William Sonneborn Ranks the 1880s

This is quite possibly the most dry post I'll ever make. I beg you to bear with me, despite all of the seemingly useless arithmetic, I'm going somewhere important with all of this.

In February of 1886, the mathematician William Sonneborn shared, via Hoffer and Zukertort's The Chess-Monthly, a new scoring system for tournaments. The goal was to provide a system that didn't merely track how many wins a player scored, but the quality of those wins - it was believed that a win against a better-performing player should count for more than a win against a cellar-dweller, but the traditional scoring system counted each one as equal. 

His explanation takes up multiple pages; I'll give you the summary:

Let's use the London 1889 tournament (see here) as an example as the numbers are very convenient. We'll compute Henry Bird's score under Sonneborn's system (I actually computed this in the final crosstable, but now we'll discuss the method).

First, we compute his "quality number," which is the number of won games divided by the total number of games. Bird won 7.5 out of 10 games, so his quality number is 7.5/10 = 0.75 - see what I mean about the numbers being convenient?

The first term in his Sonneborn score is the number of wins multiplied by his quality number: 7.5*0.75 = 5.625

The second term is the sum of quality numbers of defeated opponents: Bird defeated Müller (0.55), Miniati (0.55), Lee (0.5), Wainwright (0.4), and Mortimer (0.3): 0.55+0.55+0.5+0.4+0.3 = 2.3

The final term is half the sum of quality numbers of drawn opponents: Bird drew Gunsberg (0.75), Mason (0.55), van Vliet (0.5), Blake (0.5), and Gossip (0.15): [0.75+0.55+0.5+0.5+0.15]/2 = 1.225

Thus, Bird's score under Sonneborn's system is 5.625+2.3+1.225 = 9.15, as we saw in the crosstable:

Today's discussion isn't really on this scoring system. It obviously never caught on, though the connection between it and what we know as the Sonneborn-Berger tiebreak system should hopefully be clear - it's the same thing, minus the first term. What I'd actually like to talk to you about are some alternate applications of this system.

The first, as we saw in London, was that this could be used to construct a dynamic prize scheme: players would earn a proportion of the prize fund equal to their proportion of Sonneborn points relative to the total number of points available (in London, as 55 games were played, Bird scored 9.15/55 ≈ 0.1664 or about 16.64% of the available points). This spread out the prizes more than traditional scoring systems, ensuring everyone would get something as long as they scored at least a draw. On the flip side, players who were motivated primarily by money wouldn't feel as great a need to win every game, as the difference in prizing between the placements wasn't as large. The eventual compromise was that many tournaments would have a conventional prizing structure, but anyone who didn't win a prize would win some share of the entry fees using Sonneborn's system.

The second, and the primary subject of today's post, was that this system could be used to determine the relative strength of players across various tournaments. Sonneborn assumed each tournament had a "pot" of 100 points per player (so London's pot would have 1100 points), and a player would earn points equal to their same proportion as above. Bird, for example, would have earned (9.15/55)*1100 = 183 points, which could be compared with other tournaments in a way we'll discuss shortly.

Here's Sonneborn's breakdown of the New York 1889 tournament using this system:

The formatting is a little weird, as he uses dashes for fractions (so Weiss's quality number is 58/76, etc) and he uses mixed fractions (so Weiss's "points scored" is 35 51/152 ≈ 35.3355, etc) but the last column is the only important one. Weiss and Chigorin both earned a little under 10% of the 2000 available points (20 players * 100 points per player), Gunsberg earned a little under 9%, etc.

So what does all of this mean? We can calculate a player's Sonneborn score for any tournament, and subsequently compute their share of the "pot." By taking the average of their shares across all of their tournaments, we can compare players across tournaments of different sizes and formats. Here, for example, is Sonneborn doing just that for Steinitz's tournaments since Paris 1867:

The rightmost value in the "Result average" row (195.72) is the value we're ultimately concerned with. So, now that we've finally arrived at the actual statistic of interest, the preamble can be concluded and the real blog post can begin.

What I spent the past little while doing is going back through the most important tournaments of the decade and computing these values for a select group of players. We're going to take a look at these values, and see if we can't arrive at some sort of leaderboard for the decade. 

I ultimately decided to include 14 tournaments: Wiesbaden 1880, Berlin 1881, Vienna 1882, London 1883, Nuremberg 1883, Hamburg 1885, Hereford 1885, London 1886, Nottingham 1886, Frankfurt 1887, London 1887, Bradford 1888, New York 1889, and Breslau 1889. I tried to restrict this list to major international tournaments only - we're not including smaller international events like Amsterdam, and we're also not including any national-only events (with the exception of London 1887, as over half of the field ended up making the list so it seemed important enough).

To keep the list to only the most relevant players, I decided to only focus on players who had scored prizes in two of the aforementioned tournaments. I was initially looking at every prize-winner, but there were a couple of people who only participated once (like Johann Bauer and Jacques Mieses), as well as a couple who won a prize but were otherwise unremarkable (like Jean Taubenhaus and Alexander Wittek). When I narrowed the search to two-time prize-winners, the list shrunk to only 18 players, which was very manageable.

