What was the fastest 100m final?

Over the past 10 years, we've seen a number of exceptional sprint performances at the world class level. Of particular note has been the recent emergence of a handful of contenders to the title of "World's Fastest Man". A decade previous, we would have been talking Ben Johnson and Carl Lewis. Today, we find it hard to choose between Donovan Bailey, Frank Fredericks, Ato Boldon, and Maurice Greene. Of course, we can't forget (recently stepped-down) European Sprint King Linford Christie, or former WR holder Leroy Burrell. The increase in number of top world class sprinters makes one wonder: what really was the fastest 100m final?

Recently, I've written several articles which have discussed correcting for wind effects in the sprints: this provides an easy way to compare most 100m times run in essentially any wind condition (head- or tail-wind). Unfortunately the model doesn't take temperature into account, but susceptibility to temperature must almost certainly be an individual factor (proof: I find 15 C weather pleasant and cool, while all other Californians don their parkas). The findings have been most interesting, and have re-written the record books to a certain degree.

In the following article, I will analyze the results from key races over the past 10 years. These include the 1983-1997 World Championships (WC) finals, 1984-1996 Olympic Games (OG) finals, and the 1996 Lausanne Grand Prix (LGP) final, in which Frank Fredericks ran his 9.86s PB into a 0.4 m/s headwind. The latter race was considered by many to be the finest 100m performance ever. In fact, after wind-correction, this adjusts to a calm 9.84s, numerically matching Donovan Bailey's 9.84 (+0.7 m/s). Meanwhile, Bailey's WR mark translates to a 9.88s, and is usurped by Fredericks' Lausanne run (Table 1).

Table 1. Top 3 fastest indivuduals (as of 01 Sep 1997)
1. Frank Fredericks	9.84 (9.86, -0.4)	Lausanne GP	1996
2. Donovan Bailey	9.88 (9.84, +0.7)	Atlanta OG	1996
3. Maurice Greene	9.88 (9.86, +0.2)	Athens WC	1997

Fastest average race times

<\table> Note, however, that even though they were monumental races of their day, the 1987 WC and 1988 OG runs are ranked last! This is due to the fact that the last place finishers in each race (Pierfrancesco Pavoni ITA - 16.38, Ray Stewart JAM - 12.26) were obviously not running at peak potential. This raises a serious concern when dealing with the *overall* average times of races.

It seems logical that one can divide a race into two distinct groups: the top 4 or 5 finishers are most likely the serious medal contenders, and can be taken to represent the "quality" of the final. Those who finish 5th-8th do so for any number of reasons, which might include: (a) they don't match the calibre of the top finalists, and finish at the best of their ability, (b) they pull up in the race or are running injured, or (c) they shut down before the finish line because of mental duress (e.g. Merlene Ottey at the 1997 WC).

The average winning margin

Since the overall average time for a final can apparently be misleading, as per the conclusion of the previous section, it might make more sense to consider the *average winning margins* of each race. That is, by how much, on average, did the gold medallist defeat his competitors? Adhering to the KISS principle (Keep It Statistically Simple, not developed by Gene Simmons), there is a straightforward expression for calculating this beast:

The winning margin can help up compare top finishing places in different races, and can provide more information besides just how far ahead of the rest of the field was the gold medalist.

While the results from each race are wind-corrected to provide an easy ground for comparison, the quantity above is essentially independent of this correction. In a typical world class race (where the first and last place times fall within about a 0.3s interval), wind-correction roughly amounts to a shift of an overall constant (a couple hundredths of a second), and this overall constant cancels out in the above equation (trust me!). So, the average winning margin as calculated by this method will be the same regardless of whether or not the times are wind-corrected or official.

Tables 3, 5 rank the average finishing times for the top 3 and 4 competitors, while Tables 4, 6 order the winning margins in increasing order. This gives a sense of the "closeness" of the race: the smaller the average winning margin, the closer the finish, and the closer the calibre of the athletes in the final.

Table 2. Fastest Races (average, all competitors)
1. 1996 LGP	9.981s
2. 1993 WC	10.029
3. 1996 OG	10.033
4. 1991 WC	10.038
5. 1997 WC	10.044
6. 1992 OG	10.133
7. 1995 WC	10.161
8. 1984 OG	10.238
9. 1983 WC	10.249
10. 1988 OG	10.417
11. 1987 WC	11.100

Table 3. Fastest top 3 finishers (average)
1. 1996 LGP	9.890	(1. Fredericks 9.84, 2. Bailey 9.91, 3. Boldon 9.92)
2. 1996 OG	9.917	(1. Bailey 9.88, 2. Fredericks 9.93, 3. Boldon 9.94)
3. 1997 WC	9.923	(1. Greene 9.88, 2. Bailey 9.93, 3. Montgomery 9.96)
4. 1993 WC	9.947	(1. Christie 9.89, 2. Cason 9.94, 3. Mitchell 10.01)
5. 1991 WC	9.953	(1. Lewis 9.93, 2. Burrell 9.95, 3. Mitchell 9.98)
6. 1988 OG	10.030	(1. Lewis 9.99, 2. Christie 10.04, 3. Smith 10.06)
7. 1992 OG	10.037	(1. Christie 9.99, 2. Fredericks 10.05, 3. Mitchell 10.07)
8. 1995 WC	10.070	(1. Bailey 10.03, 2. Surin 10.09, 3. Boldon 10.09)
9. 1987 WC	10.110	(1. Lewis 9.99, 2. Stewart 10.14, 3. Christie 10.20)
10. 1984 OG	10.133	(1. Lewis 10.01, 2. Graddy 10.21, 3. Johnson 10.24)
11. 1983 WC	10.249	(1. Lewis 10.06, 2. Smith 10.20, 3. King 10.23)

