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Week 6, Game 1 – Binary vs. Precision

We encountered an interesting result from the Eagles-Panthers Thursday night game. In a poll, users picked the Eagles to win, but with scores, they picked the Panthers. So in this case, the binary was correct and the precision was not.

A quick reminder: we think the value of the wisdom of the crowd is in precision. There are several ways to determine where the public lands on either side of a given line, but over the course of a season, that number will be close to 50%. That’s how the sportsbooks make their money.

The value we believe that Crowdsourced Scores has is that it allows the contrarian view to have a bit more weight. An Eagles vote and a Panthers vote have the same value in a poll, but when there is a prediction of Eagles 28, Panthers 21 and another of Panthers 24, Eagles 23, the aggregate score leans Eagles. This becomes especially important when we consider the lines since the delta between the crowd prediction and the lines is how we define value.

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The Game 1 CPR – 3 for 3

Correct: Straight-up, Against the Spread, Over/Under. Another Trifecta!

The chart above shows the how that crowd average stabilized over the week. Initial submissions favored the Eagles quite strongly, but the scores evened out as the game got closer. The final spread predicted by the crowd was Eagles +0.6, so it was basically a coin flip. We’re certainly happy that the crowd was on the right side, even if it’s just by a hair. Meanwhile, the total stayed fairly steady throughout. The final predicted total of 47 was not within a margin of safety (more than a touchdown), but it never came close to the line of 44.

 

2017-week6-tnf

The Cynthia Frelund Experience

Cynthia Frelund’s crowd (@cfrelund) was 2.5 for 3 tonight, getting the spread and the total correct, and I’m giving them a half point for getting it right with the poll. I cut off prediction collection at 50 total predictions, and it’s interesting to consider whether 50 is a satisfactory cutoff or whether it’s not a big enough sample size.

Additionally, there is a potential that Ms. Frelund’s audience is not quite as decentralized as we’d like. It’s possible that they are influenced by other users, by Cynthia herself, or something else entirely. When you have a prediction this close one way or the other, there are a lot of different ways that you can look at the data to see if you can improve your aggregation, and there is a lesson in here, for sure. It’s just not clear what it is. 🙂

Do you see a way for us to improve our data collection? Let us know in the comments!

-Chris

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Week 5 CPR: Slow and steady

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The crowd in Week 5 was below where we would have hoped, but there is a silver lining. The crowd was at 50% (7 of 14) straight-up and on the over/under, and it 57% (8 of 14) against the spread. 50% is below where we’d like to be. For our hypothesis to be proven right, we expect to be north of 60% and perhaps even a bit higher.

On the other hand, look at the trend in the chart above, we’re seeing a steady trend upward against the spread. I focus on this generally because it has the most value in the gambling world. It has the most options to play around with, including teasers and parlays. Getting consistently good predictions with the spread will be a validator of the wisdom of the crowd. As you can see in the chart, the crowd is getting better over the course of the season, and that is the key to what we are hoping to accomplish. If we consider a down week to be 50%, it would mean that our good weeks are above that, and the average over time will be where we hope.

Best Bets and One More Crazy Ending

I wanted to start trying to see which lines the crowd seems to indicate have the most value. At this point, I’m choosing the lines that have the greatest delta between the line and the crowd prediction.

In Week 5, the crowd went 2-2. They were correct on the Cardinals-Eagles under 45, Jets to win, Bills +3, and Vikings-Bears over 40. Bills and Vikings-Bears were very close to coming through, but a loss is a loss, unfortunately. And we have to mention that the under in the Cardinals-Eagles only came through because of a crazy fumble at the goal line that turned the ball over to the Eagles instead of being placed at the one. But sometimes it’s better to be lucky than good.

Two More On the Money Predictions!

Congrats to M.R. who picked the Vikings to beat the Bears 20-17, and to M.G. who picked the Packers to beat the Cowboys 35-31. Incredible!

One interesting note to consider is that both of these scores were very common (I don’t have the data for the frequency, but I believe 20-17 is one of the most common scores). Is it better to predict a common score rather than a specific score? For our purposes, being on the correct side of the line is more important than accuracy.

Still, we like to call out when you all are able to nail a score like that.