Thus, I present to you... the top tournament players of the 1880s:

Right away, a couple of issues should become clear. I would not consider Steinitz to be the #2 tournament player on the sole basis that he just didn't really play any tournaments. Secondly, while Sonneborn's system tried to address the quality of wins, his system doesn't manage the quality of tournaments as well; Blackburne's result at Berlin 1881 and especially Zukertort's at London 1883 were almost certainly more impressive than Burn's at Nottingham, and yet he received more points both there and for London 1887 (which was very impressive, I'll give him that one). So I don't think this setup is super conclusive, but it makes for a perfect baseline for future posts.

Before we can get into that, however, I'd like to trim off a couple of names.

Henry Bird

While I've tried to make amends for my rather tasteless words thrown at Bird, the numbers don't lie: he just wasn't a good tournament player. An average of 100 is comparable to scoring an average of 50% across all tournaments, and Bird ended up well below that. As a result, I don't exactly want to include him in future discussions about ranking the decade.

To make up for that, let's take a look at some of his genuinely good games. In early 1889, The Chess-Monthly published a short biography of Bird, and asked him personally to send in some of his favourite games for publishing. I picked three that were relevant; two of them show off his attacking prowess in some of his named variations, while the third gives us a look at Bird as a defensive player (spoiler alert: he was not a passive defender).

Suspiciously absent from this collection is a Bird's Opening game, which I feel really needs to be shown if one is going to talk at all about Bird. Seeing as we were deprived of his game against James Mason in the last chapter, I figure we can kill two birds with one stone (ha, get it? Oh man I'm good):

Wilhelm Steinitz

There's an argument to be made that Steinitz was the most important player of the 1880s by default, what with him winning (and then defending) the World Championship and all that. Unfortunately, as this series focuses exclusively on tournaments, Steinitz was really just something of a non-figure in this decade; he was content to sit on the sidelines, writing and publishing a good deal but never setting foot into the arena himself. I didn't mention it during my coverage of the New York 1889 tournament, but there were a great many people who were disappointed at him for not entering, especially given that tournament was partially intended to select his successor(s). Still, he did very well in the two tournaments he did play - shared 1st at Vienna 1882 and very clear 2nd at London 1883 (3 points behind Zukertort but 2.5 points ahead of Blackburne) - and I found some interesting patterns in his openings that are worth sharing.

With the Black pieces, Steinitz's philosophy was actually quite clear. He loved a Kingside fianchetto, especially given how freely people pushed d2-d4 and opened up the center for him. Although he had disowned the motif later in the decade in his theoretical writings, his rather convincing successes in tournament practice made them a natural starting point for his relatively young school of thought.

Even after his play switched to more orthodox lines against other openings, Steinitz spent his entire career searching for the antidote to the Ruy Lopez, which became the main tournament weapon starting in this decade. Although he would later be known for championing an early ...d6 and ...Bd7, here he was still trying to improve upon the Nge7 system used in the previous decades. Blackburne crushed him in these positions fairly regularly, but not everyone fared so well, and I'm sure Steinitz would take whatever he could get against such a resilient opening as the Spanish.

I find Steinitz's play with White to be much more interesting, however, and I think it's best if we split his play into whether he follows the past, present, or future.

Past: Especially in Vienna, Steinitz loved to gambit. He played his namesake gambit a handful of times right at the start of London, though as we covered in the Steinitz Gambit blog (see here), that didn't last long. But at Vienna, the King's Gambit turned out to be Steinitz's main weapon against the weaker players. Chigorin apparently fell into that category, despite his successful debut in Berlin the year before, and the pair's first-ever game was about as exciting as one could hope for.

Present: In much of the 60s and 70s, Steinitz had disregarded the Ruy Lopez as dull, hence why he spent so much of his time on the more interesting Vienna and Italian games (and the King's Gambit, of course). He finally gave the opening a try in his 1876 match against Blackburne, and that system - c3, d3 and trying to play a slow game - became his go-to in the opening. The game I've chosen against Mackenzie is perhaps not the perfect example, since Steinitz very quickly trades off the Bishop he sought to maintain with his fifth move, but it's by far the most accurate game we'll see today.

Future: Steinitz's school actually had more elements of hypermodernism in it than most people would give it credit for. There are those that would describe Tarrasch's school, for example, as a combination of Steinitz's positional principles with a slightly bigger focus on piece development (which Steinitz sometimes lacked), and so Steinitz's name has been lumped in with Tarrasch when critiquing the modern school. It's actually quite amusing that kahns recently published a chapter on Aron Nimzowitsch (see here), who remains famous for creating the concept of overprotection; in Dynamic Chess, Richard Nevil Coles argued that Nimzowitsch did nothing other than create the term overprotection, with Steinitz having it figured out decades earlier. He gives the following game against Weiss, and while Steinitz's own writings on the game obviously never used the word overprotection (his attention was focused on the file as a whole, not just e5), it was incredibly clear just how useful such focus on the square was.

Conclusion

Hopefully this collection of games from these two polar opposite players makes up for the math lesson with which we started the chapter. The nice thing about me choosing the games myself is that there's less likely to be any duds, so look forward to a higher proportion of good games moving forward.

So, to recap: we've established a metric for measuring the relative performance of players across tournaments of different sizes and formats (single vs. double all-play-all). We've come up with a leaderboard to rank the more noteworthy players, though it has its flaws that I'd like to address. With two of those players covered, that leaves us with 16 left to talk about. What would be the perfect way to accurately rank these players?

We're gonna have some fun over the next few weeks. Thanks for reading.