The Vonderhoff index (Vonder Index or the Vanderhoff’s) is a male singles’ tennis algorithm designed to determine the « Greatest Of All Time » (GOAT) in the sport of Tennis.
Unlike the majority of GOAT rankings, it has no subjective component, that to say it is entirely based on data and statistics without a hint of human opinion or bias.
The methodological approach is also rather original in regard of current forms of All Time Greats (ATG) listings. It does not attribute intrinsic values to any metric. It means that in tennis, Grand Slams (GS) do not have any given points (ie 2,000) nor credits (like 5 stars), but rather they are all dynamic.
Therefore GS, like any other statistics, are given values according to their actual worth in the (GOAT) critical path. Any change in this path alters all values under its chain, automatically.
The critical path determines what any metric (like Slams or weeks #1) is worth for and not according to anyone’s opinion or personal criteria. This is a breakthrough approach in terms of tennis ATG listings or GOAT debates.
Invariably people, players, coaches, journalists and experts will disagree on relative values of Grand Slams (or Titles), Weeks #1 (or Rankings), H2H (or Rivalries). However they all should have a common understanding that if a player holds the record of all relevant achievements, he must be undeniably the greatest of all.
Naturally such player does not exist, at least physically. What Vonder Index does is materialising such perfect player in order to have all others compared to him.
Applying this rational empirically we can build a perfect player (or the « Ghost Player » under Vonder Index) and have all record marks and statistics attributed to him. Despite all (social and mainstream media) ontological debates over « what’s worth how much », all players can simply be compared to the perfect one (Ghost Player) and therefore be isonomically measured.
This methodology also implies that all criteria used to measure GOATs must have dynamic values. Since the Ghost Player holds all relevant records in the field, any record breaking achievement (e.g. 311 weeks #1, 20 GS) also elevates the Ghost Player’s silhouette - the critical path itself.
For example, a GS is valued, not by anyone’s opinion, but for its own record: 20. On Open Era terms it has already scratched the marks of 8, 11, 14, 17. Similarly, Weeks #1 also followed the same pattern: 268, 270, 286, 302, 350(?); and so does the YE#1: 5, 6, 7.
By applying the scarcity concept to it, we have an ever growing Ghost Player which dwarfs previous record holders. Intuitively, winning a GS today (20-19=1) is not like winning it in the 80s (11-10=1). Spending a 75 weeks as #1 in the 80s may place a player among the Top5 of all time (Open Era), but doing so in the 2020s may not even be enough to make you a Top10.
Methodologically that is because the critical path to become the Greatest Of All Time has been altered (prevailingly upwards). The abundance of a metric naturally turns any unit of it less relevant (marginal utility).
It does not mean new 2020s GS champions are credited less than 1980s champions, but that both are diminished - an 1980s GS is worth 1/20 in as much as a 2020s GS has the same 1/20 value. It only infers that winning a GS or having 75 weeks #1 (w#1) are less relevant to the world of tennis as they were in the 1990s for example. Think of how rare were double digit Open Slam champions in the 90s (only Sampras-14 and Borg-11) and how dwarfed they were by Roger, Rafa and Novak (each 20).
Of course, being a #1, winning Big Titles or Majors also depend on the quality field. The aforementioned dynamic characteristic of the Vonder Index aprioristically does not explain it. But nor does the monochromatic (there-can-only-be-one metric) and binary (havs-n-hvnots) biased « only-Slam » rankings do (a GS is a GS regardless of when, against who and how it was won). Nonetheless the Vonder Index do have a clever tactic to address this universal shortcoming - it is skeptical.
The algorithm used in the Vonder Index incorporates a series of correlation-based adjustments so that any metric must be backed by another otherwise it will be rendered as an outlier. That is how it tackles a particular competition of an Era, or more specifically the variations on the level of field.
In this case, if a player is good enough to be considered an ATG but could not collect that many Slams because he played in an Era which competition featured two or three GOAT contenders, it will sill be held high in the index. It may be superfluous to GOATs (since the greatest of all time in theory should not have feared anyone else) but it is extremely relevant to ATGs (whose careers may be affected by the amount and level of GOATs they’ve competed against).
For example: Laver, Djokovic, Borg, Sampras have great careers regardless of the field or rivalries they’ve faced. But think of Boris Backer (not many w#1) and Andy Murray (not many GS) for an instance, both faced 2-3 GOATs (contenders) in their respective Eras (Lendl,-Sampras, Federer-Nadal-Djokovic). It is of common sense that if it wasn’t by the competition they’ve faced, it is highly probable their tennis level or game play would have awarded them more achievements in other « weaker », or better put « less dominant » Eras.
