My return to the unique problems posed by quarantine qualifying is in part because Clint Bowyer tweeted that the pseudo-random draw was really messing him up and it wasn’t fair.

I wanted to know if Clint’s claim was true in general, or if he just had some pretty bad luck. And whether there were other drivers who had benefitted from this process.

This knowledge is important in light of NASCAR’s decision not to have qualifying the rest of the year. They, of course, changed the procedure just as I finished this blog, so we’ll hit the new process, too.

## The Lay of the Land

In the 20 races we’ve had:

- 4 races had qualifying: Daytona, Fontana, Phoenix and the first Charlotte race
- 1 race had qualifying rained out (Las Vegas), so we’re ignoring it totally
- The starting positions for 3 races were determined by inverting finishing positions for other races. (The second races for Charlotte, Darlington and Pocono).
- That leaves 12 races where starting positions were determined by draw.

I explained the details of the current system before and some of the problem arising from this system, so let’s focus on the numbers. We’ll start with the luckiest drivers before we switch over to the Clint Bowyer — or alleged Clint Bowyer — side.

## Is Aric Almirola the Luckiest Driver?

Aric Almirola started on the front row in six of the twelve races where a draw determined starting positions.

The probability of drawing position 1 or position 2 for a given race under the current system is 1/6 (16.7%).

Probabilities multiply together when we consider doing the same for each race. So the probability of starting on the front row twice is 1/6 x 1/6, which is 1/36 or 2.78%. You can see how much the probability goes down just from once to twice, right?

Well, the probability of starting on the front row six times is 1/(6^{6}). That’s six to the power six, which is 279,936, That comes out to be 0.002%. Mr. Almirola (who was born on PI day, which happens to also be Einstein’s birthday!) has had some serious luck with this process. If I were him, I’d be buying lottery tickets.

0.002% is a small probability, but remember: If you flip a coin enough times (like a couple thousand), you will get about equal heads and tails. But within any small number of flips, it’s possible to get all heads or all tails.

### It’s Not Just Luck

Before you suggest that Almirola is just exceedingly lucky and didn’t earn those spots, let’s note that, to even be considered for drawing P1 or P2, you have to be in the Top 12. Almirola’s on-track performance earned him the right to be in the draw.

His probability of getting the front row in the two weeks where he was out of the top 12 was 0. Not even luck can help you there.

### Wait? No Graphs?

Of course there’s graphs.

I used a three-year average of qualifying positions for each driver at each track. Then I compared that to their 2020 starting positions at those tracks.

I further divided out the three groups of tracks: The first group were the qualifying races, the second group is the invert races and the last group were all draws.

In this graph (and the ones that follow), bars pointing up show that the driver started **better** than they normally qualify. Downward bars show the driver started **worse** than they normally qualify.

Blue bars mean that the driver was in the top 12 for that draw, while bars in orange indicate they were not. Here’s the graph for Almirola

Almirola did better than usual most of the time: qualifying and draw. He picked up a total of 113 positions from draws, with only two losses of position — and those were the weeks where he fell out of the top 12.

## What About Other Drivers?

To be honest, I don’t know what to with the invert numbers. They don’t really mean anything as far as I can tell. You’re artificially trying to put the fastest cars at the back. So let’s ignore those numbers and just show the data for qualifying and drawing for position.

In the graph below, the green bars are positions gained or lost in the draw. The blue ones are positions gained or lost in qualifying.

But this graph also shows that Almirola has competition for luckiest driver: Matt Dibenedetto gained 122 positions in the draw.

You can argue that a comparison isn’t fair because he moved teams. You can see he made big gains in those races where he qualified, too: about 12.67 positions per race relative to his previous years. If he kept that up and we had qualifying, he would be predicted to gain about **152** positions. That’s less than the 122 positions he got with the draw.

So even though things turn out well for Matt, I think Almirola still qualifies as the luckiest driver when it comes to quarantine ‘qualifying’.

Other drivers on the lucky list include:

- Logano (+79.1 positions from the draw)
- Elliott (+72.4 positions from the draw)
- Buescher (+56.6)

These drivers all gained positions in qualifying and through the draw, with the exception of Elliott, who lost just a few positions in qualifying.

## Who’s the Unluckiest?

Clint may be happy to know that he isn’t first on that list.

- Jones (67.4 positions lost)
- Ty Dilon (-63.2)
- Ricky Stenhouse, Jr. (-60.0)

To dive a little deeper, let’s look at Erik Jones’ race-by-race record.

Jones, like the other two drivers on the above list, hasn’t been in the top 12 for races having a draw for starting position. He had bad finishes at Daytona and Las Vegas and hasn’t been able to pull himself into the top 12.

### Clint Bowyer

One look at Clint Bowyer’s stats and you’ll see that Clint had the same problem — except he was in the top 12 for half of the races with draws. The majority of his positions lost relative to average come when he is in the group where he cannot start any higher than 13th.

Clint can’t blame his whole season on the draw, but it certainly has not helped him. Here’s a summary of the total points Bowyer lost:

- Qualifying: -10.7 positions
- Drawing: -10.7 positions
- Total Qualifying + Draw: -21.4

The run from Pocono to Kansas is where Clint fell out of the top 12. He lost a total of 26 starting positions during that five-race stretch because it was impossible for him to start any higher than 13th.

