Tuesday, October 16, 2007
Updated approach to plus/minus stat
A few folks out there are familiar with my wonky "adjusted plus/minus" stat. This statistic does not consider touches, turnovers, blocks, assists, or scores. All that is considered is who was in and whether they scored the point. As such, this data can be compiled using a pretty bare bones stat sheet.
I have made some updates to my approach to using this stat, partially motivated by some suggestions I have received. This new approach tries to compare a player not in an absolute sense, but in stead in a relative sense based on team expectations. Here's a summary of the approach, followed by an example.
1a) For a given game, divide points scored by total points to obtain overall efficiency.
1b) Obtain expected efficiency by comparing teams in the score reporter. For instance, this comparison of Jam and Sockeye currently predicts a 15-13.3 Sockeye win. So Sockeye's expected efficiency would be 52%.
1c) Divide overall efficiency by expected efficiency to get the "expectation ratio".
For the purposes of this algorithm, I would ideally collect the predicted score from the score reporter after the tournament is fully reported, before any future tournaments. Since recent games are weighted more in the RRI algorithm, this probably gives the truest measure of what should have been expected at that tournament.
2a) Count the number of offensive points the team played in each game, and how many they scored. Divide O-point scores by O points to get offensive efficiency for each game.
2b) Divide this total by the expectation ratio to get "expected offensive efficiency"
3ab) Repeat the above to get expected defensive efficiency for the game.
I debated whether there should be some "expected O/D split" in efficiency, but in the end I decided that the character of each game is unique due to wind effects and the like, and as such it's better to assume the O/D splits are as they should be.
4a) For any given player, compute their offensive efficiency based on the ratio of O points to O scores when they were on the field.
4b) Subtract the players offensive efficiency from the expected offensive efficiency in that game to obtain marginal offensive efficiency.
4c) Multiply marginal offensive efficiency by offensive points played to get that player's offensive plus/minus for that game.
5abc) Repeat the same for defensive points.
6) If desired, add the player's offensive and defensive plus/minus together to get overall plus/minus. This can then be divided by points played, and added to expected efficiency, to get the player's adjusted efficiency.
example:
When Ripe played Bad Larry at sectionals, we lost 13-12, for an efficiency of 48%. Our expected efficency in that game was 45%, giving us an expectation ratio of about 1.05.
We scored 9 of 12 O points, for an O efficiency of 75% and an expected O efficiency of 71.6% (i.e. we scored 3.4% more often than you would expect).
We scored 3 of 13 D points, for a D efficiency of 23.1% and an expected D efficiency of 22%.
We scored 5 of 6 O points I played, 11.7% more often than expected (83.3% - 71.6% = +11.7%). When multiplied by 6 O points played, this gives me an adjusted O plus/minus of .7 points (.117*6 = .7).
We scored 2 of 8 D points I played, 3% more than expected, for an adjusted D plus/minus of .24 points.
My overall adjusted plus/minus for the game was therefore +.94.
To give some context to that: the overall range for the game went from +2.47 (scored all four of her O points, and 2/3 D points) to -.88 (scored 0/4 D points, did not play on O). For the entire weekend, total plus/minus ranged from +8.67 to -2.41. Overall plus/minus was skewed toward positive because we exceeded our expected score in most games. (Also, the negative scores tend to be lower because people who are playing well play more.)
I have made some updates to my approach to using this stat, partially motivated by some suggestions I have received. This new approach tries to compare a player not in an absolute sense, but in stead in a relative sense based on team expectations. Here's a summary of the approach, followed by an example.
1a) For a given game, divide points scored by total points to obtain overall efficiency.
1b) Obtain expected efficiency by comparing teams in the score reporter. For instance, this comparison of Jam and Sockeye currently predicts a 15-13.3 Sockeye win. So Sockeye's expected efficiency would be 52%.
1c) Divide overall efficiency by expected efficiency to get the "expectation ratio".
For the purposes of this algorithm, I would ideally collect the predicted score from the score reporter after the tournament is fully reported, before any future tournaments. Since recent games are weighted more in the RRI algorithm, this probably gives the truest measure of what should have been expected at that tournament.
2a) Count the number of offensive points the team played in each game, and how many they scored. Divide O-point scores by O points to get offensive efficiency for each game.
2b) Divide this total by the expectation ratio to get "expected offensive efficiency"
3ab) Repeat the above to get expected defensive efficiency for the game.
I debated whether there should be some "expected O/D split" in efficiency, but in the end I decided that the character of each game is unique due to wind effects and the like, and as such it's better to assume the O/D splits are as they should be.
4a) For any given player, compute their offensive efficiency based on the ratio of O points to O scores when they were on the field.
4b) Subtract the players offensive efficiency from the expected offensive efficiency in that game to obtain marginal offensive efficiency.
4c) Multiply marginal offensive efficiency by offensive points played to get that player's offensive plus/minus for that game.
5abc) Repeat the same for defensive points.
6) If desired, add the player's offensive and defensive plus/minus together to get overall plus/minus. This can then be divided by points played, and added to expected efficiency, to get the player's adjusted efficiency.
example:
When Ripe played Bad Larry at sectionals, we lost 13-12, for an efficiency of 48%. Our expected efficency in that game was 45%, giving us an expectation ratio of about 1.05.
We scored 9 of 12 O points, for an O efficiency of 75% and an expected O efficiency of 71.6% (i.e. we scored 3.4% more often than you would expect).
