Deflate Gate Science Wiki

Introduction

The “Deflate Gate” (or Deflategate) scientific analysis was conducted to answer a simple question: Were the halftime measurements of the Patriot footballs below what is expected based on environmental factors? (In the NFL, each team prepares and uses its own set of balls used for offensive play, meaning the Colts and Patriots prepared and played with separate balls during the 2015 AFC Championship Game.) This page serves as a collection of those findings, with many thanks to the readers who contributed.

While the data was not collected in a controlled scientific experiment, there was enough data collected that we can arrive at one of three general conclusions:

  1. The Patriots were likely to have tampered with the footballs, beyond reasonable doubt (i.e. environmental factors cannot explain the measurements)
  2. It’s unclear whether there was or was not tampering
  3. The Patriots were unlikely to have tampered with the footballs, beyond reasonable doubt

The most likely conclusion, based on the available data, strongly points toward outcome No. 3, with the information available exonerating the Patriots. Unless otherwise stated, all investigatory information on this page was provided by the Wells Report.

Screen Shot 2015-05-16 at 4.38.08 PM

Raw data as captured at halftime of the 2015 AFC Championship game as presented in the Wells Report.

Table of Contents

1. Summary of analysis

Methods and Variables

2. What environmental factors will change the pressure (PSI) of a football?

3. What are all the variables involved in properly assessing whether the measurements are explained by environmental factors?

4. How can we analyze the data given all of the variables involved What methods can we use?

Results and data analysis

5. What are the Results? Are the Patriot ball measurements different in a”statistically significant” way from the Colts balls?

6. How do the Results change if adjustments are made to the 3rd Colt half-time measurement?

7. Why did Exponent conclude that the balls were “statistically significant” in the Wells Report?

8. Why do the Patriots halftime measurements have greater variability than the Colt balls?

9. Could tampering account for the variability seen in the Patriot halftime measurements?

Probability of key factors

10. Why does it not matter whether the Logo or Non-Logo Gauge was used in the pre-game?

11. Why is it more likely that the Logo Gauge was used in the pre-game?

12. Why is it more likely that the Patriot balls were inflated at halftime before four Colt balls were measured?

13. Why are the Patriot balls expected to be wetter than the Colt balls?

14. What happens if the temperature in the pre-game and during the first half are slightly different than those used in projections?

15. What are transient curves and how do they affect the assessment of whether the balls were tampered with?

16. What is a “Master” Gauge conversion?

Additional Considerations

17. What about the 12th Patriot ball, the one measured on the sideline in the first half?

18. What about the post-game measurements? What can we make of them?

19. Why are other analyses shown on this site slightly different numbers than what is presented here?

PSI and Fumbling Analysis

20. Is there an observable advantage to playing with deflated footballs?

21. What about the fumbling data? Does that suggest something strange?

Summary

Based on the available data — the estimations of the pre-game measurements, available environmental factors and halftime measurements — it is extremely unlikely that tampering occurred in the 2015 AFC Championship Game. In the most likely scenarios, the halftime measurements of the Patriot footballs are completely inline with what is predicted by physics; every likely scenario produces a difference of 0.1 to 0.4 PSI between the 11 Patriot balls and 4 Colt balls due to temperature changes alone, a difference predicted and explained by New England having slightly wetter footballs. None of the major plausible scenarios are different in a “statistically significant” manner, even before accounting for differences in wetness. Based on the available data, any alternative explanation of tampering must involve the Patriots releasing only a few tenths of PSI from only a few footballs.

Exponent, the scientific consultant used in the Wells Report, reached the wrong conclusion by performing faulty analysis of the available data and analyzing an erroneous graph. Exponent’s time-based simulations (on page 57-59 of their report) find a similar degree of difference as the findings presented here when comparing the Patriot and Colt balls based on temperature alone.

What environmental factors will change the pressure (PSI) of a football?

There are two primary factors to consider:

  1. Temperature
  2. Wetness

The Ideal Gas Law describes how pressure will increase as temperature increases. Similarly, water affects the volume of the football which will in turn affect the pressure. Lowering the temperature will cause a decrease in pressure, just as introducing water will cause pressure to decrease.

For these analyses, we can estimate temperature to within a few degrees based on game-day weather reports and the HVAC system used at Gillette Stadium. We know that the HVAC was set between 71-74 degrees in the pre-game in the room adjacent to where the balls were measured by referee Walt Anderson. We believe the outdoor temperature was somewhere between 47 and 50 degrees in the first half based on weather measurements taken near the site of the game.

However we cannot precisely know the degree to with which balls were wet due to the rain falling during the AFC Championship Game on January, 18. 2015. Exponent (in the Wells Report) tested wetness by spraying footballs and then immediately toweling them dry. This “misting,” or lesser wetness test produced a small decrease in pressure of roughly 0.1-0.3 PSI difference. Headsmart Labs, in Pittsburgh, rotated balls in a 50 degree bath of water and then smudged balls with a damp towel. These tests decreased pressure by roughly 0.6-0.9 PSI. As of now, these different experiments give us a range of wetness to expect based on the environmental conditions during the AFC Game.

Additionally, there are secondary factors that have not been adequately investigated by Exponent or anyone in the public domain: Wind and humidity changes. The combination of wind and and water would lead to a further decrease in temperature of the footballs due to Evaporative Cooling.

What are all the variables involved in properly assessing whether the measurements are explained by science?

In order to answer the question “were the footballs where they are expected to be based on environmental factors alone at the time they were measured” the following variables are relevant:

  • Gauge: Which gauge did Walt Anderson measure the balls with in the pre-game (“Logo” or “Non-Logo”)?
    • The Logo gauge reads about 0.3-0.45 PSI higher than the Non-Logo gauge. (Both gauges were used at halftime.)
  • Temperature: What was the precise temperature indoors where the balls were measured in the pre-game, and what was the precise temperature outdoors during the first half? Technically, the temperature of each football matters, something that could vary from football to football. All experiments by Exponent and here are done assuming all footballs have the same pre-game and outdoor temperature.
  • Measurement Order: There is enough ambiguity in the language in the Wells Report that it remains possible that the Patriot balls were actually inflated after the 4 Colt balls were gauged during halftime.  However, it is highly likely that the Patriot balls were inflated before the Colt balls measured. Thus, only those scenarios are considered.
  • Transient Curves: During simulations, there are different observed values for how quickly a football’s pressure recalibrates to a new environment. We will use a “fast” projection, in which the PSI of the football rises more rapidly once it is brought into an indoor environment, and a “slow” projection, in which the PSI rises less rapidly once a football is brought indoors.
  • Time of Halftime Measurements: There are a number of factors that determine at exactly what time each ball was measured during the halftime period. We know the officials were in the locker room for 13.5 minutes, where they provided the following estimations for their procedures:
    • 11 Patriot balls were measured starting at 2 to 4 minutes into the period
    • Balls were measured approximately every 22 to 27 seconds
    • It took anywhere from 2 to 5 minutes to inflate the Patriot balls
    • 4 Colt balls were measured
  • Wetness: As discussed above, wetness cannot be precisely known for each ball. However, it did rain during the AFC Championship Game, a number of footballs were exposed to the rain, and it is apparent precipitation will cause a decrease in PSI.
  • Pre-Game Measurements: It is presumed that the Patriot footballs were mostly 12.5 PSI and the Colt footballs mostly 13.0 PSI as measured in the pre-game. However, these measurements weren’t written down, and referee Walt Anderson remembers two Patriot footballs being under regulations and needing to be refilled. Additionally, some Colt footballs may have measured at 13.1 PSI.

How can we analyze the data given all of the variables involved? What methods can we use?

We can analyze data based on all of the permutations that the aforementioned factors create. We will examine 2 gauge scenarios (if Anderson used the Logo or Non-Logo in the pre-game), 3 temperature scenarios (whether it was 70, 71 or 72 degrees at time of measurement), 2 transient curves (one used in Fig. 22 of Exponent’s report that represents a faster expected rate of recalibration, the other used in Fig. 24 of Exponent’s report that represents a slower expected rate of recalibration). The outdoor temperature is held constant across simulations at 48 degrees, although varying that would have a similar effect of varying the indoor temperature, an effect that is shown to have a negligible difference in results.