The index expresses it on its rankings, reflecting not only the actual glories conquered but also the potential power of each player according to their own stats and regardless of the Era they’ve played on.
On the other hand, Vonder is also very demanding of its subjects. Any player whose achievements excel those of other similar peers is required to back them up, otherwise it won’t be praised in the same proportion to its single-strike or lucky-hand lonely achievement(s). For example, Marcelo Rios, Jan Kodes and Mark Edmondson lack of convincing overall careers to justify their extremely high-level conquers, therefore their glories are still fully counted but their Vonder Rankings do not equals those of other multi-slam champions or #1 ranked players (despite being very good players and wonderful people though).
How does the algorithm recognises such patterns? Quite simple, it is holistic. And here we might dig into « Tennis Philosophy ».
The Vanderhoff method presents an holistic approach to the game of tennis. It does not reduces it to one single aspect, but evaluates all relevant sides of the sport on hierarchical order (not all titles are Slams, not all rankings numbers are #1).
Under Vonder Index, Tennis is viewed as a spectrum, composed of several layers measurable by metrics, ranging from the shortest to the longest lapses of time or, equivalently, from the least to the most complex set of actions.
As a consequence we have a wide arch ranging from « ball-hits » (shortest set of action) up to centuries (widest time lapse), being these both unmeasurable variables. In the measurable variables we have an open lacquered-fan beginning with « points » the smallest relevant metric to the largest relevant metric which are decades.
Notice that we do have smaller metrics such as service% but these are not actually relevant to the game of tennis - Top5 1stServ# : Schaller 75.7%, Barasetegui, Starace, Arese, Thierry Champion (hardly ever heard of). Points won/lost on the contrary, are much more correlated to GOAT metrics: Nadal 54%, Djokovic, Federer, Sampras, Agassi (computed since 1990).
Same is valid for the larger beyond a decade measurers, like longest career matches’ span: Muster 27 years, Connors, Bahrami, Vilas, Lopez (just a few asymmetric coincidences). However the most Slams by decade account goes with GOATs: Federer/Djokovic 15, Sampras/Emerson 12, Tilden 9, Borg 8. Another decade counter in #1 weeks displays: Sampras 276w-1990s, Djokovic 275w-2010s, Federer 268w-2000s, Connors 251w-1970s, Lendl 238w-1980s; again only GOAT contenders.
As seen, the metrics must be measurable (otherwise impossible) and relevant (otherwise meaningless). But two other criteria shall be observed: rewardability and officially measurement.
Points, in as much as games and sets, might be official, measurable and relevant, but they are not rewardable. The most Points won does not give you the Match (as clarified by Wimbledon’s 2019 final). However, the most Matches won do give you the Title.
Decades may be rewarding, measurable and relevant reflecting GOAT contenders with some accuracy. But what criteria should we used for it: most GS or w#1 count? Should it start on 00-09 / 10-19 or 95-04 / 05-14? Perhaps from 2021-30, respecting official calendars, given that year « 0 » does not exist. There is no consensus nor is it an official metric (as consequence).
Having distinguished all measurable, relevant, rewarding and official metrics in the Tennis game spectrum, we were able to narrow our scope. Putting extremities aside (points/decades) and can now focus on the very 3 pillars of the sport:
- Matches ;
- Tournaments ;
- Seasons .
All these 3 metrics are comfortably placed on the larger central portion of Tennis arch. They are interconnected in proportion to their equidistance. Seasons are composed by tournaments campaigns which in turn are composed by matches won.
All 3 factors are proxies of well known concepts of the sport:
- Rankings, measuring seasons;
- Titles, measuring tournaments;
- Rivalries, measuring matches.
Those 3 measures are the most proper reflection of the game of tennis. Without them the sport would be meaningless. For example, it is impossible to:
- conquer a Title without winning matches in a tournament (playing career rivals, Top10s, lower-ranked opponents);
- be the #1 in the Rankings without having good runs in tournaments (majors, ATPs, titles, finals, quarters);
- having a superior winning percentage or H2H also depends on how high you are ranked (Top4 seeding, top 32) so that to play lesser ranked opponents until later stages (same with career rivals, whose rankings less or so reflect their current game level).
Needless to say we need to focus on a plausible number of metrics in order to better reflect the reality of any ATG/GOAT listing. Therefore the choice between #1weeks or months, Year-End#1 or 104 weeks rankings, ATP1000 or Olympic games, H2H or W/L%, all depends on what is more hierarchically relevant/representative to tennis. And here is where the complexity of Vonder Index contrasts with its seemingly simple composition.