CPR Week 5 Summary

  • Straight-up: 7-7 (50%)
  • Against the Spread: 8-6 (57%)
  • Over/Under: 7-7 (50%)

Overall

  • Straight-up: 45-32 (58%)
  • Against the Spread: 36-41 (47%)
  • Over/Under: 43-34 (56%)

10 predictors this week! Thank you so much everyone. We cannot tell you how much we appreciate your support.

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The Cynthia Frelund Experience

This was the first time since we’ve been tracking @cfrelund‘s followers that they only got 1 out of 3 correct (just the winner). They have picked the Thursday/Monday winner correctly 7 times in a row which is notable, and they have gotten 2 out of 3 right each time at least during that stretch. As we keep saying, it’s about the long view, and Cynthia’s crowd is certainly paying off over the course of the season.

The Crowd-wisest Game of the Week

I wrote a bit about the Patriots-Bucs on Thursday already, and that game seemed to be the best crowd performance of the week. Not only did the crowd get all three picks correct, they predicted the Patriots to win but the Bucs to cover.

PREDICTION CROWD ACTUAL
Winner Patriots Patriots
Spread Patriots -2 (spread was -5.5) Patriots -5
Over/Under 50 (under 56) 33

The Wabby of the Week

The choice for Week 5 was clear: Jaguars over Steelers. I give you 20 points and the Jaguars and Monday you’re signing your house over to me wearing a barrel. The crowd missed on it as well, predicting the Steelers to cover the 7.5-point spread.

PREDICTION CROWD ACTUAL
Winner Steelers Jaguars
Spread Steelers -9.5 (spread was -7.5) Jaguars -21
Over/Under 47 (over 42) 39

Week 5 Top Performers

There was a lot of clumping together this week as the individuals seemed to reflect the crowd pretty closely.

Congrats everyone and thanks against for your help!

STRAIGHT-UP AGAINST THE SPREAD OVER/UNDER
J.M (8)
G.A. (7)
C.A. (7)
M.G. (7)
M.R. (7)
G.A. (8)
J.M. (8)
C.A. (7)
N.G. (7)
I.R. (7)
P.M. (8)
C.A. (8)
M.G. (7)
M.R. (7)
I.R. (7)
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2017 Week 5, Game 1 – The Wearing-a-Barrel Trifecta

A few weeks ago I referenced a quote from Brian Murphy about a game result being so unexpected that if you were given spread and over/under lines (prior to kickoff, of course) that matched the final outcome, you’d be signing over your house to me wearing a barrel because they’d seem absurd. (I am henceforth calling these games “Wabbies”.)

The Thursday night game between the Patriots and Bucs has the unusual distinction of being both a trifecta for the crowd and yet also a Wabby.

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The Game 1 CPR – 3 for 3

Correct: Straight-up, Against the Spread, Over/Under. The Trifecta!

The crowd predicted the Patriots to win but the Bucs to cover, and the predicted total of 50 was 10% below the line of 56. Not to put too fine a point on it, threading the needle of a favorite winning and an underdog covering is harder than it seems, as the majority of teams that cover also win the game outright.

Having said that, the Patriots have been scoring 33 points by themselves in pretty much every game this season. On top of that, it has been repeated ad nauseum this week that the Patriots have the worst defense in the league. So if I had told you that you could have select the over/under with a total of 34 points on Thursday night, the next day you’d be signing your house over to me wearing a barrel.

What’s worth noting in the data is that the Wednesday predictions were markedly lower, and that pulled the total down below the Over/Under line. We’ll begin to start tracking averages during the week to see if we can connect crowd wisdom to events that occur within the week. In this week, for example, news of Patriots TE Rob Gronkowski missing Thursday’s game came out, and the predictions reflected both the Bucs winning and the overall total staying under the Vegas line.

As we say pretty regularly, we’re trying to find value first, and accuracy is a bonus. The crowd prediction of 50 for the total was a six-point gap that indicates pretty significant value, and being right about the actual total is nice but not nearly as important.

2017-week5-tnf

The Cynthia Frelund Experience

Cynthia Frelund’s crowd (@cfrelund) was 2 for 3 tonight, getting the winner and the spread correct. Again, when the spread is less than 7, that’s pretty tough to do. But to take it a step further, the crowd predicted a spread of 4 when the actual was 5, and that’s pretty impressive. With respect to the over/under, the crowd predicted a total of 58. With a line of 56, Cynthia’s crowd was just barely on the wrong side. As we think about value of a line over time, we’ll try to find where the delta between the crowd’s prediction and the Vegas line indicates value and when it indicates staying away.