Finally, every scenario will include 8 different possible times in which halftime measurements were taken; all of these timing scenarios fall within the estimations provided by the Wells Report, and leave anywhere from 30-75 seconds for the officials to pack up and leave the locker room.

In each scenario, we calculate the difference between the actual measurement of a football and where we project the ball to be based on environmental factors (indoor PSI at a given temperature, outdoor temperature, rate of recalibration to the indoor temperature). This is a simple idea: if the balls never changed environment, we could simply measure the footballs at halftime and calculate the difference from expected (where they were in the pre-game). However, because they changed environment, and then were measured while recalibrating back into an indoor environment, time of measurement becomes critical to determine the expected PSI of a football. A detailed description is provided here. Each transient curve (rate of projection) was modeled off of Exponent’s experiments presented in either Figure 22 or Figure 24 of the Wells Report.

In total, 84 scenarios are examined and presented here, including the polynomial function for each transient curve, depending upon the scenario. Note: these results make no attempt to account for wetness. Results that attempt to pre-bake a wetness factor into the transient curves can be seen here, explained here on video.

Are the Patriot ball measurements different in a “statistically significant” way from the Colts balls?

Not in any of the likely scenarios.

Of the 12 major scenarios examined (based on 2 gauges, 2 recalibration curves and 3 pre-game temperatures) without accounting for wetness or the anomalous Colt 3rd ball, every average scenario is not statistically significant. (Just as none are significant when accounting for wetter Patriot footballs.) Below is a summary of the findings, with the values of each row representing the averages of the eight time-based permutations of the halftime measurements, with average p-value included. (All 84 simulation results and recalibration curves can be seen here):

Deflate Gate Master Gauge Results

These results are inline with what is expected; based on physics, we’d expect the Patriot balls to be slightly lower, on average, than the Colt balls because the Patriot balls were wetter. In the different permutations, the low and high extremes are +/- 0.09 PSI from the average differences shown above. The above table also make no attempt to account for the anomalous reading produced by Colt measurement No. 3, in which the Non-Logo gauge read 0.45 PSI higher than the Logo gauge.

The most likely scenario, based on the result of the “control” group (the Colt balls) is that the balls recalibrate as projected by the “Slow” recalibration curve and were measured by the Logo gauge at approximately 70-71 degrees in the pre-game. This produces results that are not statistically significant, and inline with what is expected based on variance and environmental factors.

Based on the above, the one plausible scenario that yields a near-significant result between the 11 Patriot balls and 4 Colt balls is the combination of a slow recalibration curve and Non-Logo gauge. However, that does not take into account wetness of the Patriot footballs. Even a small adjustment for wetness — say, a few tenths of a PSI for a handful of balls — renders the result far from statistically significant. It is also less than likely that the Non-Logo gauge was used by Walt Anderson in the pre-game. Most importantly, it is nearly an impossible result given the inexplicable 3rd Colt measurement; adjusting for the anomalous 3rd reading from the Colt group makes all Non-Logo differences nearly identical to the Logo differences presented above.

Note: the Master conversion used was based on Exponent’s Fig. 12, regressing a-axis values between 10 and 14 PSI to produce the following two lines:

Logo Master-Adjusted: (x + 0.2633) / 1.0625

Non-Logo Master-Adjusted: (x + 0.1333) / 1.0125

How do the Results change if adjustments are made to the 3rd Colt half-time measurement?

The third Colt measurement at half-time is an anomaly. Every other measurement, both at halftime of the AFC Championship game and during Exponent’s testing, found that balls measured with the Logo gauge read a few tenths of a PSI higher than the Non-Logo gauge. However, the Colt third measurement at halftime produced a result in which the official presumed to be using the Logo gauge measured 0.45 PSI lower than the official using the  Non-Logo gauge.

Based on likely explanations for what happened, three different adjustments can be made to the 3rd Colt measurement and applied to the larger statistical analysis:

  1. Misheard. (Non-Logo reading actually 12.15 PSI) The individual writing down the measurements misheard the number — a common phonetic error would be hearing “12-point-one-five” instead of “12-point-nine-five.” (12.55 is the other plausible phonetic occurrence, however this also breaks the trend of the Logo gauge reading higher than the Non-Logo gauge.)
  2. Switched. (Logo reading = 12.95 PSI, Non-Logo reading = 12.50 PSI) The individual writing down the measurements wrote official Blakeman’s callout in official Prioleau’s column and vice versa, either due to hearing one and thinking the other said it, or in transcribing he simply wrote in the wrong column without realizing it.
  3. Excluded. (Remove Non-Logo reading entirely.) It’s prudent to examine the results if we completely throw out the measurement due to error, without swapping in a likely adjustment explained in points No. 1 and No. 2.

Adjusting 3rd Colt Ball Deflate Gate

When applying any of these three adjustments to the 84 analyzed scenarios in the results section, all Non-Logo readings become nearly identical to Logo readings in terms of difference between team measurements. In all three cases, the difference between the Non-Logo gauge and Logo gauge scenarios is simply that Non-Logo gauge readings are an addition 0.35-0.40 PSI below expected relative to the Logo Gauge.

Why did Exponent conclude that the balls were “statistically significant” in the Wells Report?

Exponent failed to control for a major variable: the time when each ball was measured.

Instead, Exponent analyzed the balls at halftime as if they were a single point in time. Exponent also calculated the drop from pre-game measurements — independent of physics — instead of calculating the difference from the expected PSI at halftime based on physics. A further examination of their methods reveals that this approach can actually identify the wrong set of tampered balls. In short, Exponent’s method is unfavorable to any team measured early in the locker-room period, when balls were still closer to outdoor PSI levels.

Exponent Method Infographic

Why do the Patriots balls have greater variability than the Colt balls?

There are a few sources of variance to consider:

  1. The within-gauge variability
    • Exponent tested 50 gauges (Model CJ-01) and found a standard deviation of roughly 0.1 PSI, meaning 95% of measurements will be within plus-or-minus 0.2 PSI. This is consistent with what is observed in the halftime measurements, as Non-Logo and Logo gauges are not consistent in how much they differ in measurements.
  2. The temperature of all the balls will not be exactly the same. This is small, but balls kept in a bag might stay warmer when taken outside. Conversely, cold, wet footballs will recalibrate more slowly indoors if they are insulated in a bag. A 1 degree difference is approximately another 0.05 PSI of variability.
  3. As explained above, a reasonable degree of wetness based on the AFC Championship game conditions can account for nearly an additional 1.0 PSI of variability.

In sum, a wet ball could be over 1.0 PSI below where we’d expect it based on just temperature change. Note, that this is not a “water-logged” ball — none were reported to be water-logged and Headsmart did not water-log any balls. Before we analyze each data point, we’d expect to see the following based on the difference in time of possession and the final drive of the first half:

  • Colt balls were covered and not on the field at the end of the half. Thus, the Colt balls would be less wet relative to the Patriot balls.
  • A few Patriot balls that were involved in play on the final lengthy drive of the first half could be upwards to 1.0 PSI below what is expected.
  • With that said, it’s important to note that a few Patriot balls were reported to have never been taken out of the bag, so we should see a few balls that are around what we expect a dry ball to be (closer to many Colt balls).
  • The remaining Patriot balls should be somewhere in between, depending on their exposure to the elements.

Below is the average ball reading from the scenario that produces the results closest-to-expected for the 4 Colt balls (Slow Recalibration + 71 Degrees + Logo gauge):

Master Averages 71 and 48 Slow

Balls can be stratified into four groups (color-coded above). Without accounting for water:

  • The blue group is within 0.15 PSI of what is expected or higher
  • The yellow group is 0.2-0.4 PSI below expected
  • The orange group is 0.4-0.7 PSI below expected
  • The red ball is 1.0 PSI below expected

These are inline with what is expected based on environmental factors. Namely, that the blue group was likely well protected from the elements. Patriot Ball #7 can be explained by a combination of gauge variability and the possibility that it was slightly warmer than other balls. (Similarly, it is also possible it actually measured 12.6 PSI in the pre-game.) The orange group likely saw the field in the first half, and ball #10 was likely the most wet, perhaps even being the ball used on the final lengthy drive of the half.

Could Tampering account for the variability seen in the Patriot measurements?

Possibly, but it is highly unlikely.

