Monday, August 13, 2012

Denard, Usain Bolt and a bunch of math

So Denard (there's only one) made a seemingly-not-very-serious comment at Michigan's media day thing over the weekend that he could take Usain Bolt in the 40. Here's the exact quote:
"I've watched him run, and I'm pretty sure I can beat him in a 40-yard dash," Robinson said at Michigan's media day on Sunday. "I'd get a better start, and I could take him.

"At 60 yards, I'd be in trouble, and at 100 meters, he'd be gone, but I could get him in a 40."
This has resulted in people all over the internet being stupid since that's what people on the internet do. I do not like stupidity and prefer numbers, so I went seeking numbers and will now use them to produce a guesstimation (of undetermined value) as to whether Usain Bolt would only probably beat Denard in the 40 or would totally destroy him in the 40. The baseline hypothesis will be the latter since ... I mean ... obviously.

Disclaimer: I am not a physicist. But I do have a pretty good idea of how to work with numbers and like to actually use numbers/data rather than just making blanket statements that defy all logic because MORAN RABBLE. I also stayed at a Holiday Inn Express last night. So yeah.

There are basically two things to figure out. The first: How fast would/does Usain Bolt run the 40? The second: How fast would/does Denard run the 40? Figuring out the question(s) isn't difficult.

Let me start with this: Usain Bolt is very fast. He is the fastest man in the world at 100 meters and 200 meters and everything in between. He also isn't a great starter, which is backed up by the IAAF splits from the the last two Olympics. I haven't been able to find a 40-yard split (rather than a 40-meter one) from London, but I've got the raw numbers and can therefore produce a reasonably accurate one.

I'll even show the math. To start with, the Olympics people use meters and not yards; 40 meters obviously isn't the same as 40 yards, so some translation is necessary. Since a yard is 0.9114 meters, 40 yards is 36.576 meters. That's the distance we're looking at for an estimated 40-yard split. As for time, his 40-meter split won't do much good since that'd be too big; what I'm gonna do is start with his 30-meter split (3.765 seconds) and then get an as-close-as-possible time for the last 6.576 meters.

The IIAF numbers show he went from the 30-meter mark to the 40-meter mark in .87 seconds, but it's not realistic to use that number to calculate an average for only the first 6.576 meters because he was accelerating throughout; for reference, he ran the previous 10 meters in .90 seconds. Since I don't remember the calculus to get an exact acceleration number, I'm gonna figure that about the first half of an overall 0.87 split -- which, again, came right after a 0.90 split -- was run at an extrapolated 0.885 seconds. I realize that's not perfectly accurate, either, but it's the best I can do given my decade of removal from graphing calculators and whatnot, so that's the number we'll use to get a time for those 6.576 meters (again, this is a guesstimation since Bolt wasn't actually running the 40).

So if his extrapolated time for that subsection of the larger 30-to-40-meter section was 0.885 seconds, he'd have run those first 6.576 meters in 0.5819 seconds. And when added to his 30-meter time, that produces a 40-yard (not 40-meter) time of ... 4.347 seconds.

Given that Speed Endurance had previously calculated his Beijing split at 4.35, I'm satisfied with that as a realistic result. Bolt has been running the 40 (as part of the 100) in about 4.35 seconds.

BTW, this ESPN Radio guy is unequivocally wrong when he says Bolt could run a 3.73 hand-timed 40. No. The IAAF actually includes reaction times in the splits, and Bolt's was only 0.165 seconds; subtract that from his estimated time and you get about a 4.19 (more on that momentarily), so unless the guy doing the timing was drunk and/or full of Vicodin, the result would not be anything close to a 3.73 under any circumstances.

But here's the thing: Denard has never run an "official" 40, although his undoubtedly fake reported time coming out of high school was a 4.32. He also ran track his first couple years at Michigan, but he only ran the 60 meters and doesn't have publicly available splits since there aren't 7,000 cameras and IIAF monitors at a Big Ten track meet.

Could he run a 4.35? Probably. Chris Johnson ran a 4.24 at the combine back in '08, and freakin' 15 guys have run an official 4.3 flat or faster in the last dozen years. There's obviously a significant difference between the 40 and the 100; just take a look at those Bolt splits and realize that he reaches top speed at about 60 meters and then doesn't slow down at all until about the 90-meter mark.

But there's also a difference in timing, as mentioned above: The combine 40 times are electronic but are based on first movement, which eliminates reaction time. Cut reaction time off of Bolt's time and you get a probably-not-attainable-for-a-football-player 4.19 seconds. But (but but but) sprinters also use starting blocks; the guys at the combine don't. Those are obviously of some acceleration value that I can't calculate or even find, but it's not unreasonable to assume that they produce 0.1 seconds of an advantage (just imagine the hilarious unfairness if one of the eight guys in the 100-meter finals didn't get to use blocks).

With no better number to go off of, let's just use that as a ballpark figure for the blocks advantage and add it to Bolt's not-including-reaction-time number of 4.19 to try to replicate combine conditions. The result: 4.29. I feel pretty comfortable saying that his 40 time, in combine conditions and based solely on his 100-meter history, would be somewhere between 4.29 and the above-cited 4.35, give or take a couple hundredths of a second. So that's that.

Speaking of the 100-meter thing, Matt Hinton is a great writer but, IMO, kinda missed the point when he wrote this earlier today:
But even if you do fall for the superhuman times attributed to football players, the comparison to elite sprinters falls apart when you consider how much faster the latter could potentially cover that distance if they trained specifically for it, as football players do before the combine. ...

If Robinson and Bolt raced head-to-head, Robinson would likely fare much better over the first 40 yards of a 100-meter sprint than in a straight-up 40-yard sprint. But no coach anywhere would give him decent odds of actually winning at any significant distance.
The first sentence of that second graf is wrong. Bolt isn't pacing himself for the first 40 meters of the 100; he's just not nearly as fast out of the blocks as he is once he gets his gazelle legs going. That won't change regardless of whether it's a 40-yard dash or the first 40 of the 100, which is why Bolt actually specialized in the 200 before doing both.

As for the last sentence, that's exactly what Denard said: There's no way he'd beat him at 60 meters (Denard's best time of about a 6.81 would be almost a half-second back of Bolt's split of 6.45), and it wouldn't even be close at 100 meters (duh). The distance in question is 40 yards (which Bolt doesn't train for), and going back to the hypothesis-type thing toward the top of this post, a 40 time somewhere in the 4.29-4.35 range would definitely not fall into the "totally destroy him" category. It might even fall into the "lose to him" category, which was not what I expected when I started this exercise.

Unless I'm significantly off on some of my numbers, the fastest of the fast of the NFL dudes, most of whom ran short-distance track in college, could at least challenge Bolt and the other elite 100-meter guys in a one-off 40-yard dash. Justin Gatlin would probably back me up: The guy won gold in the 100 in '04 and won bronze last week and ran a 4.42 at the '08 combine in between, which provides a little reasonable-ness to my calculations above. Gatlin is world-class fast in the 100 and ran a 40 time that wouldn't have been among the top five at any combine in the last decade.

Whether Denard is one of those aforementioned fastest-of-the-fast guys isn't entirely certain without a 40 time, but Mythbusters would call this one plausible. Bolt probably would not. Either way, I'd be down to watch* and would even be willing to contribute to the Dave Brandon Memorial Give Michigan All Of Your Money Fund to do so.

*I'd even watch the two of 'em in the 100 just to have my mind blown by the reality of Denard looking like Rich Eisen.


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