On the thread that inspired the formation of this forum, we discussed ways to predict team records from their goals scored and goals against. It was determined that using a Poisson distribution for goals would work well. I did some playing with this year's MLS records...here's what I found. First I compared each teams actual points to their predicted points: Code: [size=2]Team GF GA Pts PrPts Diff Chicago 53 43 53 47.91 +5.09 MetroStars 40 40 42 41.10 +0.90 New England 55 47 45 46.60 -1.60 DC United 38 36 39 42.36 -3.36 Columbus 44 44 38 41.31 -3.31 San Jose 45 35 51 48.08 +2.92 Colorado 40 45 40 37.87 +2.13 Kansas City 48 44 42 44.02 -2.02 Los Angeles 35 35 36 40.78 -4.78 Dallas 35 64 23 24.22 -1.22 [/size] "PrPts" is predicted points. The average error of 2.7 points is comparable to what I've gotten with European leagues. Next, I compared each teams predicted record to their predicted record if they had scored/allowed a league average amount of goals (43.3), generating a number for how many points their offense and defense had earned of lost...for example, Chicago won just over two games by scoring 53 goals instead of 43.3. Code: [size=2]Team Off Def Chicago +6.45 +0.20 MetroStars -2.34 +2.16 New England +7.67 -2.36 DC United -3.83 +4.87 Columbus +0.49 -0.45 San Jose +1.18 +5.64 Colorado -2.31 -1.07 Kansas City +3.20 -0.45 Los Angeles -6.11 +5.50 Dallas -5.25 -11.07 [/size] By comparing the amount of goals scored above/below the league average with the offensive rating in the above table, we can get the amount of "goals per win" for each team--for example Chicago scored 9.7 goals above the league average, which helped their team earn 6.45 points. 9.7/6.45*3=4.51 goals per win. Code: [size=2]Team Off Gls GPW New England +7.67 +11.7 4.58 Chicago +6.45 +9.70 4.51 Kansas City +3.20 +4.70 4.41 San Jose +1.18 +1.70 4.32 Columbus +0.49 +0.70 4.29 Colorado -2.31 -3.30 4.29 MetroStars -2.34 -3.30 4.23 DC United -3.83 -5.30 4.15 Dallas -5.25 -8.30 4.74 Los Angeles -6.11 -8.30 4.08 [/size] "Gls" = goals scored vs. the league average. GPW = goals per win. So an MLS team needs to score 4-5 extra goals over a season to win another game...with the exception of Dallas the higher-scoring teams need to score a bit more to win another game. For defenses the numbers are a bit higher, but still between 4 and 5 goals needed to make a one-game difference.
Please clarify something. Bill James found in the 80's (with the offensive explosion since then, the numbers probably don't still hold) that a team needed to get 10 extra runs to move up a full game over .500. By that I mean, if you outscore your opponents by 20, you expect to go 83-79, NOT 82-80. When you talk about winning an extra game, do you also mean NOT LOSING an extra game? If you outscore your opposition by 9, will you win 2 more games than you lose, or 4? It's probably obvious from your chart, but I don't have the statistical background for that. Anyway, if in my example it's 4 games, that sounds about right to me, but I'm still a bit surprised the number isn't lower. If it's 2 games, then I'm really surprised.
Great work ... IMO, this is a very interesting result. Intuitively, I would've thought that fewer goals would buy you an extra win. At some point, I'd like to go back to those save percentages and see how much of a difference a good shot-stopper might make.
Re: Re: MLS--fun with the team statistics and the poisson distribution Yeah, that's what I mean...a team that outscores its opponents by 9 goals would be about 4 games over .500. The number of goals to get the extra win increases as teams get farther from .500...but usually that's not a huge problem in MLS.
Re: Re: MLS--fun with the team statistics and the poisson distribution Beineke, I compiled, I believe, teams' save percentages throughout MLS history. I tried doing a regression analysis, but seeing as it was the first time I'd ever tried anything remotely like that, I botched it pretty badly. If you feel like doing the work, I can give you the numbers. (sorry to hijack your thread, JG)
From what I remember, after we adjusted for offsides, there was maybe a 10% gap from the best shotstopping defense to the worst (although most teams were nearly indistinguishable). If a team allows 5 shots on goal per game, the goalkeeping gap would be 15 goals over an entire season ... and 15 goals maps out to about 10 extra points. Conclusion: Because the Burn finished 13 points behind LA, even Tim Howard couldn't have gotten them into the playoffs.