The algorithm used in Vonder Index uses only 9 metrics disposed into a 3x3 matrix. It allows us to have the exact same index value seen from 6 different angles (vertical/horizontal).
It’s holistic nature is evidenced by the contemplation of all 3 possible (that to say relevant, measurable, official, rewardable) criteria (represented by time-lapses or action-sets) pillars of the game, each of them divided into 3 metrics (manners in which we can measure a given criteria).
Beyond the Ranking / Titles / Rivalries’ pillars, we also have another listing systematisation, according to which hierarchical levels are observed. This feat is specially relevant for ATGs but also serve to the purpose of deepening GOAT’s figures, hence:
- Prime level, comprising a player’s own peak achievements and how he
performed versus other peaking opponents;
- Elite level, involving the most solid, deep and meaningful achievements;
- Career level, expressing the longevity and broad career building of these athletes.
Accordingly, the GOAT player must invariably have a wide range of good results supporting each of his great feats, instead of only one or two good criteria of excellence. Indeed, the following names comply with this pattern adamantly, in chronological order:
- Djokovic
- Nadal
- Federer
- Agassi
- Sampras
- Becker
- Edberg
- Wilander
- Lendl
- McEnroe
- Borg
- Connors
- Laver (out of OE stats)
- Rosewall (out of OE stats)
Any combined metric featuring this 12 (14) players must be regarded as highly correlated to actual GOAT statuses. Specially if further featuring Ashe, Newcombe Nastase, Vilas, Courier, Kuerten, Hewitt and Murray.
All these players have in common the fact they excel over all 3 criteria, notably: (i) Rankings/Seasons, (ii) Titles/Tournaments, (iii) Rivalries/Matches; it is of utmost certitude this methodology is empirically accurate.
Evaluating the 3 pillars in another aspect, we may affirm:
- Rankings/Seasons mean dominance;
- Titles/Tournaments bring greatness;
- Rivalries/Matches reveals consistency.
In a similar assertion:
- conquering titles determines the best among the best - one must the champion (GOATs are not runner-ups);
- having a robust winning % and solid H2H records means a consistency capable of weathering of competition fields - one must be the victor (GOATs are not losers).
This holistic characteristic explains with perfection why some players are ranked lower/higher than what their rankings or titles’ palmarés may suggest.
The consistency they’ve shown throughout their careers in W/L% (rather than on « that epic final ») are the backbones of their game. Tennis is a sport played inside a court, with real opponents/rivals, not on rankings tables or displayed on the shelves. Matches show how good you were inside those net-halved four lines.
A quick observation regarding all 3 criteria. Tennis is often reduced to Titles or even just Slams (also inaccurately used as synonyms of Majors). However real dominance is displayed in rankings and actual tennis level perceived by matches.
Theoretically we could have a player « A » who accumulated a record tally of 15 Grand Slams but who has never been a #1 and additionally is 0-10 down in H2H vs his rival B. Player « B » has 14 GS (one short), 100 weeks #1 and 10-0 dominance over his rival « A ». According to « only-Slam » approach, Palyer « A » would be the GOAT… A teratological nonsense.
Simply because all 3 pillars have been more or less converged during Sampras GOAT reign (better H2H vs.all, most Slams, most weeks#1), passed later to Federer (record w#1 and GS), and being asserted by both as their ultimate goals, it does not mean Tennis should be resumed to it (Only-Slams). Agassi pointed once that Rafa had an argument over Federer, considering their H2H and that is actually the case.
The Rivalry criteria is by far the most overlooked one in recent (20) years. The capacity of winning matches was quite relevant in Sampras/Agassi days, being evident as soon as one turned on the TV. Also back in the day, with Becker/Edberg/Wilander or Lendl/McEnroe/Borg/Connors - the « boxing » criteria of being superior to your opponent is one of the elements making Borg’s career so brilliant, despite so short.
As a matter of fact, Tennis itself would not have resisted time wasn’t by Rivalries. Laver, Rosewall, Pancho, Budge, Vines, Perry, Crawford, Cochet, Lacoste, Tilden, Wilding, Gore, Doherty brothers, Larned, Wrenn, Mahony, Renshaw twins. Most of the people were much more thrilled in the seen great rivals playing each other (essence of Tours) regardless of where, than they were by seen fancy elitist Club’s big metal cups being lended to a player for photo-sessions on a weekend rendezvous (also known as Grand Slams).