Table 4. Smallest average winning margins, top 3.
	Winning margin	Deviation from WR
1. 1991 WC	0.035	0.035
2. 1996 OG	0.056	0.056
3. 1995 WC	0.060	0.160
4. 1997 WC	0.065	0.063
5. 1992 OG	0.071	0.147
6. 1996 LGP	0.075	0.060
7. 1988 OG	0.080	0.060
8. 1993 WC	0.086	0.067
9. 1983 WC	0.155	0.243
10. 1987 WC	0.180	0.180
11. 1984 OG	0.215	0.203

While the increase from 3 to 4 finishers rearranges the lists, there are several key constants of note. In each case (Tables 3, 5), the fastest average race is the 1996 Lausanne Grand Prix, the wind-corrected World Record race which produced Fredericks' headwind 9.86 dash. The Atlanta final (1996 OG) takes 2nd and 3rd place in the averages rankings, trailing the 96 LGP average finishes by roughly 0.02s. It posts the 2nd smallest winning margin for top 3, but slips to to 4th for the top 4 finalists.

Table 5. Fastest Top 4 Finishers (average)
1. 1996 LGP	9.913	(4. Drummond 9.98)
2. 1997 WC	9.935	(4. Fredericks 9.97)
3. 1996 OG	9.945	(4. Mitchell 10.03)
4. 1991 WC	9.963	(4. Christie 9.99)
5. 1993 WC	9.970	(4. Lewis 10.04)
6. 1988 OG	10.050	(4. Mitchell 10.11)
7. 1992 OG	10.058	(4. Surin 10.12)
8. 1995 WC	10.085	(4. Fredericks 10.13)
9. 1987 WC	10.148	(4. Kovacs 10.26)
10. 1984 OG	10.165	(4. Brown 10.28)
11. 1983 WC	10.188	(4. Wells 10.26)

Table 6. Smallest average winning margins, top 4.
	Winning margin	Deviation from WR
1. 1991 WC	0.044	0.044
2. 1997 WC	0.073	0.075
2. 1995 WC	0.073	0.175
4. 1988 OG	0.080	0.080
5. 1996 OG	0.087	0.087
6. 1992 OG	0.091	0.168
7. 1996 LGP	0.097	0.083
8. 1993 WC	0.107	0.090
9. 1983 WC	0.171	0.268
10. 1987 WC	0.211	0.211
11. 1984 OG	0.233	0.235

The 1991 WC final holds its ranking as the "closest" race, yielding a winning margin of 0.035s and 0.044s for top 3 and 4 placings. As noted earlier, this race posted the most sub-10s marks ever, but after a wind-correction treatment, the average top 3 and 4 times rank only 5th and 4th, respectively. This is a good example of how a race can seem faster than it really is because of tailwind effects, but even after correction can still be considered quite an impressive sprint!

Conversely, the races with the lowest average for top 3 and 4 are the 1984 OG and 1983 and 1987 WCs. Likewise, these represent the largest average winning margins. This information is quite useful: in each race, Carl Lewis was the clear winner. Apparently he was quite ahead of his time! Interestingly enough, Lewis is also a factor in the 1991 WC race, posting his legal (and new WR) 9.86s jolt.

The 1987 WC and 1988 OG

Table 7. Stats for 1987 WC and 1988 OG, including Ben Johnson's performances.
Race	Overall average	Average (no 8th)	Average top 3	winning margin	Average top 4	Winning margin
1987 WC	10.948	10.193	10.007	0.176	10.055	0.220
1988 OG	10.417	10.059	9.970	0.180	9.985	0.180

Despite the anomalous last place times, the winning margin considered earlier is unaffected by these. For the Johnson races, we have the average top 3 times of 10.007s and 9.970s, with similar respective winning margins of 0.176s and 0.180s. According to this, the Seoul final would rank 6th for top 3 finishers, and would mark one of the largest winning margins for the races considered. In terms of top 4 finishers, we have 10.055s and 9.985s, with winning margins of 0.220s and 0.180s. Again, these constitute some of the largest winning margins, and help to show that Ben Johnson's performances were well in advance of the rest of the world (if we ignore *why* they were at such a level).

Winning margins and World Record progression

Table 8. World record progression, 1983-1997.
9.93A (+1.4)	Calvin Smith USA	03 Jul 1983	Colorado Springs
9.93 (+1.0)	Carl Lewis USA	30 Aug 1987	Rome
9.92 (+1.1)	Carl Lewis USA	24 Sep 1988	Seoul
9.90 (+1.9)	Leroy Burrell USA	14 Jun 1991	New York
9.86 (+1.2)	Carl Lewis USA	25 Aug 1991	Tokyo
9.85 (+1.2)	Leroy Burrell USA	06 Jul 1994	Lausanne
9.84 (+0.7)	Donovan Bailey CAN	27 Jul 1996	Atlanta

For the cases where the WR was set in the race, the winning margins and the deviation from the WR are the same, since they're calculated in exactly the same manner. For the other cases, the method is slightly modified. Instead of using the earlier expression involving the fraction k/(k-1), we just simply subtract the WR time from the average of the top 3 and 4.

Note a slight difference here. In order to obtain this quantity with a minimal amount of work, I have *not* wind-corrected these quantities. Had I done this, I would have spent quite a while going back through the record books to find the wind-corrected WRs of each year, since we know that a great performance can be masked by a suitably strong head-wind (e.g. Bailey's 10.03s in Abbotsford earlier this year). So, to make the numbers more "useful" to the naked eye, the wind conditions are not performed, which can skew the data a bit when the wind conditions for the WR race are sufficiently different for the race in question (case and point: the 1996 LGP winning margin v.s. the deviation from the 9.85 WR).

Musings

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