After the jump the following: This week’s Return to Average tables; a look at how many teams since 1980 have won 87 games with similar RS/G and RA/G averages to those projected of the Pirates; and, a calculation of the Pirates’ binomial probability of reaching 87 wins given their current Baseball Prospectus' 3rd Order Win Percentage.
If you are new to the "Return to Average" updates, an explanation for why we are tracking the runs allowed and runs scored numbers can be found here. The reasons why we are tracking the offensive and run prevention numbers at different rates can be found here.
The Pirates played seven games last week and scored 29 runs, for an average of 4.1 RS/G. Their RS/G for the season has decreased from 4.2 to 4.1. Last week they needed to average 4.4 runs per game to reach the projected NL average by the end of the season. That number has remained at 4.4. In other words, the Pirates offense will have to score 4.2 percent above projected NL average for the rest of the season in order to reach a NL average number of runs scored.
(Click to enlarge)
Interpretation: the goal is to have the red line meet the green line at the purple line. The purple line is projected NL average. The green line is what the Pirates will have to average to meet expected NL average runs per game by the end of the season. Red line is the season average of runs scored per game. Blue line is this week's RS/G.
The Pirates played seven games this week and allowed 40 runs, an average of 5.7 runs allowed per game. Their RA/G for the season increased from 3.9 to 4. Last week they needed to average below 3.6 RA/G to finish at 90 percent of NL average runs allowed. That number has decreased to 3.3. For the Pirates pitching/defense to finish with 90 percent of league average RA/G, they will have to allow 23 percent fewer runs than expected NL average runs for the rest of the year.
Interpretation: goal is to have the red line remain below the purple line. The lines have the same meaning as those in the first graph, except they are for runs allowed.
Runs Scored / Runs Allowed Compared By Week
For the fourth week in a row the Pirates allowed more runs than they scored (red Line above the blue line). During this stretch they posted a 13-14 record and were outscored 138-117 (-21 run differential). Prior to the last four weeks, the Pirates had only allowed more runs than they scored a total of four times. Moreover, in the four weeks prior to the current streak, they had scored more runs than they allowed for four weeks in a row.
Historical Context: Reaching 87 Wins Given The Pirates Expected RA/G and RS/G End Of Season Averages
Assumption: looking at the wild card standings, 87 wins looks like a reasonable minimum number of wins that team will need to qualify for the second wild card spot.
Runs Scored Expectation: As things stand the Pirates will need to average 4.43 runs per game (4.2 percent above league average) to reach projected NL average runs. Let’s assume they fall slightly short of that goal.
Runs Allowed Expectation: In order for the Pirates to allow less than 90 percent of league average runs, they will have to allow only 3.3 RA/G the rest of the season. In other words, they will have to allow 23 percent less runs per game than NL average to reach the 90 percent goal. That seems hard to imagine.
Based on those expectations, the Pirates will end the season scoring somewhere in the neighborhood of 94-98 percent of league average runs; and, they will allow something like 92-95 percent of league average runs. If these expectations are reasonable, and I think they are, what percentage of National League teams have won 87 games with this type of RS/G-RA/G portfolio?
Historical Precedent: Since 1980, 128 National League teams have won 87 games. Only five of those teams (4 percent) scored less than league average runs AND allowed over 90 percent of NL average runs. Moreover, only two of 87 win teams (1.5 percent) scored less than league average runs AND allowed over 91 percent of average runs. Indeed one of those two teams, the '84 Mets, was only one percent below league average runs scored. So, only one team scored less than 99 percent of league average runs AND allowed over 91 percent of average runs AND still won 87 games.
Conclusion: If the Pirates win 87 games while scoring less than NL average runs and allowing more than 90 percent of NL average runs they will be a historically unique team.
Using Baseball Prospectus’ 3rd Order Win Percentage, which projects the Pirates’ record based on their underlying statistics and quality of opponents, I calculated the binomial probability of the Pirates reaching 87 wins.
You can think of the 3rd Order Win Percentage as what the Pirates record "should be" given their underlying offensive and defensive statistics. According to this measure the Pirates are a .501 win percentage team (actual = .549).
Let’s assume that their underlying statistics remain steady (a big assumption) and that whatever factors allowed them to perform .48 percent above expectations for the first 102 games are not present in the next 40 games. In other words, let’s hold performance constant and de-luck them for the next 40 games. The question is: what is the probability that a .501 win percentage team will win 20 or more of their next 40 games?
To answer that question I ran a binomial experiment using an online calculator (here). Since I am not a mathematician by trade, I’m going to link you directly to an explanation of what a binomial experiment is (stattrek.com website). I picked up the idea of running such an experiment from this Baseball Prospectus' article and from reading some of Bill James’s old Baseball Abstracts over the weekend (specifically the 1983 and 1984 editions).
Here are the results. I think the table is self-explanatory.
As we can see the binomial experiment shows that the Pirates have 57 percent probability of winning 87 or more games. If we increase the threshold to 89 wins, meaning the Pirates would have to win 22 more games, the probability decreases to 32.2 percent.
The binomial experiment suggests that Pirates have a decent shot at being historically unique. That is, they have a 57 percent chance of winning 87 games while scoring less than NL average runs and allowing more than 90 percent NL average runs.
Please note that the binomial experiment clearly does not account for the strength of the Pirates remaining schedule, the quality of the starting pitching they'll face or injuries. It simply takes their performance over the first 122 games, assumes that the underlying statistics will remain constant, and gives us win probabilities going forward.
That’s it for this week’s Return to Average. Check back next Monday or Tuesday for another update. I should be able to post another project or two that I’m working on later this week, so check back often. Until then, enjoy the pennant race.
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