# Speed of a Football Player: Madden NFL 2006

## Abstract

The purpose of this experiment is to reevaluate speed and acceleration ratings of a football player in the video game Madden NFL 2006 under certain conditions.

## Introduction

Before all NFL players enter the league, they must run the forty yard dash, a forty yard sprint starting from rest. Elite times range from 4.2 to 4.4 s. Speed and acceleration are two vital factors to determining the time of a person's forty yard dash. If a person can fire out quickly enough they can then create the fastest possible acceleration. Next, they have to stride for the last twenty yards with relatively constant velocity. If they do this with perfect form, a perfect stance, and are naturally very fast, they might reach the elite range. This is not the case for most players, but it is all to common for strong safeties in Madden NFL 2006 to catch up and swat down a pass with ungodly speed.

One of the fastest players in the NFL is DeAngelo Hall, a cornerback for the Atlanta Falcons who ran a 4.15 s 40 yard dash, hand timed by a stopwatch. For this, he received a 98 rating for speed and a 98 rating for acceleration in the game play settings. Michael Lewis, strong safety for the Philadelphia Eagles ran a 4.53 s hand timed forty, which is still a good time. He received an 88 speed rating and an 89 acceleration rating. Keep that in mind, because his performance did not reflect his stats.

## Procedure

- Play Madden NFL 2006 and throw a pass to one of your wide open receivers. The All Pro difficulty setting produces this result more often than All Madden difficulty. (See sample videos here: overhead view, side view.)
- Have the safety catch up to your open receiver with unnatural speed and watch the instant replay.
- Calculate how far, in yards, he ran to swat the ball down. Many times it will be a triangle made with the hash marks and the initial position. If you are lucky, it will be nearly 40 yards.
- Time how long it takes for the safety to run the distance. (See the video here).
- Calculate acceleration, then velocity of the safety using standard equations of motion.
- Compare these ratings to the fastest player in the game.
- Adjust stats accordingly.

## Analysis

The vertical distance on the field was 39 yards, but the safety was three quarters of the way from one hash mark to the other, as illustrated below.

Since the hash marks are spaced 6⅙ yards apart, so

3 x 6⅙ yards/3 = 4.625 yards

Use the Pythagorean Theorem to get the hypotenuse.

(39 yards)^{2} + (4.625 yards)^{2} = c^{2}

The distance came to be 39.273 yards which is close enough to 40 yards.

Now time the dash. Every time trial came out to be about 2.61 seconds. Next convert 40 yards to 36.57 meters so you can use it in equations of motion.

Use s = ½at^{2} (since there is no initial distance or velocity) solve for acceleration and substitute numbers.

a = 2s/t^{2} = 2(36.57 m)/(2.61 s)^{2} = 10.74 m/s^{2}

To find velocity, use v = at, since there is still no initial velocity.

v = = at = (10.47 m/s^{2})(2.61 s) = 28.02 m/s

Next, calculate the acceleration and velocity of DeAngelo Hall running a 4.15 second forty using the same equations.

a = 2s/t^{2} = 2(36.57 m)/(4.15 s)^{2} = 4.26 m/s^{2}

v = (4.26 m/s^{2})(4.15 s) = 17.62 m/s

Since 4.26 is 98% of maximum acceleration, according to Hall's ratings, then 100% can be calculated.

(4.26 m/s^{2})(98%) = 4.17 m/s^{2}

The same can then be done for velocity

(17.62 m/s)(98%) = 17.3 m/s

Then compare these maximum ratings to Michael Lewis' new ratings for acceleration. Since his ratings should now be the new max, compare them like so.

(4.17 m/s^{2})(X%) = (10.74 m/s^{2}) = 2.585

Do the same for velocity.

(17.3 m/s)(X%) = (28.02 m/s) = 1.619

To get the new ratings multiply by 100. This leaves Lewis with a speed rating of 162, and an acceleration of 259. Much improved from his original ratings of 88 in speed and 89 in acceleration.

## Conclusion

The stats of an NFL player become skewed in an attempt to make the game more challenging. Acceleration increases by 291% and speed increases by 184%.

## Sources of Error

The player does not start completely from rest, and may have some forward momentum when timing started. Also, the player does not start from a stance like they normally do when performing the forty yard dash. This is a source of error that made the experiment even more ridiculous since getting into a stance increases your acceleration.

Brian Marino -- 2007

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