How well did we quantify a player’s contribution to a fantasy team.
Look for yourself. Monte Win Pct is the Winning Pct that we calculated for a player. We averaged it out here, bc the Distributive Law can be applied for our model. Hypothesis was if we took the differences of the winpct between the 2 teams that would tell us how many extra wins that the other team would have over the other, if they played each other all season. We’re interpreting that as how many games over 0.500. And we applied it to every team on the schedule, to get the difference, and we got an expect number of wins.
| FunnyName | ptscored | ptagainst | seasonsum_montediff_pergm | Expected Wins up to now | ActualWins | Expected End of Season Wins |
| WFAN long time listener | 1016 | 1047 | 0.54 | 14 | 5 | 14 |
| Draft mis-informer | 1217 | 931 | 0.555 | 14 | 8 | 14 |
| Knowledgeable Fan | 841 | 983 | -0.949 | -6 | 3 | -6 |
| Happy Fat Guy | 931 | 902 | 0.198 | 9 | 6 | 9 |
| Offers stupid trades | 1187 | 1061 | -0.37 | 2 | 6 | 2 |
| Draft drunk | 960 | 1071 | -0.342 | 2 | 2 | 2 |
| MASH Unit | 1009 | 1013 | -0.128 | 5 | 6 | 5 |
| Commish | 969 | 1056 | -0.027 | 6 | 3 | 6 |
| New Guy | 942 | 1075 | -0.166 | 4 | 4 | 4 |
| Bad year after year | 1021 | 992 | 0.361 | 11 | 3 | 11 |
| Unbearable good | 1127 | 1041 | 0.139 | 8 | 5 | 8 |
| Annoying trash talker | 940 | 988 | 0.188 | 9 | 3 | 9 |
Our contention is that players with a Monte Winning Pct of 0.500 neither add nor contribute to their team’s winning percentage more than the average player. That’s not to say they are worthless. Take them out of the line up and that winning percentage turns to 0.000.
What if one team’s Monte total winpct has a difference of 0.077 with another team’s total Monte win pct? Does that guarantee a win? Sadly, no. But if they played 13 games against each other all season, and their lineups scored what they did before, then the team with the extra 0.077, should have one extra win over the other, out of 13 games (in other words a record of 7-6, vs a 6-7 record).
My league’s fantasy matchups
Here are the actual outcomes of matchups in my league.
| Week | TeamFunnyName | TeamPts | TeamMonteAvgPlyrWinPct | VersusFunnyName | VersusPts | VersusMonteAvgPlyrWinPct | Positive means probability Team win, negative means Versus probability Versus win |
| 1 | WFAN long time listener | 119 | 0.323 | Annoying trash talker | 106 | 0.329 | -0.05 |
| 1 | Draft mis-informer | 136 | 0.468 | Draft drunk | 103 | 0.266 | 1.815 |
| 1 | Knowledgeable Fan | 77 | 0.218 | Happy Fat Guy | 101 | 0.279 | -0.549 |
| 1 | Happy Fat Guy | 101 | 0.279 | Knowledgeable Fan | 77 | 0.218 | 0.549 |
| 1 | Offers stupid trades | 140 | 0.359 | New Guy | 109 | 0.38 | -0.189 |
| 1 | Draft drunk | 103 | 0.266 | Draft mis-informer | 136 | 0.468 | -1.815 |
| 1 | MASH Unit | 129 | 0.334 | Commish | 119 | 0.234 | 0.896 |
| 1 | Commish | 119 | 0.234 | MASH Unit | 129 | 0.334 | -0.896 |
| 1 | New Guy | 109 | 0.38 | Offers stupid trades | 140 | 0.359 | 0.189 |
| 1 | Bad year after year | 142 | 0.448 | Unbearable good | 144 | 0.335 | 1.017 |
| 1 | Unbearable good | 144 | 0.335 | Bad year after year | 142 | 0.448 | -1.017 |
| 1 | Annoying trash talker | 106 | 0.329 | WFAN long time listener | 119 | 0.323 | 0.05 |
| 2 | WFAN long time listener | 110 | 0.377 | Draft drunk | 132 | 0.266 | 0.994 |
| 2 | Draft mis-informer | 138 | 0.357 | Happy Fat Guy | 91 | 0.334 | 0.211 |
| 2 | Knowledgeable Fan | 116 | 0.273 | Annoying trash talker | 107 | 0.379 | -0.947 |
| 2 | Happy Fat Guy | 91 | 0.334 | Draft mis-informer | 138 | 0.357 | -0.211 |
| 2 | Offers stupid trades | 97 | 0.361 | MASH Unit | 106 | 0.278 | 0.747 |
