## The Unbearable Likeness of Arsenal

Arsenal have been a tremendously consistent team over the past decade. However, now the tide seems to be turning against Arsène Wenger. Many fans would happily trade in that consistency for a few more league titles. If you're the fourth best team in the league over 12 seasons, how many league titles should you expect to win? If variance can swing Leicester a league title, you would think it could have thrown a few Arsenal's way, too. This is the question that Chris Anderson (writer of The Numbers Game) asked on Twitter last week: Fortunately, there are a couple of different ways we can try to answer this. One way is to use bookies' odds to estimate the probability of a team winning a match. Then, using these probabilities, we then simulate an entire season and estimate what the probability of a team winning the league really was. There are some problems with this method (see the appendix); however, it does allow us to get some ballpark numbers.

## Zero league titles

So what is the chance of Arsenal winning no league titles since 2004? By the method described above, the probability of Arsenal winning 0 league titles from 2004/05 to 2015/16 (inclusive) is estimated at 14%. With a crude simulation like this, it’s probably not wise to read too much into the exact numbers. Nonetheless, this does suggest that Arsenal have been somewhat unlucky not to bring back a few titles over the last 10 years. So how many league titles should we have expected Arsenal to win?

## 12 top four spots

It seems unfair to consider the bad luck Arsenal have had and yet not consider the good luck they have benefited from elsewhere. If failing to win a league title or two is unlikely given (the bookmakers’ opinion of) their overall performance, how unexpected is continued qualification for the Champion’s League?

The exact estimate here is <1%. When a number gets that low, it’s difficult to get a meaningful interpretation. I think the take-away message is that finishing in the top 4 consistently, even when you’re Arsenal, is very unlikely and requires large doses of both skill and luck.

## St Totteringham’s Day

According to Wikipedia, St Totteringham’s Day is “held on the day when Arsenal have gathered enough points to be mathematically assured to finish ahead of Tottenham in the league table”. Celebrated for generations without fail, there have been a few close calls in recent years (not to mention what will happen this year).

Although the individual probabilities remain high, the combined probability of Arsenal finishing above Tottenham on all of the last 12 seasons is just 15%. It is of course possible that there are some factors that the odds may not account for. However, even if you believe that the odds are missing an adjustment for Spursy-ness, it still represents an unlikely achievement. I don’t think it’s at all surprising to conclude that Arsenal were unlucky to miss out on a couple more league titles. I think most football fans could have imagined Arsenal taking the league at times in 2015/16 or 2007/08. It’s tempting to wonder what could have happened had everything gone their way just once. Old stars might have stayed; new stars might have joined. You can see how a bit of luck at the right time can kickstart a chain reaction of improvement (looking at you Chelsea 2011/12). Ultimately, looking at it like this misses the point. Most Arsenal fans aren’t disappointed by one missing title. Instead, it is the sheer repetitiveness of each season. Every year the same mistakes are made on and off the pitch. At least in Groundhog Day, Bill Murray learned a thing or two each time he woke up. A bit more silverware and the resulting improvements in the playing squad would have helped paper over the cracks. But football is (slowly) modernising and those who fail to learn from their mistakes risk falling behind.

## Appendix

### 1. Figures

We can abstract the charts above a step further and look at the finishing probabilities of the team in each season since 2004/05. You can view the same charts for all Premier League teams on github.

### Arsenal

It looks like 2011/12 marked the starkest change for Arsenal. It was in the preceding summer that Fabregas and Nasri left.

### Manchester City

Money, what money?

### Manchester United

I wonder what happened circa 2013/14?

### Method

• Take bookmakers’ home/draw/away odds
• Convert odds to probabilities.
• Using prematch probabilities, simulate each game 10,000 times.
• For each simulation:
• Assign points to home and away teams (3 points for a win, 1 for a draw, 0 for a loss).
• Add up the points and sort to create a league table.
• In the event of a tie, teams on equal points are ordered randomly.
• For each season:
• Sum the number of times a team finished in each position.
• Divide by the total number of simulations (10,000) to estimate the probability of finishing in each position.

By taking the bookies’ probabilities game-by-game, in-season effects are, to some degree, taken into account. This means that in each of the simulations, all the injuries, managerial changes, suspensions and the like happen at the same time as they did in real life. This means that the resulting probabilities grossly underestimate the amount of uncertainty in a season of football. To use a specific example, the simulation does account for the possibility of Vardy, Mahrez or Kanté having a long term injury in 2015/16. In the same way, season-to-season changes aren’t accounted for. If Arsenal had won the league in 2010/11, it may have made keeping hold of their (and acquiring new) star players over the next few seasons that much easier.

