Reading a post by The Earl about evaluating 40 times with respect to speed really got me to thinking: Why not go one step further and use the split times to evaluate the change of speed, otherwise known as acceleration.  Now I admit that you can't look too deep into these numbers for two reasons:

1. Measurables are overrated by us fans and Al Davis
2. A very small difference in time can make a pretty decent sized change in acceleration, and these are humans we are talking about, not machines;  so every time someone ran a 40 the times would be slightly different. So take that into consideration when comparing these acceleration numbers.

Now I would have thought that there would be no interest in something like this among the general public, but it seems there are some real math nerds like myself out there.  Before I go further, I would like to give credit to The Earl for opening this discussion;  and hopefully I haven't taken it one step too far (something I have been known to do, just ask my wife).  

I decided to use Chris Johnson as a comparison, as he seems to be the gold standard in the NFL right now for what "fast" is.  Using the 10 and 20 split times, along with the actual 40 time, I extrapolated the average velocities (in yards per second) from 0 to 10 yards, 10 to 20 yards, 20 to 40 yards, and 0 to 40 yards.  By using these average velocities I found the average accelerations (in yards per second squared) between those same 4 distances.  I don't want to get too in depth about how I evaluated the numbers, but I will provide a section at the end of the post giving exactly how I came up with the numbers for those of you that are curious or would like to make sure the numbers are valid (for you math nerds).  Also, the numbers I used are from the following site:  

http://www.cbssports.com/nfl/draft/history/combine/position/RB

I apologize for the crudity of the table;  I actually had this looking all nice on excel with some Dolphins colors, but I guess I'm not computer savvy enough to make it work.  Now, what do these numbers mean?  Well, you've got to compare it to another player to really get an idea of how good these numbers are.  So I decided to use someone that I see as a future lock HOF RB that has decent speed, but I never really considered a speedster.

A little bit about how to look at these stats: 

If you look at Chris Johnson's ACC compared to LT's, CJ starts off with way more acceleration but then LT has more after 10 yards.  That doesn't necessarily mean that LT is catching up to CJ, you actually have to look at the velocity from 10-20 and 20-40 to realize that CJ is still going faster throughout and would be creating increasing separation for the entire 40 yards.  His higher acceleration early just means that he reached "top speed" a lot faster, which is obviously better.  So when comparing these players, it is better to compare velocities at given stretches while the acceleration really just tells you how good their individual "gears" are.

That brings me to another point I wanted to make.  I have heard some people mention stuff like "being able to maintatin top speed".  Well, if you look at the stats, both of these players are still accelerating through the 40 yards meaning they still haven't even reached their actual top speed.  Now if there was more data, like a 30 yard split, then its entirely plausible that the acceleration from 30-40 could be negative, indicating that they were slowing down.  The acceleration from 20-30 would just be enough to outweigh the deceleration from 30-40 and make the total acceleration from 20-40 positive.

I wanted to find when a player actually starts slowing down, so I found some splits for some 100 meter races.  

http://speedendurance.com/2008/12/02/dwain-chambers-on-usain-bolt-asafa-powell-stride-length-and-stride-frequency/

Now these are professional sprinters, so take it with a grain of salt, but out of a group of 7 sprinters, 5 started slowing down between 50 and 70 meters and the other 2 slowed between 60 and 80 meters (1 meter=1.09 yards).  Looking at this info, I would say a lot of players don't reach their top speed until past 40 yards.  Now later in a game, this would be completely different because of endurance. 

Onto some of our beloved Dolphins:

I wanted to look at Kory Sheets because he’s probably the fastest player on the team and there are a lot of phinsiders that like him.  Looking at his stats, his initial acceleration is almost as good as CJ, and he actually has a higher top speed than CJ.

Brandon Marshall doesn’t have that good initial acceleration but does have a higher top speed than even Kory Sheets.

Hartline has very good initial acceleration and a decent top speed.

Bess has decent initial acceleration, but I think his strength is more changing directions than strait-line acceleration. 

Thought I would put Grice-Mullen up here since he is fighting for the KR job.  Same initial acceleration as Bess and a slightly higher top speed.

Figured I would put a non-Dolphin WR in here for comparison.  Same initial acceleration as Bess and Grice-Mullen but has a much better second gear to get to a significantly higher top speed.

I’ve been defending Pat White a lot lately and after looking at this maybe I shouldn’t have been, LOL.  He does have a pretty decent second gear though.

I have heard some people say that they think Smith may eventually end up at S because he isn’t the most athletic.  You be the judge.

Davis here shows more athleticism than Smith, but not that much.

Ranking these 11 players in terms of initial acceleration:

1. Chris Johnson (5.10 yds/sec2)
2. Kory Sheets (4.82)
3. Vontae Davis (4.63)
4. Brian Hartline (4.44)
5. Bess (4.27)
6. Grice-Mullen (4.27)
7. Desean Jackson (4.27)
8. Sean Smith (4.27)
9. Ladainian Tomlinson (4.22)
10. Brandon Marshall (3.91)
11. Pat White (3.91)

Ranking in terms of top speed:

1. Brandon Marshall (11.05 yds/sec)
2. Kory Sheets (10.99)
3. Chris Johnson (10.93)
4. Desean Jackson (10.93)
5. Vontae Davis (10.70)
6. Ladainian Tomlinson (10.70)
7. Brian Hartline (10.47)
8. Sean Smith (10.47)
9. Pat White (10.42)
10. Ryan Grice-Mullen (10.26)
11. Davone Bess (9.85)

You may be looking at these numbers thinking that it took a whole lot of time to extrapolate, but in all honesty, the hardest part is trying to figure out how you want to evaluate the numbers.  I plugged the equations into excel and now I just have to put in the split times and excel does the work for me (I would like to thank my CS150 instructor for introducing me to the wonders of excel).  So, if anybody wants stats for any of their favorite dolphins or other players in the league, just ask.

And for those of you wondering what equations I used, whether it be curiosity or validity, here it is:

1.    Velocity from 0-10:  change in distance (10 yards) divided by change in time (split 1)

2.    Velocity from 10-20:  change in distance (10 yards) divided by change in time (split 2 minus split 1)

3.    Velocity from 20-40:  change in distance (20 yards) divided by change in time (split 3 minus split 2)

4.    Acceleration from 0-10:  change in velocity (1. from above) divided by change in time (split 1)

5.    Acceleration from 10-20:  change in velocity (2. minus 1.) divided by change in time (split 2 minus split 1)

6.    Acceleration from 20-40:  change in velocity (3. minus 2.) divided by change in time (split 3 minus split 2)