This is the problem with making someone 13th pick in the same group with the guy who is ranked 24th. They will almost certainly get worse starting positions than they would have if they had qualified.

## Breaking News: How Does the New Scheme Stack Up?

NOTE: Shortly after I finished writing this, NASCAR announced they were going to change the formula. It’s going to be:

- Points position: 35%
- Finishing position at the last race: 50%
- Fastest race lap at the last race: 15%

This is definitely an improvement over what they had been doing. But let’s apply the same type of analysis to this scheme. Thanks to Bob Pockrass, I had a handy list of where drivers would have started at five races under the new scheme.

So I ran the same type of analysis to see how it stacks up.

I know it’s a busy graph, but all you need to look at is who has bars going up vs. going down. Drivers are arranged by car number, just because I was in a hurry.

Clint Bowyer should be happy with this change, along with Keselowski, Harvick, Elliott and Almirola. The latter four would have gained starting positions under the new scheme.

Results for others are more mixed, so let’s add these together and see what we find for new positions gained or lost.

It would seem that the losers under the new scheme are Johnson, Busch (that’s Kyle), and Truex, Jr. Jones and Blaney are also negatively impacted, but to a lesser extent.

And this graph shows that Logano still comes out to the positive.

This graph also tells us something else: Aric Almirola needs to go out and buy lottery tickets.

### What I Like About the New Scheme

It’s not arbitrary. That steep cutoff from 12th to 13th was just killing drivers like Clint Bowyer.

In the spirit of qualifying, it rewards speed by taking fast laps into account.

### What I Would’ve Done Differently

I’m not wild about having the finishing position at one track affect the starting position at the next. Being fast at Bristol often has nothing to do with being fast at a mile-and-a-half track.

One bad finish produces a really significant impact on your starting position, which could produce a downward spiral for some drivers.

## Making Starting Positions Even More Fair

If you want to replace qualifying, I’d argue that you need to use qualifying statistics. And I think you have to go to a weighted draw. (H/T @yetticrg, who pointed out that this is what the NBA does with their draft lottery.)

Basically, the fourteen worst teams (those that didn’t make the postseason) are eligible for those first draft picks. But to be fair (because we don’t have a playoff for worst team), they came up with a format such that:

- The team with the worst record will receive no worse than the fifth pick.
- The three teams with the worst regular season records each have a 13% chance of winning the lottery (getting first pick)
- It goes down from there. The fourth-worst team has a 12.5% of winning the lottery, the fifth-worst team has a 10.5% chance, etc.

This isn’t as complicated as it sounds. If the NBA can do it, NASCAR, with its plethora of engineers and other smart people, should have no problem. Your average teenage coder could write the program in an afternoon.

### Weighted Lottery

A weighted lottery would reward drivers for past qualifying performance a little more than either of the NASCAR methods. )

Instead of putting starting positions in the hopper, you’d put car numbers in. The first ball that comes out starts first. The drivers with more balls in the hopper have a higher probability of being picked for that first position.

The weighted part means that the better your average qualifying position at a track, the more balls with your car number on them get thrown in the hopper. That increases the chance that, for any position, your ball gets picked.

Here’s how it would look pictorially. Let’s say we only have three drivers for simplicity. We’ll call them Blue, Green and Red. In a random draw, each driver has one ball in the hopper. Each driver has 1/3 chance of being picked first.

But let’s say Blue usually qualifies first at the track, red usually qualifies second and green third. We give Blue three balls, Red two and leave green with one. The probability of being chosen first is

- Blue: 3/6 = 50%
- Red: 2/6 = 33.3%
- Green: 1/6 = 16.7%

So Green has less of a chance than under a random draw — which is fair if the chances of Green qualifying first are pretty darn low.

You can play with the number of balls and the weighting to make it ‘fair’.

Doing this with actual balls is needlessly complicated, but a computer with a suitable random number generator would handle it just fine. You could also have the computer run a couple thousand draws to make sure that it works.

You’re going to have some surprises, just like you may have some surprises with qualifying. An Erik Jones or Clint Bowyer may win the pole at a track they don’t normally qualify well at because, well, that’s how probability works.

### A Problem

There is, of course, a problem with this plan. Did you notice I’m only showing you a select group of people in the summary figure above?

There are a lot of drivers who don’t have three years of data. Like every rookie. You’d have to figure out how to treat them fairly — especially a rookie like Cole Custer who will be part of the postseason. Using their average starting position at that type of track (i.e. average for the 1.5 mile tracks, average for road courses) is one possibility

You’ve also got a question about how you treat drivers who have changed teams. Daniel Suárez has the requisite data, but I didn’t include him on the graph. Because he’s running for a non-chartered team, he lost a whopping 262.8 positions on draws this year relative to last year when he was with Stewart-Haas. It totally screwed up my chart. It seems like he deserves a little extra luck to me!

So there you have it. Clint Bowyer had good reason to be upset and should far much better with this new system — although I’m sure we will hear from other drivers.

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