We know that water must play a role in lowering the expected PSI readings based on temperature alone. Thus, the only plausible remaining explanation is that Jim McNally (alleged of deflating balls in the bathroom while transporting them from the official locker room to the field) deflated only a few balls, and likely by an amount that is lower than observed in the orange and red groups above. In other words, the tampering scheme would have involved deflating only a handful footballs by amounts smaller than the approximate 0.75 PSI drop Exponent simulated on page 241 of the Wells Report. This would have had to happen despite no former football players in TV interviews being aware that they have played with footballs varying by at least 2.0 PSI throughout their career.

Why does it not matter whether the Logo or Non-Logo Gauge was used in the pre-game?

Once the 3rd Colt ball is adjusted for, the difference between the Logo and Non-Logo readings becomes negligible. In other words, If the Colt balls are indeed assumed to be a control group, the Patriot balls measure the same degree below the Colt balls regardless of which gauge is used. Projections based on the Non-Logo gauge are simply lower than expected by equal degrees for both the Patriot and Colt balls.

Adjusting 3rd Colt Ball Deflate Gate

Why is it more likely that the Logo gauge was used in the pre-game?

There are four pieces of evidence that the Logo gauge was used in the pre-game:

  1. Referee Walt Anderson remembers using the Logo gauge.
  2. Non-Logo gauge projections do not align with what is expected for the control group, the Colt balls.
  3. The Colt’s post-game measurements
    • We currently don’t know when the 4 post-game measurements were taken because this information has not been publicized. However, unless the Colt balls were measured in the first 4-6 minutes after returning indoors, it becomes more likely that the Logo Gauge was used in the pre-game (to more closely match the observed Logo gauge average of 12.7 PSI taken in the post-game. The same post-game reading on the Non-Logo gauge averaged 12.35 PSI)
  4. The Patriots gloving routine.

With regards to No. 4, Fig. 16 on page 194 of the Wells Report demonstrates that the Patriot ball preparation briefly raises the pressure of the ball. When the rubbing stops, the ball cools down and returns to its previous pressure.

Deflate Gate Patriot Rubbing EffectAccording to page 50 of the Wells Report, the Patriots set the pressure “immediately after gloving the footballs.” Thus, as seen above, if the pressure was set a few minutes after rubbing completed (as reported), then the balls would continue to lose another few tenths of a PSI as they cooled down from the rubbing. In other words, due to rubbing in the pre-game, we know that the Patriot balls will read below 12.5, perhaps (on order of 12.1 to 12.3 PSI) on the Patriot gauge. This helps to explain why two of the Patriot balls were measured below 12.5 PSI by Anderson in the pre-game. For the Non-Logo gauge to have been used in the pre-game, the Patriot gauge  would have to be 0.6-0.8 PSI below the Logo Gauge, an unlikely occurrence given that no one has demonstrated a common between-gauge variance of this magnitude.

With regards to No. 2, since the Colts are a “control” group, their results should be as close to what is predicted by physics as possible. Yet, the Colt readings in all Non-Logo scenarios are farther from expected when compared to the Logo readings, often by a substantial margin. While it’s possible measurement variance (and some wetness) could create these results, it is less likely given that three measurements push the outer bound of what we’d expect based on dryer footballs. Adjustments for the anomalous 3rd Colt football make Non-Logo gauge scenarios even less likely.

To illustrate this, examine the Non-Logo gauge readings from the Slow Curve at 72 degrees. Note that the 3rd Colt football is unadjusted in the table below:

Master Average 72 Slow Non Logo

Average PSI levels from expected based on the Ideal Gas Law, if pre-game measurements were taken with the Non-Logo Gauge at a temperature of 72 degrees, using a “Slow” recalibration curve.

Without adjusting the for the 3rd Colt football, three of the four Colt balls are between 0.2 and 0.5 PSI below expected based on just wetness/variance alone, and those balls were definitively dryer than the Patriot balls used during their final drive of the half. Such readings are less likely than expected, unless water plays a significantly larger role than expected. In that case, the Patriot measurements would be would be inline with what physics predicts, making it more likely that the additional 0.67 PSI drop from expected came from wetness or normal gauge variability. Any tampering explanation for such results would again involve a scenario in which the Patriots deflated only a few balls and only by a few tenths of a PSI.

Why is it more likely that the Patriot balls were inflated at halftime before four Colt balls were measured?

The order of operations at halftime when each team’s footballs were measured is described as follows:

  • Set Up procedure, then
  • Measure 11 Patriot balls, then
  • Either re-inflate Patriot balls or measure 4 Colt balls, then
  • Pack up and leave

There is enough ambiguity in the language in the Wells Report that it remains possible that the Patriot balls were actually inflated after the Colt balls were measured during halftime.  This would mean the order of events at halftime was: [Set Up Testing] –> [Measure 11 Patriot balls] –> [Measure 4 Colt balls] –> [Inflate 11 Patriot balls].

This seems highly improbable given that witnesses in the Wells Report claim only 4 Colt balls were measured because they ran out of time. Additionally, it appears that gauges were switched by the two officials measuring balls, unbeknownst to anyone in the room, suggesting that after the first measurement period, the gauges were put down so the Patriot balls could be inflated

Why are the Patriot balls expected to be wetter than the Colt balls?

According to the website wellsreportcontext.com, the Patriot ball boys did not use trash bags to protect the balls during the first half from rain, but the Colts did. The Patriots also possessed the ball for 17.5 of the 30 first-half minutes. Additionally, the Patriots possessed the ball for the last 4:54 of the half (save for a quick Andrew Luck knee), a period that spanned approximately 17 minutes in realtime, with approximately 11 consecutive minutes of exposure after the 2-minute warning.

Thus, all evidence strongly points towards the Patriot footballs being more wet, on average, than the Colts footballs, with at least one or two balls being more recently “wet” (and used) at the end of the first half.

What happens if the temperature in the pre-game and during the first half are slightly different than those used in projections?

Assuming all footballs were subject to the same indoor and outdoor temperature, small changes in said temperatures will affect both groups of balls similarly. These effects can be observed in the results section — noting the difference between 71 and 72 degrees (or 71 and 70 degrees). A similar one or two degree shift can be projected if either the indoor temperature or outdoor temperature were off by a small amount.

What are transient curves and how do they affect the assessment of whether the balls were tampered with?

The transient curve, or the rate of expected recalibration, models what speed we would expect a ball to recalibrate to a different environment when brought from one temperature area to another. There are two such curves presented in the Wells Report, one that models a faster recalibration (“fast”), meaning that the balls will return to their indoor PSI more quickly, and a slower one (“slow”). These are presented in Figures 22 and 24, respectively, of Exponent’s analysis in the Wells Report.

 

 

The difference between the transient curves, or projects rate of recalibration, in Fig. 22 ("fast") and Fig. 24 ("slow") of the Wells Report.

The difference between the transient curves, or projects rate of recalibration, in Fig. 22 (“fast”) and Fig. 24 (“slow”) of the Wells Report.

What is a Master gauge conversion?

Neither the Logo gauge nor Non-Logo gauge are perfectly valid, meaning they do not measure the exact pressure of the football. As a result, the “Master” gauge conversions were used by Exponent to determine what the Ideal Gas Law predicted for the actual football pressure at a given time. Furthermore, the degree to which each gauge is “off” from the actual pressure depends on what the actual pressure is; Exponent discovered that as the pressure increased, the Logo gauge produced a larger error. Specifically, regressing the readings of Fig. 12 from 10-14 PSI produces the following lines:

Logo Master-Adjusted: (x + 0.2633) / 1.0625

Non-Logo Master-Adjusted: (x + 0.1333) / 1.0125

This means that when the actual football pressure is about 12 PSI (12.01 PSI using the above regression), the Logo gauge will read 12.5 PSI. If referee Walt Anderson used the Logo gauge in the pre-game, the footballs would have actually been closer to 12 than 12.5 PSI. But the Non-Logo gauge reflect the actual pressure more closely, meaning a 12.5 PSI reading before the game on the Non-Logo would reflect an actual 12.48 PSI pressure using the above regression.

What about the 12th Patriot ball, the one measured on the sideline in the first half?

In the second quarter of the game, a Tom Brady pass was intercepted by the Colts. Using a pre-game temperature of 71 degrees, an outdoor temperature of 48 degrees and assuming a pre-game PSI level of 12.5 PSI, such a ball would be expected to register at 11.32 PSI before recalibrating to an indoor environment.

