# Do Cautions Breed Cautions?

There are a lot of NASCAR sayings. You know them: one announcer starts and the others all join in. Last weekend at Martinsville, with three cautions in the last 50 laps, it was “cautions breed cautions”.

But do cautions really breed cautions? Or is that one of those things we notice when it happens and infer that it happens all the time, like the idea that anyone can win at Talladega?

## “Breeding”

What the statement means, of course, is that once we’ve had one caution, more are sure to follow. But how close does that second caution have to be to the first one to qualify as a descendent of the first? Five laps? Ten? Twenty?

I analyzed all the caution data from 2018 (the last complete season) and then did the same for 2008, just to see if there were any trends over time. (2019 so far looks very much like 2018.)

### Making Sense of Lots of Data

We’re talking around 200 -300 cautions per season, plus the correlations between each of them, so there are a lot of numbers running around. I needed a way to get a look at the data so I could have some idea what to investigate.

I needed a graphic: Something that tells you more than a chart of numbers. The first thing I tried was a pseudo-heatmap. I colored

• Red squares are cautions within five laps of the last caution
• Orange squares are cautions that came within ten laps of the last caution
• Cautions within 20 laps are yellow

Don’t worry about the numbers: you’re looking for patterns. You can see pretty quickly that there are some races where there are longer strings of red and orange than others. Those are the races that had a lot of cautions closely spaced.

The July Daytona race, for example (denoted by 18-Day) has a couple runs: Three cautions close together, then two more at the end. Fall Vegas also has a long run of red and orange at the end.

But this still isn’t as useful, in part because stage breaks are a different breed of caution. They didn’t exist when the ‘cautions breed cautions’ maxim was invented. The above attempt at a heatmap doesn’t show that.

## Introducing the Caution-O-Gram™

So I invented the Caution-O-Gram™, which gives you an entire race in one picture. Here’s July Daytona:

• The white bars are stage breaks
• Red bars are accidents
• Orange bars are spins

You can easily see the runs of cautions from this and you see where the stage breaks are.

Now, if cautions really caused cautions, we’d have a situation because one caution would start a chain of cautions that wouldn’t end. What we actually see are groups of two and sometimes three cautions, then a period of green flag racing.

Below are two of the 2018 races with the largest number of closely-spaced cautions.

If you look at the ends of those races, it’s sure tempting to suggest that cautions breed cautions.

## But Did the Cautions Cause the Cautions?

There’s an alternative hypothesis. Drivers are much more aggressive at the ends of races, when the trophy is on the line. They’re willing to make riskier moves and, thus, there are more accidents and spins toward the end of the race.

The Caution-O-Grams™ show that. Most of the cases in which there were two or more closely-spaced cautions happened near the ends of races. That was definitely the case at Kansas. A debris caution was followed in quick succession by two accidents.

### Cautions Don’t Always Cause Cautions

You can’t prove that something always happens, but all you need is an instance of it not happening to put a hole in the theory. At Kansas last week, they had a caution in the middle of the race that was followed by 41 laps of racing to the stage end, then 87 laps of green flag.

Some races don’t have cautions at the end. Here’s Atlanta from 2018.

Kevin Harvick led 181 of 325 laps in the first of four consecutive wins that year.

The pattern for two races at the same track can be very different, depending on whether there’s a dominant car. Look at the spring Vegas race: Two accidents right next to each other, followed by 73 laps of green-flag racing.

## Cautions: Rabbits or Pandas?

The question we’re really interested in isn’t whether cautions breed cautions, but “how often do cautions breed cautions?” In other words, do they breed like rabbits or pandas?

Let’s look at the number of laps between cautions for the 2018 season. I’ve included stage breaks because it’s rare to have a caution right before a stage break: when cautions are close to stage breaks, the caution replaces the stage break. And heavens knows there’s a good share of cautions right after stage-break restarts.

I was surprised at how large the “less-than-five” category was. As I mentioned, a good number of those are wrecks on restarts. But, in total, about 25% of the time (23.2% to be precise), a caution is followed by another caution within five laps.

### How Many Laps Before a Caution?

Using a cumulative percentage lets you see how likely it is to have a caution in the next x laps.

After a caution…

• 23.2% of the time, there was a second caution within 5 laps.
• 36.5% of the time, a second caution happens within 10 laps
• 45.5% of the time, a second caution within 15 laps
• 53.1% of the time, a second caution within 20 laps

### Was It Always Like This?

This isn’t a full study, but I pulled out the data for 2008. There were more overall cautions, but as percentages, this graph looks similar to the graph for 2018.

• 2008 has roughly the same probability of of having a caution within 5 laps of of caution: 25.3%
• The probability of having a caution within the next 10 laps, however, is higher at 44.2%
• There’s also a higher probability of having a second caution within the next 15 laps: 55.5%

I suspect that the higher ratios for second cautions in 2008 (where, remember, there were no stage cautions) are due in part to damaged cars staying on track. Those cars often shed pieces or experience another failure that leads to another caution.

It would be interesting to look at the years just before the damaged vehicle policy and see if that’s the reason.

## So Cautions Breed Cautions 25% of the Time?

Not so fast. If that were true, we’d find a good number of cases in which there’s just continual cautions and that’s not what we see. So let’s look at the second-order correlations: That is, how likely is it to have two more cautions within x laps of the first?

The numbers drop off a bit. In 2018, there were only six times out of 175 with three crashes within 10 laps of each other.

In 2018, there was a:

• 3.4% chance of having a third caution within 10 laps of a first caution
• 16.0% chance of having a third caution within 20 laps of a first caution
• 31.4% chance of having a third caution within 30 laps of a first caution
• It takes about 45 laps before you have a 50% chance of having a third caution.

Race teams use these statistics (and many other) to inform their choices. They consider things I haven’t considered here: like the probability of a second caution changes according to how far along in the race you are. Given how much data there is and the pressure of making a decision in real time, some teams are going to complex artificial intelligence programs to aid their decision making.

## Conclusion

Cautions don’t cause cautions: Drivers cause cautions.

There are limits to ‘cautions breed cautions’. There is a good chance of a second caution within 20 laps of the first, but the probability that there’s a third caution within another 20 laps is much, much lower.

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