We scored 3 of 13 D points, for a D efficiency of 23.1% and an expected D efficiency of 22%.
We scored 5 of 6 O points I played, 11.7% more often than expected (83.3% - 71.6% = +11.7%). When multiplied by 6 O points played, this gives me an adjusted O plus/minus of .7 points (.117*6 = .7).
We scored 2 of 8 D points I played, 3% more than expected, for an adjusted D plus/minus of .24 points.
My overall adjusted plus/minus for the game was therefore +.94.
To give some context to that: the overall range for the game went from +2.47 (scored all four of her O points, and 2/3 D points) to -.88 (scored 0/4 D points, did not play on O). For the entire weekend, total plus/minus ranged from +8.67 to -2.41. Overall plus/minus was skewed toward positive because we exceeded our expected score in most games. (Also, the negative scores tend to be lower because people who are playing well play more.)
# posted by Tarr : 10/16/2007 02:56:00 PM
Comments:
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Interesting. It seems more fair than rewarding the big plays (D's, goals, assists), and many would argue that flow and good defense, even without putting you on the stat sheet, is important. I especially like how easy it is to take this data.
I think that it would be interesting to compare this stat with a more typical, "DGA" style stat, and plot results over time to see how they correlate. What kind of distribution are you getting? Bell, or top-heavy with your starters?
I think that it would be interesting to compare this stat with a more typical, "DGA" style stat, and plot results over time to see how they correlate. What kind of distribution are you getting? Bell, or top-heavy with your starters?
I do have "DGA" (and drop/throwaway) stats for this event as well. It would be very interesting to look at the correlations. Without looking, though, I'd guess our turnover leader finished #5 in adjusted plus/minus. You have to be doing something right to get all those throwaways. There's also situations where you ask certain players to make a lot of tough throws. Note Tim M. talking about all the downwind punts he made at regionals in his blog. I'd guess Mark had about 40-50 throwaways in the last two games at 2003 college sectionals for Purdue, when he was taking the downwind punt responsibilities.
All of that throwaway talk aside, it's possible that the positive "fantasy" stats do have a significant correlation with these stats. I'd guess that, from most to least significant fantasy stat, the order would be something like Block, Score, Drop, Assist, Throwaway.
On data distribution: the data is not really thick enough to say for sure. But I would say both of those things are sort of true: it looks fairly bell-curveish, although the top of the bell is all starters. We ended up with:
2 players between +8 and +9
0 between +7 and +8
0 between +6 and +7
3 between +5 and +6
0 between +4 and +5
4 between +3 and +4
6 between +2 and +3
2 between +1 and +2
2 between 0 and +1
3 between -1 and 0
1 between -2 and -1
1 betwen -3 and -2
(Again, because we exceeded our expectation in 6 of 7 games, our average is positive. So the mean is in the 2s in stead of at zero.)
All 5 of the high end outliers got a lot of PT. But plenty of the other high performers got less PT, and several of the lower performers were starters. Indeed, the stats confirmed our suspicion that Mr. negative 2.41 faded on Sunday and would be more effective playing fewer points.
All of that throwaway talk aside, it's possible that the positive "fantasy" stats do have a significant correlation with these stats. I'd guess that, from most to least significant fantasy stat, the order would be something like Block, Score, Drop, Assist, Throwaway.
On data distribution: the data is not really thick enough to say for sure. But I would say both of those things are sort of true: it looks fairly bell-curveish, although the top of the bell is all starters. We ended up with:
2 players between +8 and +9
0 between +7 and +8
0 between +6 and +7
3 between +5 and +6
0 between +4 and +5
4 between +3 and +4
6 between +2 and +3
2 between +1 and +2
2 between 0 and +1
3 between -1 and 0
1 between -2 and -1
1 betwen -3 and -2
(Again, because we exceeded our expectation in 6 of 7 games, our average is positive. So the mean is in the 2s in stead of at zero.)
All 5 of the high end outliers got a lot of PT. But plenty of the other high performers got less PT, and several of the lower performers were starters. Indeed, the stats confirmed our suspicion that Mr. negative 2.41 faded on Sunday and would be more effective playing fewer points.
This might fail in cases where the entire O or entire D play well. Say in your 13-12 loss there were no breaks at all. Everyone on O would come out the same. I see you considered this, but I would include some expectation based on the expected score and the conditions, even if the latter adjustment is subjective.
Something like:
Start with O efficiency of 75% for elite, 65% for summer league (you could do an infinite series assuming each team scores on y% of its possessions regardless of starting position).
For every point of expected score differential, add x to that efficiency for the better team and subtract x from the worse team.
For moderate wind or other bad conditions, subtract 5% from each team's O efficiency.
For heavy upwind/downwind, segregate into upwind and downwind points and halve the upwind team's efficiency (e.g., otherwise 80/20 for O team, they're going downwind, make it 90/10).
Arbitrary, but I bet it would produce better results.
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Something like:
Start with O efficiency of 75% for elite, 65% for summer league (you could do an infinite series assuming each team scores on y% of its possessions regardless of starting position).
For every point of expected score differential, add x to that efficiency for the better team and subtract x from the worse team.
For moderate wind or other bad conditions, subtract 5% from each team's O efficiency.
For heavy upwind/downwind, segregate into upwind and downwind points and halve the upwind team's efficiency (e.g., otherwise 80/20 for O team, they're going downwind, make it 90/10).
Arbitrary, but I bet it would produce better results.
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