football Outsiders or Pro Football Focus.
Madden ratings explained - https://fivethirtyeight.com/features/madden/#
Overall ratings are calculated using position-specific formulas that weight individual attributes like speed, strength, and tackling. Ratings are updated each year through a Bayesian-like process of weighing new information to update old. To aggregate ratings for each player, I use a 5-part mean which includes ratings in Years 1-4 and Peak rating.
NFL rookie contract length is 4 seasons (along with a fifth year club option for first-round picks), while the average career length in the NFL is less than 4 years. As such, when building a draft model is makes sense to only consider production accrued during the first 4 years of a player's career.
Year 1 represents the Madden rating given to each player following their rookie season. For this reason, the final year for which complete data is available is the 2014 draft class (with Madden 19 providing Year 4 ratings). This decision was made to better capture NFL success, as rookie player ratings are highly dependent on draft order. For example, in Madden 2008 rookie #1 overall pick JaMarcus Russell was awarded an overall rating of 82, just 1 point lower than #3 overall pick Joe Thomas. The next year, Russell's rating was 83, while Thomas was a 97 overall. By Madden 2010, Russell was given a rating of 72 overall, while Thomas maintained his 97 overall rating. Year 3 and Year 4 ratings have been given double weight for the same reason, with the added effect of lowering the ratings of players who were not able to stay in the league for at least 4 years.
While this metric on the whole does a good job of ranking player talent and production, it is blind to players who peaked later in their careers or those who had short careers. Notable examples of each include Eric Weddle (84.6 rating, eventual 2x All Pro, 6x Pro Bowl) and Jon Beason (95.4 rating, 1x All-Pro, 3x Pro Bowl). Weddle did not reach his peak until after re-signing with the Chargers as an unrestricted free agent prior to the 2011 season, and could have presumably reached his peak while playing for another team. Beason suffered an Achilles injury during the 2011 season and eventually lost his job with the Panthers, starting in only 26 games in the years following his rating window. Beason would have been eligible to sign as a free agent following the 2011 season had the Panthers not offered a contract extension.
In the NFL, the drafting team maintains the exclusive right to employ each player for 4 years following their selection, thus it is incumbent upon the team to select and develop players who provide the most value during that period. For that reason I stand by the decision to evaluate draft selections only on a player's first 4 years in the league.

Dataset

I wrote several web scraping programs to pull data from NFL Draft Scout (an excellent resource for Combine data, and the only source I'm aware of that includes Pro Day data), Pro-Football-Reference, and CFB Reference (both Sports-Reference-operated sites, easily the best sources for football statistics in the NFL or FBS).
The dataset covers the 2006-2014 draft classes and includes players who were ranked in NFL Draft Scout's top 300 in their draft year. I have removed all quarterbacks, kickers, punters, long snappers, and fullbacks due to the relatively small sample sizes or extreme specialization that each position requires. It might be valuable to evaluate these positions later – particularly quarterbacks – but for now the model focuses exclusively on 13 "skill" positions, bucketed into 7 position groups.
The dataset restrictions exclude some notable players ranked outside of the top 300, both drafted and undrafted, who went on to varying degrees of success in the NFL. At the top extreme are 4-time All Pro Antonio Brown and Super Bowl LIII MVP Julian Edelman. But while many players on this list never played a down in the NFL, it is important to be aware of which players are excluded and it may be worthwhile to expand the dataset in the future.
I have removed players from the dataset whose NFL careers were cut prematurely short either voluntarily or involuntarily (due to injury, not ability). These players' ratings (or lack thereof) are not representative of their production and thus only serve to complicate the dataset and confuse any modeling attempts. Examples include Aaron Hernandez, Gaines Adams, and Chris Borland. The list is as long as it is depressing.
There is also a subset of players who drastically changed position upon entering the league. This is contrary to less extreme position changes (tackle to guard, cornerback to safety), which occur frequently. These players have been removed because their college statistics create noisy data. Examples: Denard Robinson, Devin Hester, J.R. Sweezy.

College Statistics

College statistics have been collected and cleaned at the FBS level from Sports Reference. Using college statistics is important because they provide information on a player's in-game performance. However, college football styles vary greatly among teams and have changed over time. Therefore we must control for differences in pace and style of play when considering college numbers. Rather than attempt to fit a model on raw season total statistics, I've decided to use neutralized per game statistics under the following parameters:
 
 
To illustrate this point let's look at Calvin Johnson and Michael Crabtree, who were both highly productive college wide receivers selected early in the first round.
 
 
The two statlines appear very similar without context. It's easy to make this distinction empirically, but little effort has been made to translate college statistics into more informative data. Johnson and Crabtree put up similar overall numbers, but Crabtree did it in an air raid style offense that relied heavily on passing while Johnson played on a more balanced offense.
 