| 2 | Draft drunk | 132 | 0.266 | WFAN long time listener | 110 | 0.377 | -0.994 |
| 2 | MASH Unit | 106 | 0.278 | Offers stupid trades | 97 | 0.361 | -0.747 |
| 2 | Commish | 110 | 0.234 | Unbearable good | 112 | 0.286 | -0.464 |
| 2 | New Guy | 119 | 0.429 | Bad year after year | 115 | 0.451 | -0.197 |
| 2 | Bad year after year | 115 | 0.451 | New Guy | 119 | 0.429 | 0.197 |
| 2 | Unbearable good | 112 | 0.286 | Commish | 110 | 0.234 | 0.464 |
| 2 | Annoying trash talker | 107 | 0.379 | Knowledgeable Fan | 116 | 0.273 | 0.947 |
| 3 | WFAN long time listener | 94 | 0.432 | Draft mis-informer | 122 | 0.41 | 0.199 |
| 3 | Draft mis-informer | 122 | 0.41 | WFAN long time listener | 94 | 0.432 | -0.199 |
| 3 | Knowledgeable Fan | 104 | 0.164 | Draft drunk | 86 | 0.215 | -0.456 |
| 3 | Happy Fat Guy | 125 | 0.332 | Annoying trash talker | 116 | 0.334 | -0.023 |
| 3 | Offers stupid trades | 170 | 0.365 | Commish | 125 | 0.337 | 0.247 |
| 3 | Draft drunk | 86 | 0.215 | Knowledgeable Fan | 104 | 0.164 | 0.456 |
| 3 | MASH Unit | 108 | 0.327 | Bad year after year | 105 | 0.394 | -0.602 |
| 3 | Commish | 125 | 0.337 | Offers stupid trades | 170 | 0.365 | -0.247 |
| 3 | New Guy | 102 | 0.378 | Unbearable good | 119 | 0.349 | 0.255 |
| 3 | Bad year after year | 105 | 0.394 | MASH Unit | 108 | 0.327 | 0.602 |
| 3 | Unbearable good | 119 | 0.349 | New Guy | 102 | 0.378 | -0.255 |
| 3 | Annoying trash talker | 116 | 0.334 | Happy Fat Guy | 125 | 0.332 | 0.023 |
| 4 | WFAN long time listener | 133 | 0.451 | Knowledgeable Fan | 106 | 0.223 | 2.054 |
| 4 | Draft mis-informer | 173 | 0.408 | Annoying trash talker | 94 | 0.334 | 0.662 |
| 4 | Knowledgeable Fan | 106 | 0.223 | WFAN long time listener | 133 | 0.451 | -2.054 |
| 4 | Happy Fat Guy | 94 | 0.388 | Draft drunk | 74 | 0.27 | 1.06 |
| 4 | Offers stupid trades | 114 | 0.309 | Bad year after year | 113 | 0.394 | -0.768 |
| 4 | Draft drunk | 74 | 0.27 | Happy Fat Guy | 94 | 0.388 | -1.06 |
| 4 | MASH Unit | 109 | 0.333 | Unbearable good | 160 | 0.406 | -0.656 |
| 4 | Commish | 122 | 0.39 | New Guy | 88 | 0.325 | 0.588 |
| 4 | New Guy | 88 | 0.325 | Commish | 122 | 0.39 | -0.588 |
| 4 | Bad year after year | 113 | 0.394 | Offers stupid trades | 114 | 0.309 | 0.768 |
| 4 | Unbearable good | 160 | 0.406 | MASH Unit | 109 | 0.333 | 0.656 |
| 4 | Annoying trash talker | 94 | 0.334 | Draft mis-informer | 173 | 0.408 | -0.662 |
| 5 | WFAN long time listener | 105 | 0.344 | Happy Fat Guy | 92 | 0.331 | 0.114 |
| 5 | Draft mis-informer | 116 | 0.463 | Knowledgeable Fan | 129 | 0.217 | 2.211 |
| 5 | Knowledgeable Fan | 129 | 0.217 | Draft mis-informer | 116 | 0.463 | -2.211 |
| 5 | Happy Fat Guy | 92 | 0.331 | WFAN long time listener | 105 | 0.344 | -0.114 |
| 5 | Offers stupid trades | 135 | 0.299 | Unbearable good | 116 | 0.398 | -0.891 |
| 5 | Draft drunk | 85 | 0.27 | Annoying trash talker | 121 | 0.385 | -1.032 |
| 5 | MASH Unit | 127 | 0.327 | New Guy | 132 | 0.319 | 0.072 |
| 5 | Commish | 114 | 0.505 | Bad year after year | 137 | 0.392 | 1.014 |
| 5 | New Guy | 132 | 0.319 | MASH Unit | 127 | 0.327 | -0.072 |
| 5 | Bad year after year | 137 | 0.392 | Commish | 114 | 0.505 | -1.014 |
| 5 | Unbearable good | 116 | 0.398 | Offers stupid trades | 135 | 0.299 | 0.891 |
| 5 | Annoying trash talker | 121 | 0.385 | Draft drunk | 85 | 0.27 | 1.032 |
| 6 | WFAN long time listener | 81 | 0.394 | Offers stupid trades | 180 | 0.306 | 0.793 |
| 6 | Draft mis-informer | 104 | 0.456 | Commish | 58 | 0.337 | 1.07 |
| 6 | Knowledgeable Fan | 74 | 0.164 | Bad year after year | 127 | 0.5 | -3.023 |
| 6 | Happy Fat Guy | 98 | 0.336 | Unbearable good | 83 | 0.338 | -0.02 |