This ball was measured by a Colt gauge on the sideline and registered at “approximately 11 PSI,” roughly 0.3 PSI below expectation based on the temperature alone (if the sideline gauge was similarly calibrated to the pre-game gauge.). This measurement ignores wetness, which would have been a factor given that the ball was involved in a drive before being intercepted. The ball was then measured three times, indoors, by the Patriot gauge. It registered 11.35, 11.45 and 11.75 PSI on those three readings (average of 11.52 PSI).

However, the ball was excluded from Exponent’s analysis due to the unknown relationship between the sideline measurement gauge and the other gauges on record. It is unknown how long the balls were in the locker room before being measured, but the Wells Report claims that it had to be “a few minutes,” as Alberto waited for James Daniel to arrive before they gauged the football. If the sideline gauge and the Patriot gauge are similar in calibration, a slower transient curve predicts that Daniel would have had the ball in the locker room for approximately 3-4 minutes before taking his first measurement. His final measurement could have been approximately 5 minutes later.

What about the post-game measurements? What can we make of them?

It is not possible to properly analyze the post-game measurements in the same manner as the halftime measurements for two reasons. First, the Patriot balls were adjusted at halftime by the officials and inflated to an unspecified degree. The Patriot post-game measurements (Logo: 13.5, 13.35, 13.35, 13.65; Non-Logo: 13.15, 12.95, 12.95, 13.25) averaged 13.5 PSI on the Logo gauge 13.1 PSI on the Non-Logo gauge.

The Colt balls were not tampered with, however we have no idea how long they were indoors before being measured. (Logo: 12.9, 12.45, 12.8, 12.7; Non-Logo: 12.5, 12.1, 12.45, 12.35) The measurements averaged 12.7 PSI on the Logo gauge and 12.4 PSI on the Non-Logo gauge. Given the environmental conditions, a dry ball, inflated to 13.0 PSI in the pre-game would recalibrate to 12.4 PSI in an indoor environment in approximately 4 minutes using a fast recalibration curve and approximately 6 minutes using a slow recalibration curve.

Why are other analyses shown on this site slightly different than what is presented here?

Previous analyses explaining and Debunking Exponent’s methodologies, and introducing time-based measurements based on permutations of scenarios, all used a “wet” projection recalibration curve for the Patriot balls. This was largely anchored to Exponent’s methodology of using a dry and wet curve (without adjusting for time) as an attempt to demonstrate the kind of results Exponent should have produced if they properly accounted for time. Additionally, they demonstrate that wet footballs recalibrate more slowly than dry footballs, which is helpful when mentally curving the temperature-based results.

The analysis here on this page is more detailed and refined in that it compares the groups without any wetness adjustment, allowing for a raw comparison of whether the balls behave as predicted before the inclusion of wetness as an explanatory factor.

Is there an observable advantage to playing with deflated footballs?

ESPN’s “Sports Science” analyzed the effect of playing with “deflated” footballs. They found that deflating a ball from 12.5 PSI to `10.5 PSI provides an NFL player with an extra 1.5% grip force, reduces the balls mass (weight) by 1.5 grams (equivalent to a dollar bill) and reduces velocity by a microscopic amount. (A 50 MPH pass of 20 yards would arrive 0.003 seconds slower.) Popular Science ran computer simulations and found nearly identical results.

Brian Burke also conducted a study on fumble rate based on outdoor temperature. Since temperature will influence the PSI of a ball, in effect, Burke analyzed 13 years (2000-2012) of PSI (and temperature) data with regards to fumbling. The results reveal an increase in fumbling in games over 80 degrees, and a sharp increase in very cold games (below 12 degrees). There are small changes between 42-51 degrees (approximately 1.9% fumble rate) and 52-61 degrees (approximately 1.75% fumble rate).

Fumble Rate by PSI Change

Per Brian Burke’s 2000-2012 study on fumble rate by temperature. Average PSI change based on predicted difference between a 12.5-13.5 PSI ball at 70 degrees.

As predicted by “Sports Science,” the difference between 40 degree and 80 degree games — a change of approximately 2.0 PSI in football pressure from 40 to 80 degrees — appears to have no impact on fumbling rates.

What about the fumbling data? Does that suggest something strange?

There is nothing in the fumbling data that suggests New England has either been a major outlier or had radically unique shifts in performance starting in 2007. Furthermore, the Patriots actually fumble more at home (where tampering was been alleged to take place). Additionally, Tom Brady has better statistics on the road.

45 thoughts on “Deflate Gate Science Wiki

  1. More exceptional work, extremely clear and well written.

    But one point to revise: the intercepted ball was measured indoors according to the Wells report, and perhaps had a long amount of time to re-equilibriate.
    p 64-65 “At approximately 8:00 pm … Daniel walked the intercepted ball inside the stadium and toward the officials’ locker room. Alberto Riveron … went to the Officials Locker Room, arriving a few minutes after Daniel…At Riveron’s request, Daniel retrieved a gauge that was near the air pump in the dressing area of the Locker Room, and they tested the intercepted balls three times before the balance of the game balls were brought back to the Officials’ Locker Room. A few minutes later, the game officials … started arriving in the officials locker room for halftime. While Daniel and Riveron were testing the intercepted ball, the first half was coming to an end.”

    As you noted, a footnote claims this was actually Jastremski’s gauge. (If so, McNally must have brought it before the game).

    Since halftime started at close to 8:28, Wells’ account is suggesting that Riveron might have waited 20 minutes or more to measure the balls. The spread in measurements may show measurement error, or it may show warming between iterations of the test, but the measurements can’t show 20 minutes of warming inside on a ball that really was going to return to about 12.5 psi.

    The Wells account also suggests that Riveron’s decision to test all the balls at halftime was made near 8:00, before he independently confirmed Indianapolis’ claim that the ball was below the pre-game range. I think it would be natural for Riveron to gauge the ball “immediately”, if he felt he had the authority to do so. If he initially felt he was merely impounding the ball (e.g. waiting for the game referee to gauge it), it’s odd that he changed his mind and gauged it after a long delay.

    Footnote 35 in the Wells report suggests discarded evidence for a “sting” scenario [“Our best understanding … is that … personnel from both the Officiating and Game Operations Departments independently made parallel decisions to test all of the game balls at halftime.”] Daniel is Game Operations and Riveron is Officiating. Kensil and Vincent are in Football Operations. I doubt the independence of such similar decisions, for a process never executed before in the history of the NFL. Inclusion of the Colts’ balls in the testing is not such an obvious choice (and in reality they were barely included).

    I think there is much more to the story of events between 8 and 8:30 which Wells left out. I imagine Riveron worked out the testing process ahead of time; with witnesses, independent testers, use of the referee’s two gauges, there was an attempt to generate evidence which would “stand up.” This “rigor” seems odd in conjunction with the supposed inattention to Grigson’s original email which suggested such testing, especially if “confirmation” of the Colts’ claim was not performed soon after the ball was brought inside at 8:00. It just may be a sloppy timeline from Wells, but I would like to know more about what Riveron was actually doing, and who he was talking to, during this time…

  2. I’ve made an update to reflect the “Master Gauge” adjustment, which change the results by a few hundredths of a PSI.

  3. ElGee —
    I’m focused on the proper burden of persuasion on the league before it finds cheating — assuming we can distinguish cheating from gamesmanship.

    In the spirit of clarifying your excellent work to date: You seemingly (at least to this criminal law professor who heavily emphasizes burdens of persuasion) conflate levels of certainty when you up front raise 3 options —

    1. “The Patriots were likely to have tampered with the footballs, beyond reasonable doubt (i.e. environmental factors cannot explain the measurements)

    2. “It’s unclear whether there was or was not tampering”

    3. “The Patriots were unlikely to have tampered with the footballs, beyond reasonable doubt”

    All three options, read literally leave it unclear. Assume proof beyond a reasonable doubt = 99% certain. Assume “likely” = more likely than not, or preponderantly probable (greater than 50%). Then (1) likely to have tampered, beyond reasonable doubt while apparently meaning .99, really means .99x.50+ which means equal to or greater than .50. “Unlikely to have tampered beyond a reasonable doubt” essentially means less likely than not. Both of these leave it “unclear whether there was tampering.”