 

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2017 Week 4 CPR: Chicken Dinner!

If Week 3 was the Upside Down, Week 4 was clearly the Right Side Up. Week 3 began with the Rams and 49ers combining for 80 points and the 49ers backdoor-ing the 2.5-point spread with minutes to play. Week 4 ended with a most improbable, at least from a betting point of view, combination of events. Not only did the Chiefs score a defensive touchdown on the Washington Stanford-band play at the end of the game; they also chose to kneel for the two-point conversion. So the Chiefs both covered the spread while still hitting the under by a half-point, giving the crowd the trifecta for the game. As an added bonus, that bizarre sequence of events led to an On-the-Money prediction for the Cynthia Frelund experience (see below). Overall, the crowd performed extremely well this week, pretty much evening out the struggles from Week 3.

Have you ever had a bet come through in some crazy, last-second fashion? Let us know in the comments!

And speaking of On the Money, we had our first On the Money prediction of the year by one of our users! G.A. correctly predicted a 35-14 win for the Packers over the Bears, and lo, it came to pass. Congratulations G.A.!

A Word on Crazy Endings and the Crowd

I could easily argue that there is no way the crowd could have predicted the ending of the Chiefs game, and the crowd was certainly fortunate to have the ending meet all three of its prediction.

So now is a good time to reinforce the theory that the crowd isn’t predicting any specific event. The crowd wisdom is seen in the long game, and the crazy endings that prove the crowd correct are generally offset by the crazy endings that go against the crowd. So while the crowd was proven correct across the winner, spread, and total thanks to the crazy ending of the Monday Night Football game, they were also let down by the similarly crazy ending of the Week 3 Thursday Night game.

It might be an interesting experiment to poll the crowd when games are close in order to discover if they can predict a crazy ending over time. We’ll add it to the backlog!

cpr-2017-week4

CPR Week 4 Summary

  • Straight-up: 10-6
  • Against the Spread: 12-4
  • Over/Under: 10-6

CPR 2017 Overall

  • Straight-up: 38-25, 60% (same as Week 3)
  • Against the Spread: 28-35, 40% (+6% from Week 3)
  • Over/Under: 36-27, 57% (+1% from Week 3)

We had 8 predictors this week, including 3 new friends to the crowd. Welcome! Thank you to those who participated for the first time and to those who continue to help out.

The Cynthia Frelund Experience

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As we mentioned above, the Twitter followers for Cynthia Frelund (@cfrelund) this week provided their score predictions for the Monday Night Game and were right on the money. They predicted the final score exactly right. They have been close on a couple of occasions so far this season, so it’s great to see the crowd come through in such spectacular fashion so early in the season.

Crowd-wisest Prediction of the Week

The crowd was feeling it this week, and there were 6 trifecta games (up from the previous high of 4) this week.

Vikings-Lions and Eagles-Chargers were both interesting because the crowd picked the underdog to win outright, but probably the best prediction this week was 49ers-Cardinals because of how close the predicted spread and total were to the actual results.

PREDICTION CROWD ACTUAL
Winner Cardinals Cardinals
Spread Cardinals -3 (spread was -7.5) Cardinals -4
Over/Under 39 (under 43.5) 33

Crowd-foolishest Prediction of the Week

There were two 0-fer games in Week 4, and the bagel crown goes to the Bills-Falcons. The crowd predicted the Falcons to cover the 8-point spread, and the lost outright.

PREDICTION CROWD ACTUAL
Winner Falcons Bills
Spread Falcons -10 (spread was -8) Bills by 6
Over/Under 49 (over 48.5) 40

It seems that the crowd may not have fully bought into the Bills yet this season, as the crowd did not predict a Bills win either in Week 3 or Week 4, so it will be worth watching to see if the crowd corrects (or overcorrects) in Week 5.

Top Performers This Week

There were a lot of good performances this week, including E.A. who was second in the straight-up leaderboard and first against the spread!

Straight-up

  • C.A. (12)
  • B.C. (10)
  • P.C. (10)
  • E.A. (new participant) (10)

Against the Spread

  • E.A. (11)
  • B.C. (11)
  • G.A. (10)

Over/Under

  • G.A. (10)
  • M.R. (10)
  • C.A. (9)
  • G.A. (6)

Thanks for all the predictions! Keep up the good work!

