Wednesday, 18 September 2013

Mike Dean and Arsenal

Mike Dean takes charge of Saturday's match between Stoke and Arsenal at the Emirates. Dean is no stranger to officiating Arsenal matches and his appearance should give rise to a sense of foreboding for every fan of the Gunners, if a recently circulated statistic on Twitter ( and Rt'd by  link) has any credence. In the last 16 Arsenal matches officiated by Dean, Arsenal has won just twice. (The stat actually claims one win in 15, but omits the late season win over Wigan that finally, after years of trying, saw Wigan relegated). Like referees, we all make mistakes.

At first glance the figures appear compelling, over the same timescale, the rest of the top teams from Spurs upwards have each won at lest half of their Dean controlled fixtures. But as is often the case with good Stoke City omens, the case for an assured victory, possibly courtesy of any anticipated generosity of spirit from Mr Dean, is an incredible weak and contrived one.

The initial use of win percentage instead of the more convincing success rate, which includes and weights draws as being worth half a win, artificially extends the apparent gap between Arsenal's fate under Dean and that of their usual rivals. 7% of wins (actually 13% when the Wigan game is included) appears a very long way away from the 50% win figure of Spurs, the next most unfortunate top club to apparently suffer at the hands of Dean.

Mike Dean and Arsenal. 2009-2013.

Sides Reffed by Mr Dean. Wins. Draws. Losses. Win% Success Rate.
Arsenal. 2 5 9 13% 28%
Man Utd. 8 2 2 67% 75%
Man City. 10 4 2 63% 75%
Chelsea. 10 4 2 63% 75%
Spurs. 8 4 4 50% 63%

If we include draws, which Arsenal accumulated at the highest rate of the five teams, the resulting success rate slightly narrows the performance gap.

Secondly, the 16 Arsenal matches are a highly correlated set of fixtures. 11 of the matches are against the other top four sides listed in the table. United finished above Arsenal in all four seasons listed, while United's near neighbours and Chelsea also gained more points than the Gunners in three of the four years. Only Spurs proved to be consistently inferior to Wenger's side. Therefore, if Arsenal's rivals perform well in this table, Arsenal, as the team the other sides frequently meet, are virtually guaranteed to do badly. In short, under the selective rules of these engagements, the Gunners are playing tough, superior sides and only wins count.

However, the biggest give away in this attempt to suggest a correlation between Mike Dean and Arsenal's poor results is the selective cut off point made at the start of the 2009 season. If we go back further and include two more games, Arsenal avoid defeat against both Spurs and Manchester United. Include a further game, away at Chelsea in November 2008 and Arsenal record a win, despite Dean's presence in middle. Add one more and Blackburn are comfortably defeated, then Manchester United are held goalless.

If you include all of Dean's missing assignments involving Arsenal, 21 extra Premiership matches show up and Arsenal, apparently unaware that they are facing their future arch nemesis, lose just once and Dean appears to be more of a lucky mascot.

To finally nail this absurd fallacy that referees are able and motivated to determine the outcome of matches involving certain sides, here's a plot of the distribution of the likely success rates achieved by the Arsenal/Dean combination over Dean's Premiership career, once the quality of opponent is allowed for.

Arsenal would have most likely expected to return a 62% success rate over those matches and they actually returned a below average sr of 57%. The chances of the pre game match up ratings being broadly correct and Arsenal recording a record of 57% or worse is a shade under 20%. So there is nothing remotely significant to see here.

Arsenal's below par return is down to random variation rather than a Machiavellian plot. But even if a strong, unlikely to appear by chance, correlation between Dean and Arsenal under-performance is proven, causation then has to be established as well. And other than anecdotal opinion, usually based around red cards, fishing trips of this type rarely attempt to substantiate the headline with such evidence. Can Dean really be held responsible for Koscielny's decision to rugby tackle Dzeko five yards from goal, rather than choosing to defend the ball in an ultimate, 10 man Arsenal defeat to Manchester City?

Even if we allow the selective start points to stand by assuming that Arsenal did something to really annoy Dean at the close of the 2008/09 season, the conspiracy still fails. Arsenal's 28%, opponent adjusted success rate has around a 1% chance of occurring through short term variation, but Arsenal weren't the only side playing under the gaze of a familiar ref in those four seasons.

The Premiership referring pool is relatively small, most of them can squeeze around a small breakfast table at the FA's St George's complex. So lots of sides regularly see different officials over a fairly regular timeframe. Sooner or later, even with odds of 1% for particular combinations of ref/club, one such pairing is going to throw up a seemingly unlikely run of good or bad results, just by chance.

The good news for Arsenal is that Mike Dean hasn't held a grudge against them since 2009. The bad news for Stoke is that if they win on Saturday, it will come unassisted and on the back of their new found passing game, rather than as a gift from the officials. And I'm sure Mr Dean, should the wider press pick up on this absurd "factoid", is professional enough not to attempt to redress an imaginary imbalance in his dealings with Wenger's side.

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