    I assume you mean to present three options: About as likely as not — unclear — somewhere between 40% and 60%; tampered beyond reasonable doubt, i.e. 99% likely; or not tampered beyond reasonable doubt 1% or less — tampered. And what of the intermediate possibilities — suppose it’s 70%, or 80% likely not tampered. The law calls it clear and convincing — midway between preponderantly probable and true beyond a reasonable doubt.

    Provisionally, this clear and convincing standard, I think should have been employed here. I’d like to see the NFL change the rule, once it’s widely perceived they acted unfairly to the Patriots, especially Brady.

    • Hi Robert — I understand that the legal system does not have that same burden of proof as science. I’m using a bit of science-speak with these 3 options — when we throw words like “prove” around, we want to be very clear and precise with what we are claiming.

      To clarify what I’ve presented here, the degree of certainty based on the measurements depends on what is being alleged. We CAN “prove” (> 99%) that Jim McNally didn’t take 5 PSI of air out of any football in that bathroom. We can prove he didn’t take 2 PSI of air out of any football.

      We can also say the 99% “proof” applies to him taking 0.5-0.75 PSI out of EVERY football — the measurements say that’s basically impossible. What’s left as “possible” is that McNally either removed something on order of 0.3-0.5 from a handful of footballs, or perhaps removed something like 0.75 PSI from one footballs. Those are also unlikely given how well the measurements match up with physics-based predictions. Is that 99% unlikely? That’s hard to say. It’s unlikely, but I’m not sure we can be as confident as we can be in our clear-cut >99% scenarios.

      Perhaps the best analogy to illustrate would be a testosterone test for a PEDs. Pretend we locked Brady in a Big Brother House and had cameras on him for a week, except when he went into the bathroom. In week 1 his test levels are 600 and in week 2 625. It’s still possible that he used a low-dose test-booster — we couldn’t “prove” he didn’t — it’s just incredibly unlikely that he went into the bathroom and administered a super-low dose of test, especially when his results are completely inline with what is expected based on natural behavior (there’s some constant variability in test levels).

      The only reason I’m not more dogmatic with those three options is that no single clear allegation has been made, and the Wells Report was VERY careful not to make a single clear allegation.

      • I’ll add — and would be interested based on your expertise — that I find the burden of proof here literally insane. The NFL has not made a specific allegation. From Vincent’s letter: “The Commissioner has authorized me to inform you of the discipline that, pursuant to his authority under Article 46 of the CBA, has been imposed on you for your role in the use of under-inflated footballs by the Patriots in this year’s AFC Championship Game”

        So the process here is “we fine you in violation of a vague thing, now it’s up to you to disprove that thing when we haven’t even proved or established a thing in the first place.”

        • One more thing about the burden of persuasion — I noticed only today on rereading Wells that while he emphasizes a preponderance as the mandated standard — in a footnote he uses McNally and Jastremski’s statements about Brady to establish to his satisfaction (but not ours) that Brady knew — by invoking the Federal Rules of Evidence standards on allowing “co-conspirators” satements — invoking and importing a criminal context which requires proof beyond a reasonable doubt — into what is essentially a civil burden of persuasion.

    • ElGee —
      I’m gathering my thoughts in preparation for an essay I’m writing and talk I’ll be delivering at the International Association of the Philosophy of Sport (IAPS) early in September, titled “Deflategate — Cheating: Playing with the Rules. ” It relates this controversy to deeper themes such as cheating, gamesmanship and sportsmanship, etc.
      I want to properly credit your work but only know you as ElGee and your blog as Backpicks. Please e-mail me and tell me how you would like to be credited.
      robert

  4. Law has focused an awful lot on the burden of proof — really the burden of persuasion, as “burden of proof” also includes burden of production — burden to introduce evidence initially (also called the burden to go forward). The League has both the production burden — which it appeared to meet by the underinflated intercepted pass — and the persuasion burden by a preponderance, which you and others convinced me it did not meet.

    My point in my earlier e-mail was that you imprecisely separated various levels of certainty. I believe that before we label a team or quarterback a cheat based entirely on circumstantial (or for that matter direct) evidence — we should be “clearly and convincingly” persuaded as to guilt — not met here, or even arguably convinced beyond a reasonable doubt (the criminal law standard) — certainly not met here.

    But in working my way through this, I’m struck by one apparently damning e-mail reference that the Wells report cited but didn’t emphasize, and the Pats reply repeated but didn’t rebut, nor did you mention, I believe.

    I’m searching for an innocent explanation to McNally text October 23,2014 right after the Jets debacle:

    McNally: The only thing deflating sun . . is his passing rating.

    Here apparently and unambiguously this links deflate to Brady’s ability to pass a football.

    Could you please suggest another interpretation, or an innocent one that naturally flows?

    — robert

    • Joe responded to this pretty thoroughly, but Ill add 2 things:

      1) It simply could be a joke (from a joker). It’s not necessarily saying “I deflate footballs Sunday, but won’t this Sunday.” Instead, it’s plausible (likely?) he’s making an anti-Brady pun by saying, “John, it’s not that the balls are going to be deflated to proper levels this week by the officials, it’s that Tom is washed up and his passer rating is going to continue to go down (or “deflate,” get my pun?).”

      2) To me, the compelling evidence in that exchange is that Jastremski is claiming the balls were 16 PSI after the Jets game…but no one seems to question how “the deflator” let them be 16 PSI. Can you imaging or suggest a explanation in which McNally deflated balls in the bathroom and yet this was the conversation after the Jet game? It makes no sense to me. We’d expect to see something like the following:

      JJ: Tom is pissed at you — he thinks you forgot to deflate some balls.

      or

      JJ: Tom thinks we should start deflating every ball, because some felt like watermelons.

      or

      JJ: Checked the balls. They were 16 PSI. Why didn’t you deflate them all?? Tom is having a cow.

      Why would Jastremski say “the REFS fucked us,” in a private conversation he believed no one would ever read, as if the Patriots were at the whims of the league standard protocol?? If McNally were indeed “the deflator,” he would have said “Jim, YOU fucked us,” or made some other comment along the lines of McNally “letting” balls get through at 16 PSI when he’s supposed to be the deflator. Do you see the issue here?

      I’m open to any explanation you (or anyone) has that can resolve this.

      • To be fair, we clearly lack full context around the Jets’ game texts, and it seems clear we do not have the complete conversational context between JJ and JM. Wells tries to find the conversational element you are looking for in the “he … said you must have a lot of stress trying to get them done” text message.

        As background, my understanding of all the texting evidence is this
        1) JJ’s phone was imaged.
        2) There were deleted messages on that phone, at least some deleted messages of relevance on Oct 16th, according to Wells’ forensic specialist Renaissance Associates. Some were wholly recovered and some were partially recovered; according to Renaissance it was unknown if there were other completely unrecoverable messages.
        3) Patriots provided a log of relevant content from JM’s phone. Presumably this was based on the surviving visible text and phone logs, and there was no attempt to image it and recover deleted messages.
        4) No information was made available from Brady’s phone.

        Now I know nothing about Renaissance Associates or reliability of the recovery process. How likely is it that there are gaps in the recovered record, and how big could they be, and how likely there are to be errors? (Even if the electronic recovery process is 100% error free, the results must have gotten transcribed by Renaissance, and then re-transcribed by Wells et al. I wondered about things such as any reversed attribution of sender/receiver, which would change interpretations. I think people have tended to downplay the value of Brady providing his phone. Since an unbiased investigator couldn’t be sure that he had a full record from JJ’s phone or JM’s phone, it would have been helpful to have confirmation or contradiction from Brady’s phone. Granted I do share the view that Wells was biased and would have cherry-picked from whatever Brady gave him in order to strengthen his case.

        Back to that conversation between JJ and JM after the Jets’ game…

        We have deleted conversation from the halftime of the Jets game, presumably between JJ and one other person, in which JJ says Brady is acting crazy about the balls and will talk more later. I don’t know how likely it is that the deleted conversation even involved JM (e.g. JJ could have been complaining to his fiance or mother), but JJ and JM were both at the game and would probably have had a chance to talk in person by the end of the night. The next morning’s recovered(?) conversation starts with a text attributed to JM in which the writer threatens to make “the next ball” a balloon, and then we have (maybe) interleaved text about JJ’s friend’s comment on the stress of selling tickets, somebody being right about something, and then back to the state of the balls and blaming the refs for them. As the week continues we have angry references attributed to JM about inflating the balls, and texts attributed to JJ which are much calmer, even though we assume that Brady yelled at JJ and not at JM.