-Chris

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2017 Week 4, Game 1 – Back to Normal?

If there is one thing that statistical analysis teaches us it is that one data point does not mean anything. However, the Thursday night game between the Bears and Packers went pretty much according to script, so it’ll be interesting to see how the rest of the weekend plays out.

The Game 1 CPR – 2 of 3

Correct: Straight Up, ATS; Incorrect: O/U

Across our 5 loyal predictors (thank you!), the crowd predicted an 11-point win for the Packers and a total of 41. The crowd was just one point off of the Bears’ actual total. Nice work!

Bad Beat: It’s hard to call the Bears touchdown in the fourth quarter a bad beat, but it is a little aggravating since our crowd predicted 41 points and would have been right on the money.

What is worth noting about that touchdown, though, is that it speaks to the concept of margin of safety. Our crowd predicted a total of 41 points and the Total was set at 45.5. The margin of safety there is just a field goal. We’re hoping that, over time, the crowd will be able to identify games in which the margin of safety is beyond the reach of a fluke score and track their performance over the course of the season.

For our curious readers, right now the crowd sees the biggest margin of safety for the Over/Under in:

  • 49ers-Cardinals: Under by 11 points
  • Washington-Chiefs: Under by 10 points
  • Panthers-Patriots: Over by 8 points
  • Bengals-Browns: Under by 7 points

Disagree with any of those? And leave a comment about why!

Also, please make sure to get your predictions in for Week 4!\

 

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The Cynthia Frelund Experience

Cynthia Frelund’s (@cfrelund) crowd on Thursday nailed the trifecta and was on the money with respect to the Over/Under. The aggregation of 50 predictions resulted in an expected 10-point win for the Packers, and their 49-point total prediction was one point away from the actual.

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2017 Week 3 CPR: The Upside Down

On Friday I joked about waking up Friday morning wearing a bucket and signing over my house. Little did I know what was in store…

I wake up on Sunday morning and groggily remember that Baltimore and Jacksonville are playing already. My hand fumbles for the phone as I wonder whether the Londoners have been “treated” to another snoozer after which they wonder when Jacksonville will get relegated. My eyes grow as wide as dinner plates (for you Calvin and Hobbes fans out there) to see the Jaguars up 37-0 before going on to beat the best defense in the league 44-7. And thus began the weekend of the Upside Down.

In the end, there were 7 games that finished with a total between 50 and 70, and 2(!) games with a total of 80. One of those 80-burgers featured the Rams and 49ers, the latter having scored 12 points in their first two games combined. The average total through Weeks 1 and 2 was around 40, and the average for Week 3 was 52.

On top of that, 3 6-plus-point underdogs won outright, and the 13-point underdog Houston Texans took the Patriots to the final seconds before surrendering the lead.

So, all in all, I think it’s safe to say that this is the week of the outlier. I saw a couple of posts on Reddit (“This ends the F*ck What You Know Week” was my favorite) expressing something similar. My sense is that there are two of these a season, but I reserve the right to say at some point that 2017 is the season of outliers.

Do any outlier weeks from past seasons stand out to you? Leave a comment!

results-through-week3

CPR Week 3 Summary

  • Straight-up: 7-9
  • Against the Spread: 6-10
  • Over/Under: 7-9

CPR 2017 Overall

  • Straight-up: 28-19, 60%
  • Against the Spread: 16-31, 34%
  • Over/Under: 26-21, 56%

We were up to 9 predictions this week, so thank you to those who participated for the first time and to those who continue to help out.

The Cynthia Frelund Experience

The Twitter followers for Cynthia Frelund this week provided their score predictions for the Monday Night Game and came through well. The predicted total was 46.5 and that actual total was 47. They predicted Dallas to beat the Cardinals by about 2 points and the spread was 3, so the crowd missed the ATS number. In the end, the crowd didn’t identify a lot of value in either line, but they still went 2 for 3.

Crowd-wisest Prediction of the Week

This week’s game in which the crowd went 3-for-3 and had the best prognostication was the Cowboys at Cardinals.

PREDICTION CROWD ACTUAL
Winner Cowboys Cowboys
Spread Cowboys by 7 (spread was 3) Cowboys by 11
Over/Under 37 (under 47) 45

The other 3-for-3 game this week was Falcons-Lions, but the delta between the crowd total and the over-under line was less than 1 point, so we can’t really say that the crowd saw a lot of opportunity in this game.