 
When we neutralize both players' statistics, we can better compare each player's level of production.
 
 
Compare those numbers to each player's NFL career statistics:
 
 
This is a cherry-picked example but it does well to show that while raw statistics are not to be trusted, college data when put into the proper context can be made more predictive. On a larger scale, we can compare RMSE of the model when including raw college statistics compared to pace- and schedule-neutralized statistics. Controlling for strength of schedule does not improve the predictiveness of the model, but controlling for pace and style of play does have a significant effect.
 
Neutralization RMSE
Raw per Game 8.065
Pace-Neutralized per Game 8.029
Pace- and Schedule-Neutralized per Game 8.058
 
Here's the full stat list, with a few notable performers:
 
Offensive Statistics
 
Defensive Statistics
 

NFL Combine and Pro Day Measurements

The final major inputs of the draft model are the physical measurements taken at the NFL Combine and university Pro Days. Pro Day measurements are harder to come by due to their decentralized and often scarcely reported nature. Fortunately, NFL Draft Scout has maintained a database of reported Pro Day measurements spanning the years in our dataset.
There is an enormous benefit in using Pro Day measurements in a model like this. It allows for a larger training set by including data on players who were not invited to the NFL Combine, but also provides much more complete data because not all players who attend the combine perform the full slate of workouts. This lessens the need for imputation and reduces uncertainty.
However, there is bias observed in Pro Day measurements. Pro Days are typically scheduled in the weeks following the NFL Combine, giving players more time to train for the specific physical events. Furthermore, they often take place at the players' home campuses in environments in which the players feel more comfortable. Lastly, many events (most notably the 40-yard dash) are hand-timed at Pro Days, leading to better reported times than the electronic times at the Combine. Each of these factors contributes to improvement in every event among the population of players who participated both at the NFL Combine and at their university Pro Day.
 
Players who participated in both NFL Combine and Pro Day
Measurement Combine Pro Day n Sigma Adjustment
40 Yard Dash 4.80 4.70 831 0.076 + 0.07
20 Yard Split 2.79 2.71 733 0.065 + 0.06
10 Yard Split 1.68 1.62 739 0.057 + 0.04
Bench Press 20.0 reps 21.7 reps 254 2.556 - 1.2
Vertical Jump 31.7" 33.6" 593 2.342 - 1.3"
Broad Jump 112.9" 115.2" 481 4.356 - 1.6"
20 Yard Shuttle 4.46 4.42 424 0.155 + 0.03
3 Cone Drill 7.34 7.22 342 0.223 + 0.08
 
In order to correct for this bias, I've (somewhat arbitrarily) chosen to shift recorded Pro Day measurements by 70% of the mean delta. Even when we correct for some of the systematic bias observed in Pro Day measurements, we must also recognize that most physical measurements aren't static. Some players aren't performing at maximum physical capacity on the day of the Combine, occasionally players injure themselves during their workout, and the measurements aren't always recorded with perfect accuracy or consistency.
A dataset with this much uncertainty lends itself well to fuzzy set theory. In simple terms, this will allow us to consider not only a player's recorded 40 yard time of 4.40, but will also consider some probability that their "true" speed is 4.39 or 4.43. So when the model attempts to predict NFL success given a player's 40 yard dash time, it's not based on a singular number but rather a distribution of times centered around that number.
Fuzzy Set Theory explanation - https://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/sbaa/report.fuzzysets.html
My approach is to generate a random forest model on the discrete data, then fit n iterations on randomly shuffled data to generate a distribution of outcomes for each player. This "shuffling" will occur randomly for each measurement using a normal distribution centered around the discrete number, with sigma equal to half of the standard deviations recorded above.
In a single random forest, data is crisply split by decision trees based on discrete information. But with enough randomly shuffled iterations, the trees are no longer binary decisions but rather probabilistic ones centered on each measurement's distribution. This is particularly relevant for players who may have measurements near decision tree boundaries. Two players with sprint times separated by mere hundredths of a second are not appreciably different in speed, but a random forest might classify them as such. The purpose of shuffling is not to fundamentally change each player's physical characteristics, rather to acknowledge measurement uncertainty. My belief is that this will improve the model outputs over a large enough number of trials.
We have a wealth of NFL Combine and Pro Day data but not every player has participated in every drill, so we'll need to fill in missing values. Because many of these physical measurements are correlated and most football positions require some degree physical specialization (size, speed, etc.), I've chosen a k nearest neighbor imputation method. The belief is that if Players A and B are similar in terms of position, size, speed, and quickness, then the two players will also have similar strength or jumping ability. The exceptions are draft age and wingspan, which can be reasonably predicted using population means.

