Monday, September 28, 2009

LONG VERSION: Introducing the Watermill Score: The new breathtakingly simple way to estimate NASCAR points system.


(Note: this is the longer version of
what I wrote a month ago.)



Introducing the Watermill Score: The new breathtakingly simple way to estimate NASCAR points system. Why it’s important, and how you can use it to affect race strategy.

I. Introducing the Watermill Score

There is a startlingly basic relationship that almost fully defines the traditional NASCAR points system as it was created by Bob Latford a generation ago.

The current Latford system gives points all the way from first to last, and bonus points for leading laps. You can score anywhere between 34 and 195 points in a single race.

But take a look at this super simple revelation: We can simplify the points system to just this: Add up for each driver just four data points:

Wins + Top 10s + Lead Lap Finishes + Races at the Finish

The total of just these four numbers gets you to basically the same rankings as the current Latford system. We have W+T+L+R. For purposes of this article, and with currently no other name I can think of, I will refer to this number as a Watermill Score. Also notice the letters W, T, L, and R all get used up in there.

II. Examples of the Watermill Score in use

Let’s briefly review two examples:

First consider the driver with the highest Watermill Score in each season this decade. Notice that in every case but one, the driver with the highest Watermill Score also scored the most NASCAR points that season. 2002 is the only exception because of a rare closeness in the competition, where seven drivers were within 226 points of the champion that year.

Notice I am *not* resetting the points for the Chase. I want to look purely at how many total points drivers accumulated during the year. The Chase reset doesn’t allow for a fair comparison.



Now let’s look at our second example, the current 2009 standings. The drivers are sorted by their NASCAR points ranking. But notice that the Watermill Score is broken up into color coded groups by score. In almost every case, the groups are in distinct blocks separating the various drivers. As the Watermill Score goes down, so do the total points for each driver.

With the exception of Mark Martin’s 56 score in the middle of the blue section, notice that each group of scores goes along perfectly with the overall points standings. If Martin had just 26 more points in the standings to go ahead of Newman, then this entire lineup would be 100% in unbroken blocks. Despite this one small difference, you can visually see very easily how the Watermill Score is a very good estimator for the overall points system.

What’s most important is that the Watermill Score has is just as accurate at the top of the points system as at the bottom. Some data (like lead lap numbers) may only be relevant to the Top 10 in points, since most people at the bottom of the standings do not have a significant number of laps led. But this score is consistently accurate throughout the standings. That’s what makes it so valuable.

III. Watermill Score Compares the Best Among Different Estimators

I attempted a modified version of the Watermill Score, using Top 5s instead of Top 10s. It turns out this metric is very good as well, but the original version is slightly more predictive. The table below shows the results, along with the value of some of the most basic metrics commonly cited by industry professionals today:



These correlations were done each year using the Top 30 in the driver points standings. (I only used 30 to remove affect of part-time teams, mid-season driver switches, teams who don’t qualify for every race, etc.)

Some thoughts about the data:

1. The correlation of the Watermill Score is high, repeatable, and consistent:
  • The Watermill Score is more correlated to the points standings than every other metric listed.
  • Notice the minimum score in blue at the bottom, .977, is better than the average score of any other metric, including Average Finish.
  • Average Finish can be deceptively inaccurate in some years (like last year with a .90 correlation and other years with .92 and .94).
  • The Watermill Score is very consistent, and always correlates between .977 and .988 every year this decade.

2. The number of wins by itself is not a great measure of success. In fact wins is a worse predictor than average starting spot.

3. Notice in every single season, Top 10s are a much better predictor of success than Top 5s.

4. Racing at the Finish (inverse of DNF) on its own is not a very important statistic, but when combined with the other data, it becomes very important as a needed measure of consistency.

In conclusion, the data shows us that the Watermill Score is in fact a truly helpful statistic, and it is the best estimator the points standings than any other dataset.


IV. How can the Watermill Score be used to affect race strategy?

Now that we’ve seen the value of the Watermill Score, we can see that the way to maximize your points during the season is to simply focus on four tasks:
  • Finishing races
  • Finishing on the lead lap
  • Getting Top 10s
  • Winning

If you win a race you’ve accomplished all four tasks, earning a Watermill Score of 4 in that race. If you crash out of a race, you accomplish none of these tasks, earning 0 watermills. A lead-lap top 10 earns you 3 watermills.

Notice that the points are split between accomplishing basic tasks (finishing and on the lead lap) while the other half is focused on up-front results (top 10s and wins). This makes a lot of sense to anybody who has been watching NASCAR for years: the Latford system punishes you for bad results just as much as it rewards you for good ones.

Notice that Tony Stewart has 66 watermills this year, an average of 2.75 per race. Matt Kenseth, in the final chase spot, has 53 watermills, an average of 2.21 per race this season. In the entire decade, nobody has ever averaged 3 watermills throughout a season.

Think about what this means for crew chiefs deciding race strategy. If you can walk away from each race with your 3 watermills by finishing in the top 10, do you really want to risk that going for the win, when the possible bad outcome if you finish off the lead lap?

Example 1: Fuel mileage game
You can fill up right now on caution and guarantee yourself a Top 10 finish. The other option is to stay out and hope your fuel will make it to the end. Reward is a win, risk is you run out of gas and finish off the lead lap.