Back in the day, Slams were awarded only to club members and even nationals, let alone the questionable challenge (post-Final match) rounds. Professionals ?Forbidden to join, as in much of the sports around the world, let’s not forget tennis is not an island - even if Australia, England, Île-de-France and Manhattan may be - decoupled from the history and the rest of the globe.
Majors are the most important tournaments in tennis, not necessarily GS. It must inexorably count Championships (1913-23) and Pro-Tournaments along the way as well.
Bellow, the approximate number of Majors according to their existence, perception and cast of top players - since the best players play in the best tournaments: (surfaces)
- 1877 - 1904: 1 - 3 (2)
- 1905 - 1926: 4 - 5 (3)
- 1927 - 1967: 5 - 7 (2)
- 1968 - 2020: 3 - 4 (3)
This helps us in understanding Grand Slams as the most praised and valuable conquests, but not as a divine allowance to immortality. It is valuable, but not infinitely so.
The question of « how may ATP250 may be equivalent to one single Grand Slam » is wrong. We should ask instead: how hard it is to win a GS? And how much harder than winning a Big Title (Master1000, Finals, Olympics or equivalents) or an Overall Title (ATP250 / 500 / Davis Cup / ATP Cup). Those are the correct inquiries.
Such doubts are the only relevant ones to sports’ unbiased Greatness, all the others may be left to discussions on bar/pubs or weekend debates in tennis Clubs. Best of all, such problems can be solved by numbers alone instead of pop-up « experts » and internet-pools, thus having a precise and single correct answer.
Besides « how many units » of some metric have been won by the record holder player (dynamic determinants of the Critical Path / Ghost Player) we also have « how many players » have won at least one unit of some metrics (holistic correlation of rarity). Even though not taken directly into account, it serves as a good correlation bench mark.
There are about 57 GS champions, about 700-800 BT winners and thousands of (over) all Titles (AT) champions.
About 100-200 have been ranked as Top10s, 27 hold #1 for a week, and only 17 closed the season as on top of the rankings.
Only 8 have >80% of an overall Career W/L (Nole, Rafa, Roger, Bjorn, Jimmy, John, Ivan); on the Elite level just 7 >60% vs. Top10s (Boris, Pete, Rod in, Jimmy, Jonh out); and mere 5 have 60%> vs.Top5s (none of the Big3), this is Champions level, where GOAT rivals face each other on big stages in pursue of greatness (only Bjorn is over 70% here).
It all doesn’t mean that Grand Slams (57 players) are worth less than >60% of career W/L (8 players) but it does give us a glance of how hard the latter is to be obtained. It also points that all >80% career W/L players are also GS champions and successful #1, while many GS Champions are not #1 and hundreds of victories away from the career 60%W/L mark.
Should we consider a « Divine Palyer », the one winning all matches (100%W/L, v.All, v.T10, v.T5/Rivals) and possible tournaments in a season. In terms of Titles he would have won: 4 GS, 1 ATPF, 9M1000 or all 14 BT (15 on a Olypic Gold year). In rankings, he might have accomplished: 52 weeks as #1 (and also Top#10) and a 1 YE#1.
This gives us the perspective of rarity/scarcity, since no matter how good a tennis player may be or play, he can at best be/win:
- 100% vs.Top5;
- 4 Grand Slams;
- 1 YE#1.
Regardless of our won perception of the game or how media/ex-players/pundits rank it, the best possible season could give you 4 Slmas but only 1 Year-End.
Therefore it is axiomatic that being a Year-End #1 is much harder than winning a Grand Slam. It is relevant, because it changes our pre-conceived axiological notion of the sport.
As a matter of fact, there are many more Grand Slam Champions (57) than Year-End #1s (17). Record GS is 20 while record YE is 7*. A considerable difference.
Finally, s a hint of the future, the Vonder Index has since long placed Djokovic at GOAT levels along with Federer and Nadal already by 2015 - 5 years later Novak closed in 20GS and 311 w#1. It also ranked Murray close or above many #1s as early as 2012 - 4 years later he would became an improbable #1. Since early 2019 it points to Medvedev au par with former Slam Champions and retired #1 ranked players.
That comes out of no surprise, since the best players in our sport has basically since always demonstrated their potential, and the index captures it.
It is not to say that a GOAT is always prodigious since earl ages, nor that past 30 players cannot display greatness, on the contrary. It is because they have always been very good players (as displayed in the index) that they manage to achieve great feats early on (or gather glories later on) their careers. Those are stories the Slam-only count and Rankings-table are not capable of telling you because it’s too early, or until it’s too late…
Hope we have clarified most of the doubts regarding the Vonder Index. For any further questions we are at disposal for providing all necessary support.
Tennis Espresso Journal Team