tag:blogger.com,1999:blog-6059983310325678283.post8745491115024384577..comments2024-01-17T05:39:39.990+00:00Comments on The Power of Goals.: How Real Is Manchester City's Late Scoring Spree ?Mark Taylorhttp://www.blogger.com/profile/15514407542599931686noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6059983310325678283.post-44402248065059788392012-12-26T15:32:47.462+00:002012-12-26T15:32:47.462+00:00A quick way to sim City's goals from the 85th ...A quick way to sim City's goals from the 85th minute onwards.<br /><br />Take the Wigan away game this season as an example.<br /><br />City had around a 63% chance of winning that game, so they'd expect to score about an average of 1.9 goals and concede 0.8 gls in this game. If you stick those average goal expectancies into a Poisson & calculate each actual score combination which lead to a City win, total the individual probabilities, they will add up to 63% <br /><br />The match actually had 4 minutes of injury time. From the 84th minute and 31secs onwards City's goal expectancy had declined from 1.9 at the start and a goal expectancy of about 0.281 gls remained. <br /><br />Stick 0.281 into a raw, unadjusted Poisson and you will see that the chances of City scoring exactly one goal in the short time remaining will be about 0.212. The probability of exactly 2 goals being scored by City was 0.0298, three goals 0.00279 etc.<br /><br />Set up an excel spreadsheet for all City's games, not just the Wigan one and calculate the probability of exactly one, exactly two, exactly three etc goals being scored in the final stages of the matches based on the actual amount of injury time played and how much City's goal expectancy had declined to by the 84:31 minute.<br /><br />Set up a random number cell (=rand()). This will generate a random number between 1 and 0. For the Wigan game assign say between 0 and 0.212 of the randomly number to simulate the scoring of exactly one goal by City over that time span. Do similar for two goals, three goals etc.<br /><br />Run as many sims as you feel necessary and sum the number of simulated seasons where City score x amount of goals after the 84:31 minute. Mark Taylorhttps://www.blogger.com/profile/15514407542599931686noreply@blogger.comtag:blogger.com,1999:blog-6059983310325678283.post-28836537954497439772012-12-26T13:34:06.590+00:002012-12-26T13:34:06.590+00:00"Poisson simulations using City's actual ..."Poisson simulations using City's actual goal expectations from the 85th minute onwards in their last 56 games saw 24 or more late goals arriving in around 7% of the trials. "<br /><br />Mark, can you expand more on the Poisson simulations?Anonymousnoreply@blogger.com