The earlier post Graphing Formula 1 seasons 1985-2018 had its scope limited to 1985-2018 because of how strange the earliest days of the sport were. Several times in the 1950s there were two drivers sharing the race win, or sharing the second place, or both. This does not really work for my approach of visualizing the results by a graph with edges connecting the drivers finishing in positions 1 and 2. But from 1960 onward, every Formula 1 race (with one exception in 1983) had exactly one driver finishing first, and exactly one driver finishing second. So these seasons can still be drawn as graphs, which is done below. Some features not seen in 1985-2018 range are highlighted below.
- Trees: 1961, 1963, 1971. From 1972 onward, every season has a triangle.
- Disconnected forest: 1966
- Bipartite non-tree graphs: 1960, 1969, 1970. All have girth 4.
- Maximal girth: 5 in 1980
- Most vertices: 14 in 1982
- Three connected components: 1960, 1967, 1968
- One edge away from 5-clique and non-planarity: 1973 [also occurred in 2019]
- 1991 and 1998 remain the only pair of isomorphic seasons in the range 1960-present.
Apart from graph-theoretical observations, this period is strewn with driver fatalities in a way that would be unimaginable in modern motorsport. I tried to keep some balance between highs and lows in these brief summaries. No videos of fatal crashes appear here.
(The layout could be better.) Both two small components have something to do with banked oval circuits, something not normally associated with Formula 1 today. The year 1960 was the last year when Indianapolis 500 was a part of Formula 1 championship; it contributed the Rathmann-Ward component after 29 lead changes in the race. Monza race was inconsequential for the championship, which was already won by Brabham. As for Hill-Ginther, the inclusion of Monza’s old banked oval in the Formula 1 race track led to the race being boycotted by several teams, allowing the otherwise uncompetitive Ferrari team to finish 1-2-3.
Phil Hill gets to keep the initial, to avoid confusion with Graham Hill who will appear on this page soon and will stay around for much longer.
Our first tree. One would guess that Gurney should be the winner, but he finished 4th in the championship won by Hill. The teammates Hill and von Trips scored three 1-2 finishes in the season, which only one of them would survive. The fatal crash of von Trips in Monza ended the use of the 10km Monza circuit in Formula 1.
The first appearance of Graham Hill on this page is also the last appearance of Phil Hill. The former won his first championship. At 1962 French Grand Prix, the absence of Ferrari drivers and multiple retirements combined to create the small component.
Another tree. Also the record gap between the largest and second-largest vertex degrees, Clark with 6 vs Ginther with 2. No surprise here: Clark won 7 out of 10 races.
A very close one: Hill collected more points than Surtees, but only the six best results counted for the championship, which went to Surtees.
A single triangle prevents this from being a tree, but it’s one of the most distinguished triangles one could imagine: Clark-Hill-Stewart. They finished 1-2-3 in the season, which was Stewart’s first season in F1.
As if Formula 1 was not dangerous enough in the 1960s, in 1965 French Grand Prix came to Circuit de Charade winding around an extinct volcano, with no run-off areas and with volcanic rocks falling on the track.
The only disconnected acyclic graph in the catalog. At its center, Brabham won his third and final championship. The season opener at Monaco created the small component, with the teams scrambling to adapt to the new engine specifications (3L instead of 1.5L):
Although Stewart won the opener, he would only finish 4th and 5th for the rest of the season.
Another three-component year: Rodríguez-Love comes from the season opener in South Africa, and Gurney-Stewart from Spa-Francorchamps. The triangle Hulme-Brabham-Clark finished 1-2-3 in the driver standings. Hulme somehow managed the feat without a single pole position.
The last (ever?) three-component graph, although the layout does not make this clear. The Siffert-Amon component is not particularly notable, other than being the first victory by a Swiss driver. The Ickx-Surtees component was created at French Grand Prix, the place of Schlesser’s fatal accident.
Five Grand Prix drivers died in racing accidents in 1968, including Clark who won the season opener. Safety measures would begin to be introduced next season at the insistence of several drivers led by Stewart.
At the center of the large symmetric component, Hill won the championship.
Stewart’s first championship. The seasons 1969-1970 produced the only two connected graphs of girth 4.
Stewart and Rindt again appear in a 4-cycle in a girth-4 graph. This time Rindt won the championship, but it was awarded posthumously. On the brighter side, Fittipaldi made his F1 debut this year, and took his first win at the U.S. Grand Prix. The first Grand Prix for a Brazilian driver, and definitely not the last.
The last acyclic graph in F1 history (so far). The natural guess is correct: Stewart was the champion. Fittipaldi is again on an edge of the graph – his appearance is due solely to his 2nd place in Austria, where Siffert took the last win of his career.
Both Siffert and Rodríguez, who appear at distance 2 from the center of the graph, died in separate racing accidents during the year.