| 6 | Offers stupid trades | 180 | 0.306 | WFAN long time listener | 81 | 0.394 | -0.793 |
| 6 | Draft drunk | 109 | 0.329 | MASH Unit | 118 | 0.337 | -0.069 |
| 6 | MASH Unit | 118 | 0.337 | Draft drunk | 109 | 0.329 | 0.069 |
| 6 | Commish | 58 | 0.337 | Draft mis-informer | 104 | 0.456 | -1.07 |
| 6 | New Guy | 59 | 0.323 | Annoying trash talker | 146 | 0.334 | -0.105 |
| 6 | Bad year after year | 127 | 0.5 | Knowledgeable Fan | 74 | 0.164 | 3.023 |
| 6 | Unbearable good | 83 | 0.338 | Happy Fat Guy | 98 | 0.336 | 0.02 |
| 6 | Annoying trash talker | 146 | 0.334 | New Guy | 59 | 0.323 | 0.105 |
| 7 | WFAN long time listener | 110 | 0.45 | New Guy | 108 | 0.322 | 1.146 |
| 7 | Draft mis-informer | 129 | 0.413 | MASH Unit | 116 | 0.387 | 0.237 |
| 7 | Knowledgeable Fan | 81 | 0.276 | Commish | 89 | 0.398 | -1.098 |
| 7 | Happy Fat Guy | 137 | 0.445 | Offers stupid trades | 103 | 0.246 | 1.792 |
| 7 | Offers stupid trades | 103 | 0.246 | Happy Fat Guy | 137 | 0.445 | -1.792 |
| 7 | Draft drunk | 141 | 0.325 | Unbearable good | 135 | 0.342 | -0.157 |
| 7 | MASH Unit | 116 | 0.387 | Draft mis-informer | 129 | 0.413 | -0.237 |
| 7 | Commish | 89 | 0.398 | Knowledgeable Fan | 81 | 0.276 | 1.098 |
| 7 | New Guy | 108 | 0.322 | WFAN long time listener | 110 | 0.45 | -1.146 |
| 7 | Bad year after year | 96 | 0.272 | Annoying trash talker | 55 | 0.277 | -0.049 |
| 7 | Unbearable good | 135 | 0.342 | Draft drunk | 141 | 0.325 | 0.157 |
| 7 | Annoying trash talker | 55 | 0.277 | Bad year after year | 96 | 0.272 | 0.049 |
| 8 | WFAN long time listener | 146 | 0.381 | Bad year after year | 81 | 0.286 | 0.849 |
| 8 | Draft mis-informer | 134 | 0.468 | Unbearable good | 127 | 0.456 | 0.107 |
| 8 | Knowledgeable Fan | 84 | 0.173 | MASH Unit | 93 | 0.284 | -1.005 |
| 8 | Happy Fat Guy | 75 | 0.39 | New Guy | 101 | 0.33 | 0.543 |
| 8 | Offers stupid trades | 129 | 0.298 | Draft drunk | 109 | 0.329 | -0.279 |
| 8 | Draft drunk | 109 | 0.329 | Offers stupid trades | 129 | 0.298 | 0.279 |
| 8 | MASH Unit | 93 | 0.284 | Knowledgeable Fan | 84 | 0.173 | 1.005 |
| 8 | Commish | 112 | 0.389 | Annoying trash talker | 117 | 0.327 | 0.558 |
| 8 | New Guy | 101 | 0.33 | Happy Fat Guy | 75 | 0.39 | -0.543 |
| 8 | Bad year after year | 81 | 0.286 | WFAN long time listener | 146 | 0.381 | -0.849 |
| 8 | Unbearable good | 127 | 0.456 | Draft mis-informer | 134 | 0.468 | -0.107 |
| 8 | Annoying trash talker | 117 | 0.327 | Commish | 112 | 0.389 | -0.558 |
| 9 | WFAN long time listener | 118 | 0.506 | Commish | 120 | 0.403 | 0.928 |
| 9 | Draft mis-informer | 165 | 0.411 | Offers stupid trades | 119 | 0.29 | 1.096 |
| 9 | Knowledgeable Fan | 70 | 0.223 | Unbearable good | 131 | 0.334 | -0.997 |
| 9 | Happy Fat Guy | 118 | 0.283 | Bad year after year | 105 | 0.394 | -0.999 |
| 9 | Offers stupid trades | 119 | 0.29 | Draft mis-informer | 165 | 0.411 | -1.096 |
| 9 | Draft drunk | 121 | 0.379 | New Guy | 124 | 0.385 | -0.055 |
| 9 | MASH Unit | 103 | 0.191 | Annoying trash talker | 78 | 0.374 | -1.462 |
| 9 | Commish | 120 | 0.403 | WFAN long time listener | 118 | 0.506 | -0.928 |
| 9 | New Guy | 124 | 0.385 | Draft drunk | 121 | 0.379 | 0.055 |
| 9 | Bad year after year | 105 | 0.394 | Happy Fat Guy | 118 | 0.283 | 0.999 |
| 9 | Unbearable good | 131 | 0.334 | Knowledgeable Fan | 70 | 0.223 | 0.997 |
| 9 | Annoying trash talker | 78 | 0.374 | MASH Unit | 103 | 0.191 | 1.462 |
A little extra explanation on the Monte winning pct.