        It think it is odd that JM would seem so angry about this rather than JJ. This is the exchange which made we wonder if there were errors or transcription errors identifying the correct sender, although if the report is accurate, a lot of this might very well be humor – JJ got over being yelled at, but JM was needling him that he would make Brady yell at him again). If JM was genuinely angry, then I’d have to say that the Wells interpretation gets more plausible.

        I think the key takeaways here are
        1) that there are lot of possible interpretations of the Jets’ game text messages, and
        2) that the Wells report obtusely tries to limit the interpretation of this set of texts into one continuously discussed topic based on the “available” preceding texts alone, without acknowledging that there was a likelihood of an intervening in-person conversation on multiple and unknown topics, and without acknowledging some chance of gaps/errors in the text recovery process. [This obtuseness is close to explicit in footnote 49 on p. 77 of the Wells report.]

        For me, with the science debunked, JM’s apparent anger in these messages is really the one and only piece of evidence in the whole report which makes me wonder why he felt an inexplicably strong personal stake in the ball inflation levels, and if that could mean he was doing something beyond his job description. But, I think it could be humor.

  5. I would characterize that text as suspicious, but not damning. I realize you said “apparently damning.” The damning interpretation seems similar to the Wells Report’s interpretation on p. 81. The report continues at that point to say “Both McNally and Jastremski rejected this interpretation of the message. They offered no reasonable alternate explanation …” The report does not report what supposedly unreasonable explanation(s) they did offer, or whether Jastremski and McNally offered similar explanations.

    Alternative explanations will seem more plausible if they can be anchored in known context. With Jastremski’s and McNally’s explanations suppressed, we are handicapped in our ability to generate plausible alternatives. We can never be sure we have the full context of a text, based solely on what was selected for inclusion/investigation in the Wells report.

    Agreeing to accept that handicap for the sake of argument, the exact logic of the text seems to be that over-inflated balls will “deflate” Brady’s passing rating, and something else would normally be expected to deflate that Sunday, but won’t.

    With the context we actually have been given, it is reasonable to identify the “something not deflating” as the footballs, but this is not a certain inference. Even so we’re teetering on the edge of the excluded middle fallacy here, and I think Wells fell into it. There’s not just a binary choice between over-inflating the footballs to punish Brady vs cheating deflation of the balls. It was a normal part of Jastremski’s ball preparation to deflate the balls during preparation, to the lower bound of the legal limit.
    There are several complements consistent with the proposition in the text, including but not limited to:
    1) legally deflated balls will improve Brady’s rating and illegally deflated balls will improve it more
    2) legally deflated balls will improve Brady’s rating but improperly deflated balls will hurt it
    3) legally deflated balls will neither help nor nor hurt Brady’s rating, but improperly deflated balls will help it
    4) neither legally deflated or illegally deflated balls will help Brady’s rating, they just won’t hurt it.

    None of these possibilities is damning, because each contains an alternative for legally deflating footballs consistent with the text. It seems that Wells felt he could deduce “cheating football deflation” as the implied normal alternative to the “punishing football inflation” specified the text, but cheating is only a possibility; it can’t be deduced, and there’s no evident reason to favor it as a more likely possibility either.

  6. I appreciate the last two replies. I have three other questions about which I would appreciate perspective:
    1. What is the significance of discarding the measurements of the intercepted ball? In what way could/should they have been used?
    2. The Patriots initial reply to the Wells Report: “. . ball tampering at the AFC Championship Game . . would, if anything ha[ve] disserved the quarterback. How?
    *3. Why did Kraft, the owner, agree to accept whatever penalty was dished out if he genuinely believed his team innocent? Doesn’t this signal a belief in their guilt? He seems to reserve his greatest indignation for the suggestion that he didn’t fully cooperate. Why did he insist only that the evidence didn’t prove guilt, rather than indignantly suggest actual innocence?
    In short, what was his motivation to cave?

    • I have answers for your first two questions, but only speculation for the third.
      1) The circumstances of the halftime ball measurements were made with gauges whose accuracy became known later, and under relatively constrained circumstances (we know the measurements were within a 13:30 minute window fully occupied with known activities of approximately known durations, with only a couple permutations for the ordering of the activities. In contrast the measurements of the intercepted ball were made with gauges of unknown accuracy, and with much less constraint in time over when the gaugings took place. There isn’t enough information around the measurements to tell whether the ball was at an expected pressure based on its time inside to re-warm.
      2) Brady inspected and selected very consistently pressurized balls in the locker room preceding the official’s gauging and “certification” of compliance. The tampering hypothesis is that Brady is sensitive to small changes in pressure, and yet tolerated an imprecise hurried deflation in the bathroom. The end state would be balls whose grip Brady hadn’t tested and which, empirically speaking, probably have an additional few tenths PSI spread between them in pressure (be less consistent). There has to be some (unknown) point at which the balls become too deflated for Brady, too different from from what the Patriots use in practice, or must use in away games. If you start with the premise that Brady is such a perfectionist about small amounts of PSI, then it seems he would be dis-served by using imprecisely deflated balls he didn’t have a chance to approve.

      Kraft’s options to contest the team penalties have been discussed elsewhere in some depth. As to measuring his indignation levels and parsing his statements between “innocent” vs “not proven,” perhaps you can cite the statements which lead you to this… If I were in Kraft’s position, while I might have long term personal relationships with Brady and Belichick which might convince me of their personal innocence, I might not feel the same level of trust that JJ and JM hadn’t gone rogue without knowledge of others. Consequently I might not feel comfortable going all in on the team’s actual innocence of any tampering.

    • Robert — I’ve had more than one legal issue in my life that I’ve dropped. I was entirely in the “right.” I likely would have “won” had I continued the fight. I’ve also advised close friends to drop 2 cases (which they ultimately won) because of the financial, emotional and psychological burden it can take when you fight people close to you or people you work with.

      I can’t speak for Kraft at all, but it’s simply incorrect to assume that because someone doesn’t litigate that it means they feel they aren’t in the right. Kraft’s legal steps (basically aligning against the league and the other 31 owners) are far different than Brady’s, who is represented by Union and has a CBA.

  7. ElGee
    The problem with that analogy:
    1. He needn’t engage in complex litigation to appeal to the Commissioner – they have a lawyer on retainer, and already paid for a very well crafted legal response poking holes in the Wells report. The costs were minimal – the risk was 0.
    2. He announced he would accept the sanctions 5 days before they were determined, even as he challenged the findings on which they would be based.

    The way it went down suggests his belief in his own team’s guilt, especially insofar as he reserved his greatest indignation at the suggestion he had failed to fully cooperate while challenging the evidence instead of indignantly insisting “it never happened.”

    I understand this does not amount to an admission of guilt, but it sure falls short of a declaration of innocence. Perhaps the answer lies in his reference to being “one of thirty two” – suggesting that the league might be better served by his punishment, although he and the team would not.

  8. One of the first things you learn when you do fault analyses is that you do not ‘close’ a branch of a fault tree until you have enough evidence to do so. The technical team that the Wells Report used in the Deflate-Gate investigation apparently did not even CONSIDER (let alone actually follow up on) some branches on the Deflate-Gate ‘fault tree.’

    The Wells Report itself had data (if you believe their data – which is what they used to implicate the Pats/Brady) that unequivocally proves (through physics/thermodynamics) that the Pats and Brady were telling the truth the WHOLE time. Amazing that they missed it.