### Data

Data was originally sourced from football-data.co.uk. The odds used were from the following bookmakers:

• 2004/05: Bet365
• 2005 to 2012: Betbrain average
• 2012/13 to 2015/16: Pinnacle closing odds.

### Code

The code, data and figures used for this analysis are on github.

## Men on Posts and Starting Fires

• That ignores the fact that the current iterations of pressing come in many varieties and are substantially different than what you saw from the 70's through the 90's
• Pressing variations really matter for evaluating top level tactics and play, which means they really matter for top level coaching
• The instructors, who were otherwise quite good, displayed no real understand of this particular topic. Or really of shot locations and effectiveness. Which, if we're trying to train and develop better coaches and in turn better players, is probably a big deal.

Maybe this type of subject material doesn't matter at level 2, and I was expecting too much, or maybe English coaching education is still struggling dramatically to overcome decades of ineptitude to catch up with modern times. I honestly don't know. Which finally leads me back to the current crop of commentators. Aside from Carragher and Neville, who clearly put a lot of research and work into their craft, the commentators currently discussing football on television generally don't understand modern tactics. How could they, when the tactics they were brought up playing were bad, and the coaching education failed to correct for that? Nor do they have an analytical mindset, which would help to educate viewers on the reality of the game versus the perception. They commentate on games in 2017, but were almost exclusively trained in England, and brought up playing a style that almost doesn't exist any more at the top levels of play. So what are they there for? The occasional interesting anecdote about mentality and what players feel like before a big game? To provide a constant stream of footballing cliches that provide no insight and are rarely relevant to the moment at hand? We get nothing of interest from so many talking heads on television. No funny anecdotes about current players or managers. No tactical insight. No statistical insight. No points about technique and detail about what a player could or should have done better. Half of the matches I and many other viewers watch each week have foreign commentators. I almost never feel worse off because of it. And THAT is a take away that should shake everyone involved in the production side of football, right up to the top levels of Sky and BT Sport.

## StatsBomb Podcast: March 2017 #2

[soundcloud url="https://api.soundcloud.com/tracks/312532434" params="auto_play=false&hide_related=false&show_comments=true&show_user=true&show_reposts=false&visual=true" width="100%" height="450" iframe="true" /] Ted Knutson and James Yorke field questions from listeners and talk about new metric xG Chain Downloadable on the soundcloud link and also available on iTunes, subscribe HERE Thanks!   Theo Walcott radar gif:     Ross Barkley, shot maps:

## StatsBomb Goes to Sloan Sports Analytics Conference

• The marriage of tracking data and event data will be a key to unlocking the future. We need both data sets and we need to be able to analyse them as part of the complete picture of what is happening in a game. I also feel very strongly that we need it not only for games, but for training data as well. The reason for this is that football games only produce a moderate sample of data for us to analyse, but training happens constantly. You'll have to be careful about what training data you include as having valid incentives, but it will dramatically increase the sample size and our ability to evaluate player skill sets as a result.
• Right now data analysts work for clubs but often are wedded to the coaching staff. Their direct line of report is to the manager, which means if the data is starting to say uncomfortable things about performance, or the coach disagrees with it, it often gets muted or is considered wrong. That's definitely not how it should work. That's especially true because analysts tend to build a large store of institutional knowledge that is valuable to keep inside of a club, and not be chucked out every time the club changes a manager or a head coach.
• A combination of football people asking questions and quants then finding the answers, then sending them back to football people for a sense check, is another key to unlocking useful things in the sport. One of the problems we see again and again when researchers without game expertise get involved is really brain dead studies like the one Garry Gelade discussed at the OptaPro Forum, or mistakes made in interesting studies that ruin their credibility. Tyler Dellow flagged one from this past weekend in a hockey research paper where it had inverted which side certain players play on - an extremely easy mistake to make in programming. Unfortunately this type of mistake means the study would be blown apart the moment you brought it to a coaching staff, regardless of how good it was.
• There is still plenty of low-hanging fruit out there for football clubs to take advantage of, they just need to open their minds and talk to the right people. It's very straightforward to create the edge in recruitment, and the money it saves by avoiding mistakes is massive. If I can figure out the set piece edges, so can plenty of other people. I'm not that smart, and it's not that difficult, which is why I have historically avoided the topic. The same is true in so many other areas. Football is too big and too complicated a sport for one person to be an expert in all the different facets of the game. Because of this, clubs need to constantly seek out new information and perspectives.

