03-29-2019, 04:49 PM
Thanks MT. For now, it might be best to just summarize in text my findings, but hopefully the attachment issue will be resolved soon.
Similar to results I had presented a couple of weeks ago with regards to Stanford Softball's remaining non-conference schedule, I simulated
the remaining 25 games of the regular season (presuming no rainouts, which might be a big if at this point :) ) using game outcome probabilities
derived via Massey ratings. For the data scientists on the board, stating some upfront assumptions that represent limitations of the work:
For ease in simulation computations, as well as not having the exact formula to update Massey ratings in the middle of the simulation (i.e. run the simulation "hot"), I assumed:
1) each game was independent of each other
2) Massey ratings, and by extension, game outcome probabilities were static (in practice, when a team wins a game, their Massey rating improves slightly, and thereby future game outcome probabilities likely improve slightly too, dependent on movement in the opponent's rating).
I ran the simulation 100,000 times in R. With the above limitations, I found that the most likely outcome, in keeping with presented statistics on the Massey web site, would be for a 35-17 finish, with an 11-12 Pac-12 record. The distribution of Pac-12 wins was fairly normally distributed, centered around 11 wins (with a 20% chance of finishing with exactly 11 Pac-12 wins).
For perspective, 11 Pac-12 wins (with already at least one rainout that would have been a likely win over Cal, given 4-0 scoreline at the time of canceling the game) would represent a 8 win conference improvement over last season (remarkable, all the credit to the players and the coaches), and would be nearly the same number of Pac-12 wins (13) that we had in 2013 (our last NCAA tourney appearance, in which we were roughly the #20 team in the country, and assigned a high #2 regional seed in Lincoln, Nebraska).
We have a 37% chance of finishing with a winning Pac-12 record (which is just amazing, given where we were just one year ago).
Regarding overall wins (at the end of the regular season), the most likely outcome is 35 wins, with the distribution more right skewed (so our chances of 35+ wins is greater than our chances of fewer than 35 wins). We are virtually guaranteed of finishing with a winning record, with a 99.999% chance of that occurring (to quote Dr. Strange in Avengers Infinity War: "how many scenarios do we [lose] 1." 1 simulation out of 100,000 had us finishing with a .500 record or worse). The analysis also indicates that we have only ~1% chance of finishing with 30 or fewer wins. By the same token, we have ~2% chance of finishing with 40+ wins.
I can provide other statistics that others might be interested in, but in summary, we don't even need a simulation to tell us how much of a rousing success this season has been. The NCAA tournament drought is almost undoubtedly over, and the bigger question might be whether we host or not. With regards to that question, I think we need to finish with a winning Pac-12 record to host (given the Pac-12 is slightly down compared to prior years, and the Big 12 has nearly caught the Pac-12 in RPI for the second best conference; there is one lock in OU to host, and three other strong contenders just out of the Big 12 (Texas, Oklahoma State, Texas Tech). Pac-12 has three lock hosts in UW, UCLA and Arizona. SEC has several locks in Tennessee, Alabama, Florida, LSU, and several other contenders to host such as Auburn, Ole Miss and Kentucky. Florida State out of the ACC is a lock to host. Minnesota is a strong contender to host out of Big 10. ULL is also a contender to host out of Sun Belt.
We are #18 currently in RPI, which means we are likely just on the outside of the top 16 teams that host. Given what my analysis projected as the most likely outcome, I have this weird feeling that the Cal Game #3 rainout that we likely would have won might loom large in a hosting decision. However, this is why we play the games, so let's beat our projected finish (starting with the Ducks this weekend).
Similar to results I had presented a couple of weeks ago with regards to Stanford Softball's remaining non-conference schedule, I simulated
the remaining 25 games of the regular season (presuming no rainouts, which might be a big if at this point :) ) using game outcome probabilities
derived via Massey ratings. For the data scientists on the board, stating some upfront assumptions that represent limitations of the work:
For ease in simulation computations, as well as not having the exact formula to update Massey ratings in the middle of the simulation (i.e. run the simulation "hot"), I assumed:
1) each game was independent of each other
2) Massey ratings, and by extension, game outcome probabilities were static (in practice, when a team wins a game, their Massey rating improves slightly, and thereby future game outcome probabilities likely improve slightly too, dependent on movement in the opponent's rating).
I ran the simulation 100,000 times in R. With the above limitations, I found that the most likely outcome, in keeping with presented statistics on the Massey web site, would be for a 35-17 finish, with an 11-12 Pac-12 record. The distribution of Pac-12 wins was fairly normally distributed, centered around 11 wins (with a 20% chance of finishing with exactly 11 Pac-12 wins).
For perspective, 11 Pac-12 wins (with already at least one rainout that would have been a likely win over Cal, given 4-0 scoreline at the time of canceling the game) would represent a 8 win conference improvement over last season (remarkable, all the credit to the players and the coaches), and would be nearly the same number of Pac-12 wins (13) that we had in 2013 (our last NCAA tourney appearance, in which we were roughly the #20 team in the country, and assigned a high #2 regional seed in Lincoln, Nebraska).
We have a 37% chance of finishing with a winning Pac-12 record (which is just amazing, given where we were just one year ago).
Regarding overall wins (at the end of the regular season), the most likely outcome is 35 wins, with the distribution more right skewed (so our chances of 35+ wins is greater than our chances of fewer than 35 wins). We are virtually guaranteed of finishing with a winning record, with a 99.999% chance of that occurring (to quote Dr. Strange in Avengers Infinity War: "how many scenarios do we [lose] 1." 1 simulation out of 100,000 had us finishing with a .500 record or worse). The analysis also indicates that we have only ~1% chance of finishing with 30 or fewer wins. By the same token, we have ~2% chance of finishing with 40+ wins.
I can provide other statistics that others might be interested in, but in summary, we don't even need a simulation to tell us how much of a rousing success this season has been. The NCAA tournament drought is almost undoubtedly over, and the bigger question might be whether we host or not. With regards to that question, I think we need to finish with a winning Pac-12 record to host (given the Pac-12 is slightly down compared to prior years, and the Big 12 has nearly caught the Pac-12 in RPI for the second best conference; there is one lock in OU to host, and three other strong contenders just out of the Big 12 (Texas, Oklahoma State, Texas Tech). Pac-12 has three lock hosts in UW, UCLA and Arizona. SEC has several locks in Tennessee, Alabama, Florida, LSU, and several other contenders to host such as Auburn, Ole Miss and Kentucky. Florida State out of the ACC is a lock to host. Minnesota is a strong contender to host out of Big 10. ULL is also a contender to host out of Sun Belt.
We are #18 currently in RPI, which means we are likely just on the outside of the top 16 teams that host. Given what my analysis projected as the most likely outcome, I have this weird feeling that the Cal Game #3 rainout that we likely would have won might loom large in a hosting decision. However, this is why we play the games, so let's beat our projected finish (starting with the Ducks this weekend).