    Summary: There were 3 possible reasons for why there was a noticeable difference in pressure drops (what they used to implicate the Pats) between the Pats’ and the Colts’ balls that day:
    1. The Pats tampered with the balls
    2. The Colts’ balls were originally inflated in a locker room that was about 55degF (highly unlikely!)
    3. The Colts’ balls were left too long during half time and warmed up and increased in pressure
    They only considered option 1:
    1. The Wells Report was laser focused on option 1 only, and started going down that path, looking at text messages, etc., etc., trying to make something out of what they found. Meanwhile, the Pats’ balls did EXACTLY what physics/thermodynamics (and Wells’s own data!) says they were SUPPOSED to do! Even with the text reports they failed to explain the one that says, “The refs F’d us; inflated balls to 16 psi!” (paraphrased) … that text essentially explains everything going on with the text messages – it was a ‘dance’ between the refs and the ball guys; nothing more.
    Regardless, those texts are irrelevant to this whole thing because PHYSICS exonerates the Pats/Brady
    Here are the other options:
    2. Possible, theoretically, but not plausible, and highly unlikely. Even if this happened, it still exonerates the Pats/Brady
    3. This is what actually happened, most likely! The refs left the Colts’ balls lying around while they were measuring the Pats’ 12 balls. This option is also further supported by how the refs only had time to measure 4 of the 12 Colts’ balls (again, according to the Wells report).

    The Pats/Brady were telling the truth the whole time! You cannot argue against PHYSICS!!

  9. Joe —
    Thank you for the links — the first, the League’s statement opens — each one of the three that constitute Kraft’s reaction, however, says “the page is missing’ or some such. Could I trouble you to resend, and then I’ll respond.

    Before I write my own take, I have two additional points I need clarified — from you and/or Elgee to whom I will reply in a moment.

    I know the Wells/Exponent basis for concluding that Anderson measured with the non-Logo gauge is flimsy at best, but I’ve tried to make sense of it, at least Exponent’s claim. And as I understand it, it’s this: Both the Patriots and the Colts independently pre-set their footballs at 12.5 and 13 respectively using their own gauges. That preset essentially matched Anderson’s pregame readings on whichever gauge he happened to use. Since the non-logo gauge essentially matches both the calibrated meter, and all others utilized (except the logo) it was likely used as Anderson’s pre-game measure.

    Now, that argument fails because:
    a. the gauges other than the master were the same model as the non-logo, so of course it would match it
    ** b. the intercepted ball as measured three times comes close to matching the predicted pressure if and only if originally measured by the logo gauge. (Exponent does not at all count it because it couldn’t locate this gauge — Jastremski’s

    But that leaves the question unaddressed as far as I can tell — did they recover the gauge the Colts used to set their balls at 13? Did it more nearly match the readings of the Logo or non-Logo. I can’t find any answer in either the Wells, Patriots counter, or Exponent’s appendix

    2. I’m still not clear on the rebuttal to the Exponent claim that even if science explains the greater pressure drop in the Patriots balls — and it does — it does not explain the greater variation? Again, how do you explain that?

    3. And finally, for now — why didn’t the Colts balls drop from their half-time warmed up measurements to their post game measurements. And why did the Patriots balls drop so little in the second half to their post game measures?

    Again, thanks for your reply — the statement by Kraft that I read expressed disappointment in the process and conclusion, but real indignation in the suggestion that they didn’t fully cooperate. Please resend the links.

    robert

    • Hi Robert —

      1. Others have commented on this as well. There seems to be no effort to locate the Colt or Patriot gauges, which of course is somewhat mind-boggling. And there are even further issues with Exponent’s logic — if gauges drift over time, were the Colt and Patriot gauges more in-line with Anderson’s Logo gauge? What about the Patriot ball rubbing? That suggests that if their gauge were more closely calibrated to the Non-Logo gauge that it’s actually more likely Anderson used the Logo gauge. Exponent completely overlooks this in, my opinion, what is an attempt to simply try and prove Belichick wrong that rubbing could impact the halftime reading without thinking of any other implications.

      2. The variation is primarily expected from unequal exposure to rain: http://www.backpicks.com/deflate-gate-science-wiki/#Variance

      3. The Patriot balls were re-inflated at halftime to an unspecified degree. http://www.backpicks.com/deflate-gate-science-wiki/#Postgame

      The issue with doing deeper analysis on the post-game measurements is that Wells did not report what time the measurements took place. This is strange, because as a researcher that’s one of the first questions to ask since there is such a paucity of data in this scenario (Exponent should have asked for the video footage timestamps and accounts of measurements in the post-game. Wells should have noted if they were, for some reason, unattainable.)

      So we don’t know if the balls were measured after 3 minutes (while recalibrating) or after an hour hour. The Patriot balls were re-inflated to 13.0 PSI (pg 73)…but on what gauge? (Is this ever stated?) Because Patriot balls were re-calibrating, we’d expect to see Patriot balls OVER 13.0 PSI in the post-game, assuming those measurements were taken after the balls had re-calibrated to the indoor environment. You’ll notice that is indeed the case on the Logo gauge — that Exponent reported this information and still continued to overlook time as a variable confounding the halftime measurements tells you how incompetent or biased their work was.

  10. Joe —
    Thank you for the links — the first, the League’s statement opens — each one of the three that constitute Kraft’s reaction, however, says “the page is missing’ or some such. Could I trouble you to resend, and then I’ll respond.

    Before I write my own take, I have two additional points I need clarified — from you and/or Elgee to whom I will reply in a moment.

    I know the Wells/Exponent basis for concluding that Anderson measured with the non-Logo gauge is flimsy at best, but I’ve tried to make sense of it, at least Exponent’s claim. And as I understand it, it’s this: Both the Patriots and the Colts independently pre-set their footballs at 12.5 and 13 respectively using their own gauges. That preset essentially matched Anderson’s pregame readings on whichever gauge he happened to use. Since the non-logo gauge essentially matches both the calibrated meter, and all others utilized (except the logo) it was likely used as Anderson’s pre-game measure.

    Now, that argument fails because:
    a. the gauges other than the master were the same model as the non-logo, so of course it would match it
    ** b. the intercepted ball as measured three times comes close to matching the predicted pressure if and only if originally measured by the logo gauge. (Exponent does not at all count it because it couldn’t locate this gauge — Jastremski’s

    But that leaves the question unaddressed as far as I can tell — did they recover the gauge the Colts used to set their balls at 13? Did it more nearly match the readings of the Logo or non-Logo. I can’t find any answer in Elgees excellent 1st analysis, either the Wells, Patriots counter, or Exponent’s appendix

    Again, thanks for your reply — the statement by Kraft that I read expressed disappointment in the process and conclusion, but real indignation in the suggestion that they didn’t fully cooperate. Please resend the links.

    robert

  11. Elgee —

    Here I think you’re onto something — the psychological toll on a relationship well established between Kraft and Goodell.

    I replied to Joe and would ask your take as well:

    I know the Wells/Exponent basis for concluding that Anderson measured with the non-Logo gauge is flimsy at best, but I’ve tried to make sense of it, at least Exponent’s claim. And as I understand it, it’s this: Both the Patriots and the Colts independently pre-set their footballs at 12.5 and 13 respectively using their own gauges. That preset essentially matched Anderson’s pregame readings on whichever gauge he happened to use. Since the non-logo gauge essentially matches both the calibrated meter, and all others utilized (except the logo) it was likely used as Anderson’s pre-game measure.

    Now, that argument fails because:
    a. the gauges other than the master were the same model as the non-logo, so of course it would match it
    ** b. the intercepted ball as measured three times comes close to matching the predicted pressure if and only if originally measured by the logo gauge. (Exponent does not at all count it because it couldn’t locate this gauge — Jastremski’s

    But that leaves the question unaddressed as far as I can tell — did they recover the gauge the Colts used to set their balls at 13? Did it more nearly match the predicted readings of the Logo or non-Logo. I can’t find any answer in your excellent 1st analysis, or Wells, Patriots counter, or Exponent’s appendix

    robert

  12. What’s your guess re Exponent — biased or incompetent?

    And leaving aside obvious grounds for rejecting it, do you UNDERSTAND Exponent’s logic for assuming Anderson uses Non-logo? As I contrast the Wells report to Exponent’s appendix I’m struck that Wells which embraces almost everything, fails to repeat Exponent’s logic, resting on a complete non-sequitur.

    • I’ve added a new post that demonstrates their bias. Please check it out and let me know if you have questions.

      I do understand their logic for thinking he used the Non-Logo gauge, it’s just shaky and shallow. Some deeper investigation was needed, obviously.

      • Let me add some food for thought to your examination of the impact of “wetness” on football psi measurements.

