Thursday, January 29, 2009

Flagging myself

"The best laid plans of mice and men oft go awry."
-- Robert Burns

Please excuse the pseudo-intellectual literary opening, but I've had this blog post rattling around in my head for a few weeks, ever since I came upon a startling discovery -- or so I thought.

I've been having fun with correlations lately. In a nutshell, when you try to correlate two sets of statistics -- say, offensive yardage and wins -- you come up with a number between -1 and 1. If your number's close to -1, you'd say there's a negative correlation between the two -- in my example, that would mean that the lower your offensive yards, the more wins your team will get (which we'd all agree to be false). If the number is close to 1, you'd have a positive correlation. In this case, we'd say that high offensive yardage totals tend to produce teams with more wins (which we'd figure to be true). If the result is near zero, then there's minimal or no correlation between the two stats.

You can have all sorts of fun with correlations and, thankfully, Excel makes them easy to compute. You might remember these two posts from last summer, where I tried to figure the correlation between rushing average and raw passing yards, along with passing average and raw rushing yards. My results were inconclusive and, the CORREL() function in Excel bears that out. Over the sample size that I used, passing yards correlates to rushing average at -0.096 and rushing yards correlate to passing average at 0.129. Both are essentially insignificant.

So, awash with glee at the new toy I found, I decided to see if I could find any other statistical connections that everyone "knows" that I could disprove. I immediately went to penalties. After years of watching John Randle (and now Kevin Williams) jump offsides seemingly every defensive series, I wanted to see how badly penalties hurt a team. In theory, if penalty yards significantly hurt a team, then we should see a high negative correlation between penalty yards and wins.

The early results: not so much. Here are what I got when I tried to find the correlation between penalty yards and wins over the last three seasons:

2008: 0.021
2007: -0.067
2006: -0.081
06-08: -0.043

That's not so damning, then, is it? The correlation between penalty yards and wins from 2006 to 2008 is virtually nil. Obviously, big penalties at crucial times, like that late pass interference call, or a defensive hold on the game-winning drive that lets a team convert a third-down, are huge, but, in the grand scheme of things, maybe being 1st-and-20 after an offensive holding call early in the second quarter isn't such a big deal. Take a look at the penalties stats page on and you'll see some of 2008's best teams -- like Dallas, Tennessee, and the NY Giants -- near the top of the list in penalty yardage, while some of the worst -- like Cincinnati and Seattle -- near the bottom. There's definitely no clear correlation, at least for 2008.

So here I was, all ready to come out with a bunch of theories as to why this was so, as to why penalties really had little effect on a team's performance. First, though, I thought I'd expand my research and take it back three more years, from 2003-2005, just to have a bigger sample size. Here's what I got:

2005: -0.266
2004: -0.259
2003: -0.280
03-05: -0.262


A correlation of -0.262 is still not huge, but it's a good deal larger than -0.043, and could be considered at least mildly significant. By comparison, another pair of stats you'd expect to have a significant negative correlation -- offensive turnovers and wins -- clocks in at -0.435 for 2008.

That pretty much sunk my post and all the ideas I had regarding the minimal impact of penalties. Still, I think the data shows that penalties are not quite as catastrophic as most people would have you think (especially over the last three years) and some of my original theories still probably hold.

Especially in the John Randle/Kevin Williams examples, good defensive lineman try to anticipate the snap count. Sometimes this results in offsides, other times it results in great jumps that disrupt the offense. Similarly, as they say, "offensive holding occurs on every play," and it might be that the good O-linemen have figured out how to hold without getting caught, while the bad ones don't even attempt it and thus are flagged less often (while also being bad). And, not that they ever call offensive pass interference except about once a month, but every "good, physical" receiver pushes off at least a few times a game. Now the "dumb" penalties -- personal fouls, 12 men on the field, and so on -- have nothing to do with gaining an advantage or are the result of canny play and should clearly be avoided. But the rest might not be quite so bad.

Finally, I think that penalties have less of an impact on a game than people tend to give them credit for. In 2008, the typical team had 89.6 penalties called against it, or about 5.6 per game. Each team was involved in an average of 123.75 plays per game (not counting special teams), so that means a penalty was called on a team on less than 4.5% of its plays -- and maybe less than 4% if you include special teams in the mix. Yes, it sucks to have that bad penalty at a crucial time, but is 1st and 15 after a false start really that horrible? If you convert the first down anyway, the penalty was essentially meaningless. If anything, maybe coaches should save those timeouts for delay of game more often. And maybe fans shouldn't get quite as riled up about their players making a penalty that gives the other team free yards.

Doesn't mean I won't shout at the TV the next time Kevin Williams jumps offsides.

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