A top 10 guarantees 3 watermills.

A win gets you 4 watermills. Finishing off the lead lap gets you 1.

So if you had a 50/50 shot of making it, the risk-weighted watermill score is .5*4 + .5*1 = 2.5 watermills, which is *LESS* than the guaranteed top 10.
In fact, you’d need at least an 67 percent chance of making it to get your risk-weighted watermill score back up to 3 points, the same as you’re guaranteed top 10. Then you’d have .666*4+.333*1 = 3.0, the same as the guaranteed top 10.

This math suggests that in most cases, unless you are almost absolutely sure you can make it all the way, you are better off not risking a top 10 to go for the win.

However, if you were running further in the pack, and filling up the tank would guarantee you a lead lap finish OUTSIDE the top 10, then your math is very different. Filling up the tank guarantees you 2 watermills, but stretching fuel means you might win (4 watermills) or finish off the lead lap (1 watermill). Now the math is much easier, because you are risking less. All you need is better than a 33 percent chance of being able to stretch fuel for the risk to be worth it.

By just focusing on whether you’ll win, get a top 10, and finish on the lead lap, a crew chief can more quickly and easily come up with the best risk/reward strategy, without having to worry about the more complicated points scheme. As we’ve shown, if you can win the competition of Watermill scores, you will also win the championship.


Example 2: potential flat tire?

Many times we’ve heard a driver complaining that he might have a flat tire. Or we’ve seen instances where there is a fender rubbing the tire, and nobody is sure whether that will cut it down flat. Sometimes it’s not obvious if the tire is actually going down, so what’s a crew chief to do?

Go back to the watermill score. 1 watermill for finishing a race, 1 watermill for staying on the lead lap. Even on bad days, if you can just get out with 2 watermills, that’s not too bad. As we’ve seen, the best seasons average less than 3 watermills per race. So a few 2s won’t kill you, but a few zeros will.

If you pit on green, you’ll probably lose a lap and potentially never recover. If you stay out, and the tire does go bust, you’ll probably crash the car in the wall and won’t finish the race. How do you approach it?

• If you are already off the lead lap, go ahead and come in to fix the tire. At this point your best bet is to get 1 watermill for finishing the race, so you lose nothing extra by falling back another lap or two. Come in and pit, get the new tires.

• If you are on the lead lap, outside the top 10, you have 2 watermills right now. Lose a lap to pit and you have 1 watermill. Stay out and crash and you get 0 watermills. Stay out and nothing happens, you keep your 2 watermills (with some potential upside of reaching the top 10). The math here suggests you only pit if you think there’s more than a 50 percent chance of the tire actually being flat. If you are just guessing, and you think it’s less than a 50 percent chance of being a flat, stay out.

• If you are on the lead lap, in the top 10, you’d now have 3 watermills if the race ended now. Again your options are to crash out, lose laps by pitting, or stay in the top 10 by staying out. In this case you only pit if you are more than 66% sure that it’s a flat. Even a 50/50 guess is worth staying out, because your risk weighted watermill score in that case is .5*3 + .5*1 = 1.5.

• Similarly, if you are leading the race, then you only pit if you are more than 75% sure you have a flat. Since it’s such a big loss to lose those laps, you might as well take the chance on getting your full 4 watermills, stay out and see what happens.

Again, without thinking about the complicated points system, crew chiefs can very quickly think about risk/reward and whether it’s worth pitting now. This depends on where you are running on the track. Be smart about accumulating watermills and you will do well in the points standings.

Example 3: Four tires, two tires, or no tires?

If you are in the top 10 right now, going into the last stop of the race, and fuel mileage isn’t a concern, what is your tire strategy?

If you finish in the top 10, you get 3 watermills. If you take 4 tires, you can guarantee yourself a top 10.

If you take no tires, let’s say that gives you a 20 percent chance of winning (4 watermills), 50 percent chance of finishing in the top 10 (3 watermills), and 30 percent chance of finishing below the top 10 (watermills). The weighted average of all this is .2*4+.5*3+.3*2 = 2.9, or worse than the guaranteed 3.0 you could have had by taking four tires. As long as the chance of falling outside the top 10 is higher than your chance of winning, then it’s a bad strategy. You need your chance of winning to be higher than your chance of falling outside the top 10 for this to be a good idea.

Let’s say by taking two tires you change your chances to 30 percent winning, 60 percent staying in the top 10, and 10 percent falling out the top 10. In this case it makes sense to go with the two tire strategy, since the risk-weighted watermill average here is .30*4+.60*3+.10*2 = 3.2, better than the 3.0 you’d get for taking four tires.

Again, these examples do not focus on what specific place you are in or what your competitors in the standings are doing. I also do not give you the specific percentages for what different gambles are worth. That’s where a good crew chief comes in, using his smarts and experience. What I am suggesting is a simple way to take those percentages, risk-weight them to the watermill score, and be able to more simply and quickly come up with appropriate race-time strategy. Because the overall points system is too complicated to quickly figure out, by following this simpler program, and thinking about the four simple tasks (winning, top 10s, lead lap finishes, finishing the race), this concept can help teams look past all the endless combinations of results and focus only on these four tasks that matter, and that can help them win a championship.


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