Wednesday, March 31, 2004

Mat Mladin was not my first choice to win the Daytona 200. Nor my second. In fact, I doubt I would have made him my third choice. How wrong I was. In fact, nearly every opinion I had before the race was proven soundly wrong in the end by Yoshimura Suzuki.

The biggest surprise to everyone who thought they knew the Daytona 200 was that a three stop race strategy could be superior to a two stop race. In post-race interviews Mat Mladin revealed that his team held a three hour long skull session in the hotel room one night and poured over every bit and byte of available data from the 2002 race. In the end the teamed decided that a three stop strategy was faster than a two stop.

To put Mladin and company's theory to the test, I entered lap times provided by the AMA for the six factory sponsored riders into Excel and created race models for the two stop and three stop strategies. But before I delve into that, a re-cap of the race.

I have always found that reports or charts showing interval times from the race leader for every lap of the race provides the best view, in numbers, of what happened in the race. From the interval time chart one can see that Ben Bostrom, Eric Bostrom, and Miguel DuHamel pulled away from Mat Mladin, Aaron Yates and Jake Zemke over the first three laps of the race. Mladin and Yates caught back up over laps four and five while Zemke, due to being farther back at the start, needed three times as many laps to catch the leaders.

By lap ten we had a six rider lead group. The following lap Yates was four seconds out of the group after missing the entrance to the chicane. Mladin and Zemke lost distance when they made room for Yates' cut across the chicane.

Eric Bostrom grabbed the lead at this point. Ben Bostrom and DuHamel stayed with Eric Bostrom, and the trio gradually opened a gap over Zemke and Mladin while Yates was a lonely sixth.

Eric Bostrom pitted on lap 15 and re-joined the race 25 seconds down. Mladin pitted on the following lap and was 28.563 seconds after his out lap. But considering that Mladin was 6.641 seconds from the leaders when he pitted, Mladin made a pit stop and out lap approximately three seconds faster than Eric Bostrom.

Ben Bostrom controlled the lead way out until lap 21. The elder Bostrom then pitted and promptly rubbished the clutch of the Honda.

By lap 22 the five remaining factory riders had each had one pit stop. Eric Bostrom had a two second lead over Mladin. Yates was 5.5 seconds down from Bostrom, while DuHamel and Zemke were a long 15 seconds away from Eric Bostrom.

Mladin crept up to Bostrom over the next four laps, and at the halfway point of the race it was a two rider run for the lead. Yates was now fading away, quickly, while Zemke and DuHamel were losing time at a rate of half a second per lap.

Leaders Bostrom and Mladin pitted together on lap 30. Yates was promoted in to the lead, but his advantage over Zemke and DuHamel was shrinking fast.

Like the first pit stop, Mladin put three seconds on Eric Bostrom at the second pit stop. Eleven seconds behind leader Yates at this point, Mladin made up time at the astonishing rate of four seconds per lap over the next three laps.

The effectiveness of the three stop strategy was proven by lap 35. A mere 1.272 seconds covered the remaining five factory riders, though Mladin and Eric Bostrom had pitted twice, while Yates, Zemke, and DuHamel had pitted once. All five riders were planning another stop, though Yates, Zemke, and DuHamel needed to get more laps out of their tires. That is, Bostrom and Mladin needed to make their final two sets of tires last 27 laps, DuHamel needed needed to make his final two sets of tires last 37 laps, and Yates and Zemke needed to make their final two sets of tires last 40 laps.

Mladin took the lead on lap 37 for the first time since his holeshot at the start. Eric Bostrom was putting heat on Mladin while Zemke and DuHamel faded out of view. Yates was a half minute behind after his second pit stop on lap 37.

Zemke and DuHamel pitted on laps 40 and 41, respectively. Bostrom led for three laps after following in Mladin's tire tracks for three laps. Then the oil cooler on Bostrom's Ducati started leaking and Bostrom's race was over.

Note to self: never ride directly and closely behind a Yoshimura Suzuki GSXR1000 superbike at 180 mph on racetracks with small stones on the surface.

Mladin then held the lead until the end. A pit stop on lap 45 resulted in Mladin sharing track position with Yates. Mladin lapped the circuit a half second quicker a lap over the next two laps. Yates was out two laps later after the infamous incident with Anthony Fania. Zemke and DuHamel, several seconds behind Mladin, never threatened the tough Australian over the remaining laps.