        As you point out, wetness is a factor which must be taken into account when considering whether there may have been tampering. But there is more to consider than just wetness. In addition to the rain at Gillette Stadium on the night of the game, there was a substantial wind. During the first half winds were in the range of 16 mph to 19 mph. Wind gusts were between 28 mph and 33 mph. This has not been taken into account anywhere (to the best of my knowledge), but it needs to be if one is interested in producing a valid analysis. A damp football exposed to wind will be subject to evaporative cooling (something most middle school students understand, even if Exponent does not). The temperature of such a ball could easily be several degrees lower than the surrounding air temperature. One needs to run an Ideal Gas Law calculation based on actual ball temperature, not the ambient air temperature.

        Every source I have read indicates that the Colts’ footballs were kept in trash bags, protected from rain and wind. This was not the case with the Patriots’ footballs, which were exposed to the weather conditions. Test a wet football absent any wind, and you aren’t duplicating actual game time conditions. Compare a wet football exposed to wind to other footballs held in a protective trash bag, and you’ve (intentionally or unintentionally) stacked the deck.

  13. Thank you Mike. These did open. I found the second especially valuable. After reviewing all three, however, I’m still struck that he didn’t clearly and loudly proclaim: “We are innocent. We didn’t do it!” Instead, he proclaims — ‘the evidence isn’t there.’ That may strike you as a distinction without a difference, but it strikes me as significant. THe innocent rarely protest — ‘they didn’t prove it’ rather than ‘I didn’t do it!”

    robert

    • My analogy would be your kid getting into trouble when you weren’t a first hand witness. Your child is accused, not you, but it’s implied you are a bad parent and a bad family. You believe your child is innocent from your general knowledge of the child and your firsthand knowledge of your excellent parenting. Do you necessarily say “we are innocent”, or just “I’m sure you’re sincere in your accusation, but I doubt it; I think there’s been a mistake”?

      Kraft has basically the same 2nd hand knowledge as the rest of us about the deflation, and he isn’t being personally accused of involvement in or knowledge of a plot. Instead he is accused of and punished for tolerating or creating a “team culture” which accepts cheating.

      To me the condensed version of what he’s saying is “I don’t think we did it, I don’t think a reasonable scientist would have concluded that we did anything, and further even if you do accept Exponent’s science and statistical claims that known natural causes don’t explain everything, the texting evidence is too indirect and too ambiguous to conclude there was a plot at all and justify unprecedentedly harsh penalties for intentional violation.” I think the way Kraft has expressed himself is just a matter of him being honest about the limits of his knowledge of the innocence of the people accused, and trying to be being as fair minded as he can be to opposing points of view.

  14. Possibly this consideration has been raised before, but on game day the barometric pressure at Norwood airport fell 7 mb from 4:00 pm to 8 pm, approximately. By my calculations this is 0.1 psi, approximately. I assume this means that all of the football’s would undergo a likewise pressure adjustment downward.

    This is NWS data online with the game day barometer curve.

  15. I put my “inner physicist” to work using data from the Wells report (I did get a B+ in high school physics over half a century ago!), but I took an approach I haven’t seen elsewhere. Specifically, I focused on the post-game psi readings of a sample of four of each team’s footballs (Wells Report, page 73). I’d appreciate any and all comments on my analysis.

    After testing the Patriots’ footballs at halftime, each football was inflated sufficiently to bring the pressure up to 13 psi. We don’t know which gauge was used to determine 13 psi, but it doesn’t seem to matter. No air was added to the Colts’ footballs. That being the case, I started by assuming that once full equilibrium was reached, the pressure of the Colts’ footballs would be the same as it was pregame.

    It found didn’t matter which gauge was used after the game, the Colts’ footballs all had psi readings below the pregame figures (either 13 psi or maybe 13.1 psi). Assuming it was 13 psi (which is slightly less favorable to the Patriots). I determined how much the psi readings should increase once the Colt’s footballs reached full equilibrium. Depending on which gauge is assumed (the Logo Gauge gave psi values .35 psi to .4 psi higher than the Non-Logo Gauge), the Colt’s footballs showed a post-game average of either 12.7 psi or 12.35 psi, requiring an increase of either .3 psi or .65 psi respectively for full equilibrium.

    Next I looked at the post-game readings for the Patriots’ footballs, which averaged 13.45 psi or 13.05 psi, again depending on which gauge was used. If the Colts’ footballs had not yet reached full equilibrium, then neither had the Patriots’ footballs. So I assumed that the final psi readings for the Patriots’ footballs would increase by the same .3 psi or .65 psi of expected expected for the Colts’ footballs. That would bring the Patriots’ footballs to a final reading of 13.75 psi or 13.7 psi, again depending on the gauge used.

    Pregame, the Patriots footballs reportedly measured 12.5 psi. If the post-game measurements would yield readings of 13.75 psi or 13.7 psi (the difference between the two numbers seems inconsequential), then the amount of air added to each Patriots’ football increased the pressure by 1.2 psi or 1.25 psi, depending once again on which gauge used. Using an online Gay-Lussac calculator and assuming the temperature was 72 degrees in the officials’ locker room and 48 degrees on the field at halftime, the expected drop in psi at halftime would be 1.23 psi … splitting the difference between the 1.2 psi and 1.25 psi of air I believe was added. That would seem to validate the science.

    However, one thing that has bothered me for some time is the rather wide range of halftime psi readings for the Patriots’ footballs compared to those of the Colts’ (Wells Report, pages 68 and 69 respectively). Could it be that some Patriots footballs were deflated and not others? Is this evidence of tampering? I don’t think so, and here is why.

    If we assume any single psi reading could vary by plus or minus .2 psi (I chose that figure because the intercepted football was measured three times by the same person using the same gauge, yielding readings of 11.35 psi, 11.45 psi and 11.75 psi … a difference of .4 psi between the lowest and highest reading), I went back to the halftime readings of the Patriots’ footballs. If we assume that the original psi readings came from the Non-Logo Gauge (the one Exponent says Walt Anderson used), the halftime psi levels should be between 11.10 psi and 11.50 psi (12.5 psi minus 1.2 psi, plus or minus .2 psi). Four of the footballs fell within this range, five were lower than would be expected, and two were higher than would be expected. If we assume that the original psi readings came from the Logo Gauge (the one Walt Anderson remembers using), the halftime psi levels should be between 11.05 psi and 11.45 psi (12.5 psi minus 1.25 psi, plus or minus 2 psi). Again, four footballs fell within this range, two were lower than would be expected, and five were higher than expected. If we assume a football that measures outside the expected range was tampered with, then air must have been added to those footballs measuring higher than expected. Seriously, how likely is that?

    It seems to me that if tampering is insufficient to explain the Patriots’ halftime psi levels, then either we are working with bad data or there are physical forces at play that have yet to be identified. Considering the slipshod manner in which pregame measurements were performed, I suspect bad data. The old acronym is as good today as it ever was. GIGO … garbage in, garbage out.

  16. Elgee —
    In preparing to submit an amicus to the federal court — in the end, they declined all amicus briefs — rereading Exponent’s Appendix 1 for the fourth time, I suddenly discovered objective bias that your excellent and comprehensive critiques to date do not yet include. Please see my most recent blog post at robertblecker.com called “The Smoking Gun”

    In short, Exponent’s Figure 3 is a carefully and deceptively constructed photo to support its biased and ungrounded assumption that the ref misremembered which gauge he used.

  17. Here is another factor regarding the question “Why do the Patriots balls have greater variability than the Colt balls?” that I haven’t seen addressed elsewhere.

    The New England Patriots’ offense was on the field for nearly all of the last half of the 2nd quarter. (The Colts did run the final play of that quarter … an Andrew Luck kneel down.) During that period of time, the Patriots’ footballs were in play and exposed to the elements. The Colts’ footballs, on the other hand, were not in play, but were sitting on the sideline in a ball bag. This means the Colts’ footballs spent a considerable amount of time enclosed in a confined space. It seems to me that, under those conditions. warmer footballs would tend to lose heat while colder footballs would tend to absorb heat. Place footballs (or any object, for that matter) with different temperatures in an enclosed space long enough, and they all would eventually reach the exact same temperature.

    Under these conditions, it seems that the Colts’ footballs should have demonstrated less variability, since they had been held in an environment perfectly designed to reduce and (if left there long enough) eliminate any variability.

    Does this make sense to anyone else?

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