Crowd-foolishest Prediction of the Week

Of course, for every two wise predictions, we figure that there will be one foolish prediction.

There were 4 games to choose from this week. This week’s winner for the discrepancy between the prediction and the actual was Steelers-Bears.

PREDICTION CROWD ACTUAL
Winner Steelers Bears
Spread Steelers (-7) by 14 Bears by 6
Over/Under 46 (over 44) 4

I can only chalk up the big gap in the predicted win to the perception of the Bears quality versus the Steelers, though certainly, a second look would indicate that the Steelers have not exactly set the world on fire yet this season.The other

The other notable miss was Seahawks-Titans because the actual total was twice the predicted total. However, the game was predicted to be close, so again, it’s not as clear that the crowd saw a lot of value. Also, until our crowd grows a bit bigger, Seattle games are always going to be discounted since most of our participants are from the Pacific Northwest and a bit biased.

Top Performers This Week

We had a 4-way tie for straight up winners this week which has to mean something, but who knows exactly what.

Straight-up

  • G.A. (9)
  • P.C. (9)
  • M.R. (9)
  • D.C. (9)

Against the Spread

  • M.R. (7)
  • D.C. (6)
  • G.A. (6)

Over/Under

  • C.A. (10)
  • P.C. (9)
  • E.P. (6)
  • G.A. (6)

Thanks for all the predictions! Keep up the good work!

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2017 Week 3, Game 1 – The Bad Beat

God bless the internet. Today I get to paraphrase one of my favorite lines of all-time, courtesy of Brian Murphy (now of, as best as I can tell, KNBR). I give you an O/U of 79 points before the Rams-49ers kickoff Thursday night.

“You wake up [Friday] morning wearing a barrel, and signing over your mortgage to me, thank you very much.”

I’m sure I’m not the only person who wonders whether their actions did, in fact, affect something totally out of their control, especially when it comes to football. By posting to Twitter the Crowd prediction (Rams by 4, total of 34) ahead of time before the Rams-49ers game, I am nearly convinced that it turned what people expected to be a low- to medium-scoring affair into a barnburner.

Nevertheless, there are two quick takeaways:

  1. Crowdsourcing the scores is about the percentages rather than any individual game.
  2. Crowdsourcing is hard to do for outliers.

Percentages

The crowdsourcing scores concept is in line with any other gambling strategy. Blackjack and craps strategies are both about maximizing odds against the house over a number of rounds. If you follow the strategy, over time the percentages will normalize, but it doesn’t apply on any given hand. If you’ve ever read “Bringing Down the House”, you’ll be familiar with the story of one of the players losing over $100,000 on one hand even though he followed perfect strategy. Over time, the team came out well ahead, but on that one hand, luck worked against them.

For a game like Thursday in which the 49ers hit on a backdoor cover when the spread is only 2.5 by scoring 19 in the 4th quarter, it can be doubly frustrating because the win for the crowd seemed well in hand, and to have can feel like a win is being snatched from your fingers. All we can say is that we expect the crowd to be right more over time, so stick with us.

Outliers

It would definitely be an understatement to say that Thursday night’s game was unexpected. The average score for all games through Week 2 was in the mid-40s, and the 49ers had scored a total of 12 points. Thursday’s game nearly doubled the average score, and the 49ers tripled their season points total in a single game.

In Week 2, the crowd went 6 for 9 on the Over/Under when the delta between the O/U line and the crowd prediction was greater than 5. Thursday was the first of 8 games with that kind of delta, so we’re hopeful that we can expect 5 of the remaining 7 to come through.

In the meantime, does anyone have a barrel I can borrow?

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2017 Week 2 CPR: Finding the Sweet Spot

Overall, a decent performance from the crowd this week both straight up and against the total. The crowd is still behind in the spread portion, and we expect that as we get more users to contribute predictions, this number will improve.

CPR Week 2 Summary

  1. Straight-up: 12-4
  2. Against the Spread: 5-11
  3. Over/Under: 10-6

CPR 2017 Overall

  1. Straight-up: 20-11, 65%
  2. Against the Spread: 10-21, 32%
  3. Over/Under: 19-12, 61%

The main challenge is still the total number of predictions. We’re still hovering around 5 but are hopeful that success breeds success. Nevertheless, the over/under number is leaves room for optimism.

