Monday, May 20, 2013
Cost of a penalty
Bill James pointed out something interesting, with an assist from his reader:
A while ago, a reader brought forward the idea of using the hockey concept of making a team short handed when they commit an infraction. Your replay was that the man advantage penalty in hockey was too severe. The success rate on power plays in the NHL was about 18% this season and the short-handed team scored on about 2% of their disadvantages. That would indicate the average penalty being worth about 1/6 of a goal in a sport where there are about five goals scored in a game on average. I am not sure how that compares to the severity of the average football penalty. It does seem to be more severe than the loss due to a basketball foul, though far less damning than a soccer penalty kick. I am not arguing with your assessment of hockey penalties; it just got me trying to compare the impact of the types of penalties assessed in various sports. Asked by: mathias2
Answered: 5/19/2013 There is a good article there. If 5 goals are scored in a typical hockey game, it probably takes about 5 goals to increase a team's expected wins by 1.00. ..thus, the cost of the penalty is probably about .03 wins. Actually, a charging foul in basketball might be close to that. A charging foul in basketball probably costs you a point. In basketball (NBA) I would guess that it takes about 25 points to increase a team's expected wins by one, so one point in baseball would be about .04 wins. ..thus, a charging foul in basketball would appear to be comparable to a man out penalty in hockey. If I have the math right. . .
Pretty simple concept, right? The average NHL team scores an average of .606 PPG and allows .065 SHG, for a net of +.541 goals. They have 3.32 PP opportunities, therefore, per PP Opp, the net effect is +.163 goals. To convert goals to win is roughly 6 goals per win. So, that +.163 goals translates as .027 wins. That is, when a referee calls a penalty, he's basically shifting the win expectancy by .027 wins.
I don't know anything about basketball, other than what I read. But, we'll work through it. If a team has possession, they are expected to score an average of one point. It sounds like a charging foul requires loss of possession, the opposing team gets two free throws (average of 1.5 points), then the original team gets the ball back (is it a live ball if the second free throw is missed?). Did I get that right? Anyway, 1.5 points is my guess here.
As for points to win conversion: shockingly the correlation of point differential to win differential is r=.97. That is absurdly high, which makes one wonder why we even need to keep score at the game level. Just keep a running tally of total points, because you'll end up with virtually the same result. 0.97. NBA squeezes all the random variation out of the game, until all you have left is pure talent. Is this what NBA fans really want? Anyway, the conversion for the 2013 season is 30 points per win. So, the 1.5 points converts to .050 wins. Yowza, the man advantage penalty in hockey is less onerous than a charging penalty in NBA?
(I should point out that this presumes that it's a tie game in NHL at a random point. Late in a game, where the penalized team is down by one goal, and the time is a HUGE factor. So, not only do you give the man advantage, but now you have up to two fewer minutes in the game at even strength.)
Baseball is easy. The penalty for batters or pitchers is an automatic ball or automatic strike (though, I've never actually seen those penalties called). A ball or strike is worth around .08 runs, which is .008 wins.
Football. Let's see. If I remember right, 35 points is one win. And 10 yards is one point. So, a standard 10 yard penalty is worth one point, which is .029 wins.
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The average NHL team is only getting some 3.3 PP opps per game, and those opps are worth .027 wins.
The average NBA team is getting how many penalties called? I don't watch it, but I'm guessing, what, 20, 30 calls a game? That is HUGE. Each opp is worth .050 wins. So, referees are all over the game in terms of impact. I guess to counterbalance that, an NBA game REALLY lets the player's talent shines through.
NFL team gets what, 10, 15 penalties a game? Each of those is .029 wins.
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The next step, for some Straight Arrow reader out there, is to compare the effect of referees' calls, to the effect of players' talent, on the impact of the game.
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I'd also like to see it for the other sports (soccer, golf). Note: I'm not talking about missed calls, but actual penalties (whether called by the officials, or self-reported).
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