The lap time chart is most helpful in understanding pit stops. Pit stop laps stand out of the spaghetti and meatballs of lines and data points from racing laps. Here we can see that the Yoshimura Suzukis were clearly the quickest on the combination of pit stop and out lap time. Of all the Yoshimura pit stop laps Yates had the best, at 2:11.635, on the first pit stop. The next fastest pit stop laps were Mladin's third, second, and first at 2:11.914, 2:12.803, and 2:13.483, respectively. Yates' second pit stop was fifth fastest overall at 2:14.828. The next two fastest pit stop's were Eric Bostrom's at 2:15.427 and 2:16.647.

The slowest pit stops for the factory teams were the Honda riders. Yes, yours truly wrote on ?Soup Net before the race that the Hondas would have the fastest stops - another dead wrong prediction. Jake Zemke did his two pit stop laps in 2:16.801 and 2:16.869, and Miguel DuHamel did his in 2:17.326 and 2:17.491.

DuHamel's pit stop laps were, on average, 4.68 seconds per lap slower than Mladin's. DuHamel's two stops cost him over nine seconds on the track to Mladin, and DuHamel finished the race 7.095 seconds behind Mladin. You don't need to be an Einstein to figure out why DuHamel did not win.

The lap time data is most interesting when by the stint lap number. The out lap after a pit stop is assigned the value one and following laps are counted from there.

In Mladin's case one can see that his third stint lap is usually his best, though the second stint lap is nearly as good. Lap times begin to steadily increase after the third stint lap. The final stint lap has the highest lap time, after excluding the first stint lap, of course. But the final stint lap includes the entrance in to the pits which should be expected to be slower than a normal racing lap (please note that the factory teams pit well beyond the timing and scoring antenna loop that crosses pit road).

Jake Zemke's stint lap times are interesting to compare to against Mladin's Zemke's lowest lap times tend to come about five laps into the stint, versus three laps for Mladin. Further, Zemke's second stint lap times tend to be rather high, suggesting that Zemke needs a bit more time to be comfortable with his tires.

DuHamel and Yates, on the other hand, generally produced their lowest lap times on the second stint lap. Yates' data shows an outlier data point from lap 11 of the first stint. This was the lap Yates missed the back straight chicane. If one ignores this sole outlier data point Yates' lap times show quite consistent trend, much like Mladin's - and, in my eyes, better than either Zemke's or DuHamel's.

Eric Bostrom's lap times are a different story. Unlike the previous riders, Eric Bostrom's times were quite low and failed to increase significantly through the stint. The reason for this difference could be one or several factors: Bostrom's Ducati being a V-twin and the other riders' bikes being in-line four cylinders, or Bostrom's use of Michelin tires and the other riders' use of Dunlop tires, or simply due to a difference in riding style. Whatever the reason, Eric Bostrom's lap times were fast, and consistent from lap to lap and stint to stint.

The qualitative trends observed in the data can be quantified by descriptive statistics. Over the years the most frequent statistical question I have been asked regarding lap times is which rider had the lowest time. Yet my personal favorite statistic is the median lap time. The median lap time is a time where there is an equal number of laps faster than this time and an equal number of laps slower than this time. It is a good representation of the average racing lap time of a rider, and much better than taking the arithmetic average of the lap time data. The arithmetic average includes pit stop laps and other laps a rider would rather not talk about. These unusually high lap time laps have a strong influence on the average value, yet little influence on the median value.

The variation in lap time data is also important in analyzing a rider's performance. Normally one would calculate the standard deviation of the data to quantifying variation, but I do not like that approach. Like the arithmetic average, the standard deviation uses all the laps, including the unusually long lap time laps, and I find it to be misleading. I prefer taking the difference between the fastest lap time and the median lap time to represent lap time variation. The lower this difference, the lower the variation in lap time data. This is simple to calculate, and simple to explain to the statistically-challenged members of the paddock.