I thought Wiebe did an excellent job moderating, and feedback from the audience and Twitter was that people were genuinely excited by what we said. I guess that's a success. Friday evening I hung out with more soccer people including seeing some of the guys at US Soccer again. Federation challenges are really interesting, and there's only a moderate amount of overlap with what we do at the club level, so it's always intriguing to discuss what their future might look like. Saturday When I go to the U.S. these days, my body never adjusts. Too many years of children and 6AM wake ups mean I never sleep past 8:30 here in England, which means I rarely sleep past 4AM when I visit America. Thus I had breakfast early and was chilling in the speakers' room waiting for the gambling panel to start. While most of you probably know me from my work on football analytics, my "real" expertise is gambling. I have spent the vast majority of my time since 2005 in and around the world of sports betting, including 8 years at PinnacleSports.com, and two years inside of Matthew Benham's Smartodds operation. (We worked on football and for the football teams, but we sat in the middle of a giant gambling operation.) I started at Pinnacle in early 2007, just after they left the U.S. market. While I was there, we either created or completely rebuilt all of their non-U.S. sports departments, and I fought for a year to create the Live Sports department, which means I was overseeing development and application on the initial models for Live MLB, NBA, Soccer and Tennis. I am likely one of the only people in the world to work for a long time inside one of the giant discount books as well as in and around one of the world's biggest betting syndicates. In gambling, unlike in football stats, I'm a strange sort of unicorn. The funny thing is, no one knows this. Pinnacle people rarely travel, and we never have a forum to talk about our work. Thus when you sit down next to even seasoned gamblers like Ma and introduce yourself, you can expect a deluge of really interesting questions. Example: How much volume and profit did Pinnacle have the year before they left the U.S. Market? Example2: Why did the stupid owners get arrested? I also talked a bit to ESPN vet Chad Millman and Joe Brennan Jr, who is apparently a fan of the StatsBomb podcast. My takeaways from the gambling panel

• Sports betting is a game of skill. This is especially true when the vig is low. (My words, not theirs.)
• The U.S. still has no idea when/if/how they will legalize sports betting. This remains baffling to me since the NFL spreads are talked about in every major news organization in the country, but you still can't bet on them outside of Vegas.
• Because of the above, the probability that they legislate in a way that makes it possible for a discount (translation: low price like a Pinnacle, IBCBet, SBOBet) sportsbook to exist is fairly low. Margins in Vegas are 5% on average (-110/-110 in American odds). Margins at discount books are often 1.5 to 2.5% and they take all action, which means they tend to earn considerably less than that per dollar wagered. Because of this, if you tax them in the way of sin taxes and take a percentage of gross revenue, you make it impossible for them to exist in your jurisdiction without a dramatic price hike. Europe is a mess of disjointed gambling laws that typically screw customers in favour of tax receipts, which in turn drives them toward better priced options which are quasi-legal where the government then does not get tax receipts. Because Vegas exists already, there's a chance the U.S. may end up with something sensible that allows competition, innovation, and is customer friendly, but I wouldn't hold my breath.
• Because the U.S. doesn't have legal sports betting, the sports data feeds are pretty poor. The reason behind this is that there is no value equation available to them to make it real-time. Gambling would fix that because the amount of money books can lose from past posts to people with better/faster TV feeds is stupidly large.
• Internet sports betting is a tech industry. There is no other tech industry where the U.S. has simply chosen to be absent.
• In-running betting typically increases fan engagement. In Asia, in-running volume can often be 3-5 times what the volume is on pre-game (they didn't say that but I know this from experience). Worried about falling viewership numbers on TV for various leagues in the U.S.? That could potentially be halted or reversed with legalized gambling.
• The other thing that legalized gambling would do is drive massive amounts of advertising dollars straight to the networks and sports teams/leagues themselves. We saw it briefly with Draft Kings/Fan Duel, but that would be a drop in the bucket compared to what would happen with an open U.S. market for sportsbooks.
• No one realises how massive eSports gambling is just now in the rest of the world, or could be in the U.S. if it goes legal. The audience for these events is already huge, and it crosses over to people traditional sports often don't, which is a new market segment for sportsbooks.