A One-off Crowdsourcing Exercise

Cynthia Frelund (@cfrelund), who is an expert in statistical analysis, posted a poll on Twitter and solicited scores for the Week 2 Monday Night Football game between the Lions and the Giants. I did a quick aggregation of 50 predictions and the result was Lions 23, Giants 19. The crowd went 3-for-3.

There were some extreme outliers, but even with predictions such as 13-10 or 16-10, the prediction coalesced after about 30 or so.

So crowd, we need to get to 30! Tell your friends! 🙂

Crowd-wisest Prediction of the Week

This is a new feature we’ll be running every week, highlighting the game(s) that the crowd was the most prescient in predicting. The primary qualification is that the crowd has to get the winner, the spread, and the total results correct. After that, it comes down to accuracy.

This week’s game was the Cardinals at Colts.

PREDICTION CROWD ACTUAL
Winner Cardinals Cardinals
Spread Cardinals by 2.25 (Cardinals favored by 7.5) Cardinals by 3
Over/Under 32 (under 44) 29

We don’t measure success specifically on this kind of accuracy, but it’s always interesting to note.

The larger takeaway is that the deltas between the lines, the predictions, and the results. The Cardinals were favored by 8.5 points, and the over/under line was 44. We believe that, over time, the crowd can identify the lines where the perception of the teams is significantly different from the actual quality, and this is a great example of that.

Crowd-foolishest Prediction of the Week

Of course, for every two wise predictions, we figure that there will be one foolish prediction.

There were two bagel games: Vikings at Pittsburgh and Washington at Rams. I’m discounting Vikings at Steelers because of the late-breaking news that Vikings QB Sam Bradford was not going to play.

PREDICTION CROWD ACTUAL
Winner Rams Washington
Spread Rams by 4.5 (favored by 2.5) Washington by 7
Over/Under 38.5 (under 46) 47

Clearly, the Rams’ big win over the Colts and Washington’s struggles against the Eagles gave people the impression of a bigger discrepancy in quality than there actually was. In the end, the game was quite close and was only decided in the last few minutes so it will be interesting to see if there is an indicator when the crowd believes a game will be close one way or the other.

Top Performers This Week

Big week by user B.C. who topped all three leaderboards!

Straight-up

  1. B.C. (13)
  2. C.A. (11)
  3. P.C. (10)

Against the Spread

  1. B.C. (10)
  2. P.C. (8)
  3. C.A. (7)

Over/Under

  1. B.C. (9)
  2. G.A. (8)
  3. P.C. (8)

Thanks for all the predictions! Keep up the good work!

-Chris

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2017 Week 1 CPR: When is a crowd a crowd?

I took a philosophy class (I think) during my freshman year of college, and I still remember a story from that class (for some reason). Socrates places a grain of sand on a table and asks his students whether it is a heap. He adds a second and asks again, then a third and fourth and so on. Ultimately, it is determined that there is no specific point at which a collection of grains of sand is a heap. (This is called the Sorites Paradox for those who are interested.)

I mention this because the crowd had a relatively average week this week:

  1. Straight-up: 8
  2. Against the spread: 5
  3. Over/Under: 9

So, the crowd is better than 50% with straight up picks and against the over/under but well under 50% against the spread.

What do we make of this?

Well, as I mentioned in an earlier post, the wisdom of the crowd is measured over time, so we’re not panicking yet. (As my favorite NFL writer Gregg Easterbrook says, there will be plenty of time for that later.)

But the broader idea that we want to develop is to determine when a crowd is a crowd. This week, we had five predictors. (Thank you to those who submitted predictions!) Is that enough to make a crowd?

For the crowd to have predictive skill, we believe that the highs and lows need to be normalized. This allows biases to be averaged out, and last minute predictions won’t have a strong effect in one direction the another. One game that I recall being affected last season was the Raiders-Chiefs Thursday night game. There were five total predictions, and two predictions came in pretty late that swung the crowd predictions from the Chiefs to the Raiders.

So overall, it would make sense that the prediction truly reflects the crowd when it shows a degree of stability. (I’ll do a more detailed assessment of how to address these statistics in a later post.) As you all continue to provide predictions, we’re excited to see, over the course of the season, when we’ll be able to identify the sweet spot when a critical mass of predictions has been submitted to give us a level of confidence in a given prediction.

Thanks for all your contributions so far. Keep up the good work!

-Chris