Deflategate

The following analysis has been referenced in multiple places, most notably by Dr. John Leonard in his Sports Illustrated essay on Deflategate.

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:

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

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

1. Summary of analysis

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:

Temperature
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):

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:

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.)
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.
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.

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.

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

There are a few sources of variance to consider:

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.
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.
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):

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.

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:

Referee Walt Anderson remembers using the Logo gauge.
Non-Logo gauge projections do not align with what is expected for the control group, the Colt balls.
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)
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.

According 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:

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.

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 reflected 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).

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.

Thinking Basketball