Just two years after Fittipaldi became the first Brazilian driver to win an F1 race, he became the youngest (to that point) F1 champion.
This is the closest Formula 1 ever came to a non-planar graph: the only edge missing from a 5-clique is Cevert-Revson. One can imagine a few ways in which a 5-clique could be completed. One was the Dutch Grand Prix, where Cevert was second – if Revson won instead of being 4th. Instead the event was noted for the death of Roger Williamson which better fire safety measures would have prevented.
The final chance to complete the 5-clique was the U.S. Grand Prix, where Revson progressed from last place at start to 5th at finish. But by that point Cevert was already dead. As for Revson, he would be killed in a testing accident a few months later.
This was Stewart’s last championship and last season in F1.
A rare graph of diameter 6, which shares this record with the 1962 and 2009 seasons. The champion, Fittipaldi, is at the center of a wheel subgraph. Three of his neighbors are future champions.
Lauda’s “unbelievable year” in which he won the championship by a wide margin. His only retirement of the season, in Spain, is responsible for the small component Mass-Ickx (poorly placed on the layout). The concerns over the safety of the circuit led to Fittipaldi not taking part in the race. The race cost the lives of five spectators and was ended after 29 laps instead of the scheduled 75.
The Silverstone race was shortened as well, but for a different reason: a strong hail storm. It turned out to be Fittipaldi’s last race victory.
Hunt won by 1 point over Lauda in a season that is difficult to summarize. Lauda had a near fatal crash at the old 22.8 km Nürburgring circuit, which luckily did not end his career.
The following race was in Austria where Ferrari withdrew in protest against Lauda’s disqualification in Spain (and Lauda was in no condition to race anyhow). This race created the Watson-Laffite component and still remains the last F1 race without Ferrari.
Lauda won the championship despite sitting out the last two races of the season, and despite winning only 3 of the races (versus 4 won by Andretti). The season had more than its share of fatal accidents, but I prefer to highlight the Swedish Grand Prix, which was the first victory for Laffite, as well as first for a French team.
Laffite’s victory was unexpected enough that the race organizers did not arrange for La Marseillaise performance during the podium ceremony. Well, better late than never:
Andretti won the championship, and remains the last American driver to do so. Peterson appears on the graph for the last time – he died following an accident at Monza. Fittipaldi finished 2nd at his home race, marking his final appearance on these graphs – although with two grandsons currently racing, we might see the name Fittipaldi in F1 again. In other family notes, the season marked important steps for two drivers who became both F1 champions and fathers of F1 champions: first win of Gilles Villeneuve and first race of Keke Rosberg. Villeneuve’s first victory came at his home race.
Schechter won the championship for Ferrari, the last driver to do so until Schumacher in 2000.
The only non-bipartite triangle-free graph here; it is a 5-cycle with four appendages. The mostly-French cycle of Jones-Piquet-Arnoux-Laffite-Reutermann finished 1-2-6-4-3 in the championship. This was also the debut season of Prost, who does not appear on this graph, but is present on a dozen of the graphs that follow (continuing into 1985-present).
The graph offers little clue to who might win the championship (Piquet did). The French Grand Prix was interrupted by heavy rain when Piquet had the lead. But since less than 75% of the distance was covered, the race was restarted, and Prost won on the strength of the shorter second stint. His first victory could be considered a fluke at the time, but he had 50 more afterwards.
In a messy season that tied the record for diameter 6, Rosberg won despite scoring just one race victory – a situation made possible by a career-ending injury to Pironi, who led the championship at the time of his crash. Villeneuve scored his final victory in San Marino, two weeks before he was killed during qualifying in Belgium. On the brighter side, Lauda un-retired and won twice, preventing the graph from splitting into two sizable components. Without him, Villeneuve-Pironi-Piquet-Patrese would have been the largest small component in F1 history.
A very close one: Piquet by 2 points over Prost. The small component Watson-Lauda comes from the United States Grand Prix where they started 22nd and 23rd, respectively. Winning from 22nd grid position… has not happened in F1 since, and is unlikely to happen anytime soon, given there are fewer than 22 cars nowadays.
Should this small component even exist? Piquet, Rosberg, and Lauda finished 1-2-3 in Brazil but Rosberg was disqualified for a push start. Ordinarily, that would mean that Lauda becomes 2nd, creating a Piquet-Lauda edge, and thus connecting the graph. But no… instead of Lauda and others being promoted, the second place simply was not awarded to anyone. So, oddly enough, this race contributes no edge to the graph.
This time, it’s Lauda over Prost by 0.5 points. How frustrating that had to be, especially considering that Prost won 7 races versus Lauda’s 5. The fractional points came from the rain-stopped race at Monaco.
The Monaco race also contributed the Prost-Senna edge to this graph, in Senna’s first season.