Engineered Features

Perhaps the most essential component of a machine learning model is feature engineering.
Modern feeling toward physical measurements taken at the Combine is highly dubious, and I agree that each measurement taken in isolation cannot alone adequately define athleticism, much less predict success. However, there exist more complex metrics which can better perform both tasks across a large enough sample.
 
Body Mass Index (BMI)
 
Speed Score
 
Height-Adjusted Speed Score
 
Vertical Jump Power
 
Broad Jump Power
 
Quickness Score
 
Weight-Adjusted Bench
 
Catch Radius
 
The models also include several features designed to summarize the collection of college statistics being used.
 
Offensive Usage
 
Defensive Disruption
 
S&P Market Share

Cross-Validation and Tuning

I've tuned the model using stratified k-fold cross validation, leaving out each draft class as OOB observations. As a result, every player has been included in both the training and validation sets. Each position group has been fit with its own unique hyperparameters to optimize predictions.
 
Hyperparameters by Position Group
Position Number of Trees Max Depth Max Features Min Leaf Samples
WR 100 5 10 3
FS 250 5 10 1
CB 50 10 20 2
SS 40 10 10 2
ILB 30 15 5 2
RB 40 10 10 1
TE 20 10 3 2
EDGE LB 50 5 10 2
EDGE DL 250 15 10 2
C 50 5 5 3
DT 100 3 10 1
OT 20 5 3 2
OG 20 10 5 2
 
Additionally, the model performed best when aggregating predictions from 3 randomized sets, as shown in the plot below. However, this fuzzy approach failed to outperform discrete features during cross-validation. I expected the opposite, but it seems treating each measurement as precise leads to the best fit.
 
RMSE Using Various Methods
Method RMSE
Discrete 8.027
1 Random set 8.122
2 Random sets 8.069
3 Random sets 8.063
5 Random sets 8.098
10 Random sets 8.115

Results and Further Research

By and large the model does surprisingly well considering the lack of more traditional evaluative inputs. NFL teams have the resources of scouting departments providing more detailed player evaluation, experienced coaching staffs evaluating personnel fits, and front offices to balance financial considerations and positional value. Each of these factor into draft decisions and improve ranking methods beyond the scope of this model.
 
Model results by position
Position RMSE n Most Important Features
WR 7.523 314 Underclassman, Usage, Age, Srimmage Yards, Total TD, Receiving Yards
FS 7.621 128 S&P Share, Age, SOS, 20-Yard Shuttle, Height, 40-Yard Dash
CB 7.604 292 Age, Quickness Score, Height-Adjusted Speed Score, S&P Share, Height, 20-Yard Dash
SS 7.437 107 Run Stuffs, BMI, Defensive Disruption, Quickness Score, Tackles, TFL
ILB 7.649 291 S&P Share, Age, Tackles, Height-Adjusted Speed Score, Vert Power
RB 8.121 194 Rush TD, Rush Yards, Age, Total TD, Scrimmage Yards, Height-Adjusted Speed Score
TE 8.097 139 Scrimmage Yards, Receiving TD, Receiving Yards, Offensive Usage, Hand Size
EDGE LB 8.846 90 S&P Share, Disruption, Catch Radius, Tackles, Weight, Age
EDGE DL 7.445 190 Age, TFL, Weight, Height-Adjusted Speed Score, Quickness Score, Underclassman
C 8.948 82 3-Cone, Weight, Broad Jump, Quickness Score, Hand Size, Age
DT 7.823 211 S&P Share, TFL, Tackles, Disruption, Run Stuffs, 3 Cone
OT 8.882 222 Age, Vert Power, Arm Length, Speed Score, Weight
OG 8.819 140 Adjusted Bench, 20-Yard Dash, Catch Radius, Quickness Score, Age, Weight
 
When properly optimized, the model can achieve RMSE below 8 during cross-validation. Unsurprisingly, it struggles most with offensive linemen, who lack individual statistics. In particular it struggles with centers, whose responsibilities in the NFL are as much mental as physical. Interestingly, NFL teams have had great success evaluating centers, as 4 of the 5 first rounders were named to All-Pro teams in their careers, and all made the Pro Bowl at some point.
As mentioned in the introduction, the model could be improved substantially by including draft selection or consensus rankings. Furthermore, team-specific random effects could likely explain some of the residuals. I may eventually explore these research questions, but my short-term priorities are on visualization and presentation of data.
 
If you've made it this far, check out my github for the source code: https://github.com/walt-king/NFL-draft-research
This was created using Python for web scraping, data collection, modelling, and visuals. I used R to create the player dashboards. Comments, thoughts, and feedback all greatly appreciated.
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