Imagine that the average player scores 20pts/week. That is what the diagram displays. Add 4pts to each bin, and let’s say that’s Tom Brady’s score distribution. The average player in the Monte win pct, is 0.500. Let’s say Tom Brady is 0.63. If we dropped 100 balls in each the average player’s bin, and 100 in Tom Brady’s bin. And we subtracted balls in average player’s bin, from Tom Brady’s bin, and vice versa. Tom Brady should have 13 extra balls in bins where his scores are higher than the average player. That is what I believe the Monte numbers are to be interpreted.
Now imagine that the average player scores 20pts/week. Now let’s say he has a team mate. So is the team going to score 20 or 40 pts? Obviously 40pts. What if they face a team that averages 21pts a game, each? That means they will average 42pts a week. Does this mean our intrpeid first team that they are doomed to lose this game because 42 Obviously no, because they dont always score 40pts, and the other doesnt always score 42pts. That’s where the difference in Monte winning pct comes in.
Let’s say instead of pts, we say both players on first team are Monte 0.500. They are average players. If they faced other average players on another “Monte AVERAGE” team (comprised of monte average players), they have an equal chance of winning or losing. But the other team in our example is better than the average team. Let’s say each player on second team is 0.510, or 0.10 better than a player on the first team. Does this mean that they have a 0.51 or 51 chance of winning or the difference between the 2 players(0.010/each * 2 players = 0.020 difference, higher probablility to outscore the other team), which is supposed to how much more likely they are to outscore the other team. Which in this case, the other team is our hypothetical Monte average 0.500 winning percentage team. But a similar case can be made for team that aren’t average. Because they are both measured from this hypothetical average player.
You might ask who exactly is the hypothetical Monte Average player? It’s whatever player comes out of the computer simulation with a winning pct of 0.500. It means whenever the computer put him in a lineup, he was just as likely to win the game, as he was to lose the game, against another random lineup. He was even steven. And this changes depending on how good the other players are, because better Monte Players score more, and more often, than the average Monte player, teams that they are on, tend to win slightly more (See above for what good position WINS pct players have to over come, once they are put into a monte simulation). There may not even be a real average player that has winning pct of 0.500. But we could probably make up a player and his stats, where if we re-ran the simulation, he would be 0.500. However, the computer simulation, is just that, a simulation. There is a degree of error involved. As well as in real life, past outcomes don’t guarantee that the future outcomes will turn out exactly out same way. So a player at 0.503, might as well be considered our Monte 0.500 average player.
There is an relationship to Wins Pct and the Monte Probability Percentages? Even if we subtract 0.500 from WinsPct, divide by number of sqrt positions (this seems to get it closer to Monte, than by starting slots of 9) on a team, and re-add to 0.500 to get closer approximation to a player’s contribution to his portfolio beating another portfolio. But still the relationship isnt perfect. So we’ll continue examining if we can use WINS pct as a faster approximation of Monte Percentage. (Using Monte Percentage, we come up with an expected number of wins that is pretty close actual. The trick is, how accurate are our forecasted distributions. Remember we are using nothing but point scored distribution to determine win pct for one team vs another).
beyondtoiletbowl 