The increase in lap time per lap can also be calculated using linear regression. Linear regression finds the equation for a straight line that best fits through a set of data points. The slope of such a line is the rate that lap times increase per lap. In calculating slope values I ignored the lap times from the initial lap of the stint - and in Zemke's case I ignored the first two. I also ignored the final lap times of each stint, except for the final lap of the final stint from Yates, Zemke, and DuHamel (Yates had not slowed down before his surprise crash, and Zemke and DuHamel were fighting for second and valuable points on the final lap of the race. Mladin's last lap looked like a cruiser by his standards after building a modest cushion over Zemke and DuHamel).

The final descriptive statistic I looked at was the average out lap time. The out lap, as a reminder, consists of the pit stop and first lap that follows.

These statistics for the six factory riders are:

Rider | Fastest | Median | Difference | Slope | Out Lap |
---|---|---|---|---|---|

Mladin | 1:49.913 | 1:51.084 | 1.171 | 0.176 | 2:12.733 |

DuHamel | 1:49.447 | 1:51.608 | 2.161 | 0.138 | 2:17.409 |

Yates | 1:50.029 | 1:51.559 | 1.530 | 0.209 | 2:13.232 |

E.Bostrom | 1:49.227 | 1:50.925 | 1.698 | 0.063 | 2:16.110 |

Zemke | 1:50.159 | 1:51.580 | 1.421 | 0.132 | 2:16.835 |

B.Bostrom | 1:49.493 | 1:51.081 | 1.588 | 0.113 | n/a |

These values show that Mladin had an advantage in consistency on the race track, and quickness in the pits and getting back up to speed. Mladin, like teammate Yates, had lap times that increased at a rate higher than the other factory riders. Why this was so could be debated until next year's Daytona 200: did Mladin and Yates push their tires harder at the beginning of the stint and cause some sort of over-stressing? Did the Yoshimura Suzuki GSXR1000 superbikes have different engine and/or drivetrain characteristics that over stressed the tires? Or different suspension set-ups that were unfavorable to the tires? It's an impossible question to answer conclusively.

The biggest question though was: what advantage did Mat Mladin gain from a three pit stop strategy?

To answer this question I made a mathematical lap time model from Mladin's actual lap times. The model assumed the following:

1. The lap time for the start lap is independent of a two stop or three stop strategy.

2. The lap times for the in laps (last lap of a stint) and the out laps are independent of a two stop or three stop strategy.

3. The lap times for laps between start/out laps and in laps can be predicted from the equation: Lap Time = 0.176*(Stint Lap Number) + 1:49.722. This equation was derived from a linear regression of Mladin's actual lap times, excluding start, in, and out laps.

4. The lap times for in laps is 1:54.591. This is the average value from Mladin's three in laps.

5. The lap times for out laps is 2:12.733.

6. Stints are 19 laps long for a two stop strategy, and 14, 14, 14 and 15 laps long for a three stop strategy.

With this set of assumptions the predicted total time for a three stop race is 1:46:47.670. This is marginally faster than Mladin's actual race time of 1:46:51.490. Reasons why the predicted time is better than the actual include that Mladin's actual final race lap was ignored from the linear regression since the time suggested that Mladin was riding the race out rather than trying to impress the stopwatches. Another possible reasons is that Mladin's stint lengths were different from the lengths used in the predicted time model.

For a two stop race the predicted total race time is 1:46:44.437. This approximately three seconds faster than the predicted time for a three stop strategy.

That either strategy has approximately the same total race time should not come as a surprise. Mladin's teammate Yates, using a two stop strategy, was within a second of Mladin on laps 35 and 45. I have to assume that the equipment and tires available to Yates were available to Mladin.

Of course there are probable a number of other factors not included in the model that exist in actual racing. For example, the model assumed that lap times increase linearly. Mladin's race times tended to increase somewhat quadratically; that is, the time lost per lap was relatively low at the beginning of Mladin's stints and relatively high towards the end of the stints. Tires are another factor - maybe the factor. Tires have a finite life, and if Mladin believed that tire life was not substantially better than 19 laps, then a three stop strategy is a no-brainer. Indeed, slow motion video broadcast during the race suggested that Mladin had a dubious rear tire at the end of one stint due to variations in blackness as the wheel revolved.

In the end it seems to me to be a question of where a rider places more confidence: in his tires, or in his pit crew. In Mladin's case the race result speaks for itself.