An Explanation Of The New Statistics Page

Last night I posted a new page to the website detailing individual stats for the top 10 or so players in a few categories in the league. I’ve been working on this for about two weeks, most of the work was developing a method to analyze everyone’s results given the results from all of the scoresheets that have been submitted to me. It took me a little while to feel comfortable enough with how the numbers shook out to at least post a draft version of it for everyone to see. At this point, there are four categories of statistics available: Two of the categories (Attempts and Wins) should be pretty self-explanatory, Attempts is simply the number of times one individual has played in a game over the course of the season and Wins is the number of times the individual has won. The other two metrics, Total Score and Raw Score, are a little more complicated and require some explanation.

Raw Score

The Raw Score is a lot easier to explain. Since we don’t keep track of the actual scores of the games (which would be the most logical way to determine how well one is doing), the point of the raw score is simply to put a weighted value on the result of every time the individual plays a game. This is done to assign a very rough value to what the player has contributed to the team, which is something that can’t be done with percentages alone because of the small sample size that we have to work with. In most sports, it’s easy enough to do this type of thing by calculating a percentage – the percentage of times you hit the ball or make a shot is descriptive enough of how well a player can hit or shoot. If everyone played at least 100 times, this wouldn’t be an issue – we could just use the straight-up “batting average”, so to speak, as the main metric for evaluating an individual’s success. With an eight week season and the opportunity to play four times in a match at a maximum, the most that one individual could have is 32 attempts – not nearly enough to justify using a percentage as a metric to gauge one player’s success rate. This is especially true considering that the players leading the league in attempts aren’t even on track to getting close to that number, much less a credible figure for determining a success rate.

Enter the raw score – each game a player plays contributes the following to a player’s raw score:

  • .2 points for every doubles win
  • .3 points for every singles win
  • -.15 points for every doubles loss
  • -.2 points for every singles loss
  • .025 points are added for every win away from the player’s home bar (conversely, .025 points are taken out of each win at home)

Doubles have less weight because the outcome is less likely to be in the individual player’s hands. Also, the small adjustments for winning at home versus away reflect the idea that the player will (most likely) have developed a comfort level with their home machines by the end of the season. I’m not expecting everyone to become extremely proficient in such a short period of time, hence the reason why these adjustments are very small.

Total Score

At this point, we have  an admittedly rough score to assign to everyone. The advantage of doing it this way is that it rewards attendance and making attempts to play, but still penalizes the player if they do not win. However, there’s still some disadvantages to it, and it’s mostly because we don’t keep the score of the games – it’s hard to really assess how well a player is doing by simply counting their wins and losses. It’s certainly a lot easier to consistently do well if your opponents are putting up the equivalent of a 5 million point game on Metallica on every game you play as opposed to your opponents putting up the equivalent of a 50 million point game.

Since we don’t have scores to go off of, the next best thing is to look at who the person has beaten. In terms of probability, I would argue that three wins against the top three players in the league are more likely to have been good games than three wins against the bottom three players of the league. It’s not saying that one can’t have good games against players who are struggling, it’s more that it’s more likely that it took playing a good game to beat the players who are consistently doing well.

So, enter the Total Score – calculated as the sum of the individual’s Raw Score and the “Win Quality” bonus that they are awarded for beating highly ranked players in the league. The Win Quality bonus is calculated by taking the bested opponent’s raw score WITHOUT taking into account the game that had just been played (as in, the person’s Raw Score had they NOT played this match against this person) divided by the number of matches that the opponent has attended. This bonus is added each time a player wins a game against someone who has a Raw Score above zero. For doubles matches, the average of the adjusted Raw Scores for the two losing players is awarded to the two winners. It’s still not a perfect metric because even the best of us still have bad games every now and again, and someone may be overcompensated for how well they actually did during the match. Without having the actual scores from the games, though, I feel that this is the best we can do.

 

At some point soon I think I will add the total Win Quality bonus to the statistics page, as well as statistics for each team and everybody’s Pinball NYC affliation. I’ll also add some examples to explain the calculation of the scores in the future, as I can imagine my explanation may not make a whole lot of sense without them. The formulas for the scores may also change during the season, based on any feedback or odd results that we get – all of which will be documented here if applicable.

Congratulations to everyone currently ranked in the top 10 of either metric, and good luck in the second half of the season!

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